diamond magnetometry for low-temperature applications · sergei masis submitted to the senate of...

Diamond Magnetometry for Low-TemperatureApplications

Sergei Masis

Diamond Magnetometry forLow-Temperature Applications

Research Thesis Submitted in partial fulfillment of the

requirements for the degree of Master of Science in Nano-technology

Sergei Masis

Submitted to the Senate of the TechnionIsrael Institute of Technology

Adar 5775, Haifa February 2016

Acknowledgements

This research was carried out under the supervision of Prof. Eyal Buks, in the in-dependent program of Nano-technology and Nano-science. The Generous FinancialHelp Of the Technion Is Gratefully Acknowledged.

Eyal always says he is not a supervisor but an advisor, and I would like to thankhim for this most important lesson of always think and behave as an independentresearcher. That being said, Eyal is always available for his students to come anddiscuss their progress and doubts, never avoids getting his hands dirty with anexperiment or a derivation. One special gratitude is reserved for supporting myideas of diamond magnetometry, once accepting them he personally became a strongdriving force for this project.

I would like to thank Oleg Shtempluck and Valery Kochetok for their constanthelp. Non of this would be possible without their willingness, efficiency and creativ-ity.

I thank my mentors Gil Bachar and Oren Suchoi for guiding my first steps andteaching me all I know of how to operate the clean rooms or navigate myself throughthe academy.

I would like also to thank Nick Rolston and Ran Fisher. Nick came for onesummer semester, but conducted a great work, with his samples and measurementspresented in this work. Ran’s advices were of an enormous help to kick start thediamond project.

Finally, I cannot praise high enough the contribution of Nir Alfasi to the secondpart of my research, who became a full time and equal partner.

Orthogonally, I thank my loving family and friends, particularly one Kate Lint,for pushing, believing and pulling even when I, myself, stopped.

i

Contents

0.1 List of Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii0.2 List of Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii0.3 List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . iv0.4 List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

1 Magnetometry with Nitrogen-Vacancy Centers 21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.1 Diamond Preparation . . . . . . . . . . . . . . . . . . . . . . . 71.2.2 Cryogenic Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.3 Optical Table Setup . . . . . . . . . . . . . . . . . . . . . . . 12

1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3.1 NV0 Correction . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3.2 2D Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.3.3 Measuring Shielding Currents in Superconductors . . . . . . . 18

1.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.4.1 Reconstruction of NV-center Resonances . . . . . . . . . . . . 181.4.2 Type II Superconductors in Bias Magnetic Field . . . . . . . . 20

1.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2 Superconducting Circuits 232.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2 Josephson Junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3 DC-SQUIDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.4 RF-SQUIDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3 Outlook 34

A Critical State Model for Jc(B) 37

ii

Table of Symbols

0.1 List of Units

eV Electron-voltdBm Decibel-milliwattGHz GigahertzK KelvinKeV Kilo electron-VoltmA Milli AmperMHz Megahertzms MillisecondmT Milli Teslanm Nanometerns Nanosecondppm Parts per millionT Teslaµm Micrometer

0.2 List of Constants

D 2.87GHz The energy separation between the mS = 0 and mS = ±1substates of the 3A2 triplet in zero magnetic field.

Des 1.42GHz The energy separation between the mS = 0 and mS = ±1substates of the 3E triplet in zero magnetic field.

E ∼ 5MHz Axial zero-field splitting parameter in Hh 6.626× 10−34[Js] Planck constant~ h/2π h-barµ0 4π × 10−7H/m Vacuum permeability constantΦ0 h/2e Flux quantumΦτ Φ0/2π Normalization constant between the superconductor

order parameter and magnetic flux

iii

CONTENTS

0.3 List of Abbreviations

AC Alternating currentAlOx Aluminum oxideBS Beam splitterCCD Charge-coupled deviceCFB Coherent fiber bundleCW Continuous WaveDC Direct currentDC-SQUID Direct current superconducting interferometer deviceESR Electron Spin ResonanceFIB Focused ion beamif Intermediate frequency mixer portJJ Josephson Junctionlo Local oscillator mixer portMLA Microwave loop antennaN Nitrogen AtomNb NiobiumNV Nitrogen-Vacancy centerNV0 Zero-charge NVNV− Negatively charged NVODMR Optical Detection of Magnetic ResonancesOF Optical fiberMW MicrowavePCB Printed circuit boardPL Photoluminescencerf Radio frequency mixer portRF Radio frequencyRF-SQUID Radio frequency superconducting quantum interferometer deviceSC SuperconductingSEM Scanning electron microscopeSQUID Superconducting quantum interference deviceTEM Tunneling electron microscopeV Vacancy in the diamond latticeZPL Zero phonon line

0.4 List of Symbols

1A1 Lower energy dark singlet of the NV−

1E Higher energy dark singlet of the NV−

iv

CONTENTS

2A Excited doublet of the NV02E Ground doublet of the NV03A2 Ground triplet of the NV−

3E Excited triplet of the NV−

4A2 Quartet of the NV0

B0 [T] A constant in Kim’s modelC Carbon atom

Bx′(y′,z′) [T] Magnetic field in the x′(y′, z′) direction.B∥ [T] Bz′

B⊥ [T] B2x′ +B2

y′

Bf Scalling magnetic fieldBz Magnetic inductance in the perpendicular direction.C3v The point group symmetry of an NV centerCJ [F] Capacitance of a Josephson junctionE [J] Energy of a JJEJ [J] Josephson energyg ≃ 2 Lande g-factorH RF-SQUID HamiltonianH NV− HamiltonianH∥ The parallel part of HH⊥ The perpendicular part of HHa [T] Applied magnetic fieldHc [T] Critical magnetic fieldH↑ [T] Maximal applied magnetic fieldH↓ [T] Minimal applied magnetic fieldI [A] Current through a JJIc [A] Critical current of the Josephson junctionJ↓ [A/m] Sheet current at minimal applied magnetic fieldJc [A/m] Critical sheet currentJc0 [A/m] Critical sheet current in the zero magnetic field limitL [H] Loop inductancemS -1,0,1 The three spin substates of the NV− triplets 3A2 and 3EQ [C] Charge associated with a JJ

Sx′(y′,z′) 3× 3 spin S = 1 matrix corresponding to the x′(y′, z′) direction.V [V] Voltage across a JJxp [m] The width of the region with critical currentβL LIc/Φτ RF SQUID hysteresis parameterγg gµB/h Electron gyromagnetic ratioλ [m] Wavelength of an RF signal in a transmission lineΦ [Wb] Total magnetic flux through a loop

v

CONTENTS

Φx [Wb] Externally applied magnetic flux through a loopΦx,b [Wb] The minimal external flux required to modify

the total flux in a RC-SQUIDµB

e~2me

Bohr magneton

ν± Hz Energy separation between the mS = 0 and mS = ±1 substates.θ ° Superconductor order parameter phaseθ1(2) θ jump across the first (second) JJ of the DC-SQUIDθx(y,z) ° Angle of rotation about the x(y,z) axis

vi

List of Figures

1.1 NV center (a) Diamond unit cell, with an NV center aligned alongthe [111] direction. (b) Scheme of the NV center PL spectrum inarbitrary units (a.u.). Denoted from left to right are the excitationfrequency used in this work and the ZPLs of NV0 and NV−. Dis-tinguished ZPL peaks are typical for cryogenic temperatures. (c)Energy level diagram of the NV center, NV0 on the left and NV−

on the right. Solid (Dashed) lines indicate radiative (non-radiative)transitions. The more common transitions 3E(mS = ±1) →1A1 and1E →3 A2(mS = 0) are depicted, though the 3E(mS = 0) →1 A1

and 1E →3A2(mS = ±1) occur. Photoconversion transitions via theconductance band necessarily modify the charge state. Spontaneouselectron trapping of the NV0 is depicted by the 2E →3A2 transition. 3

1.2 Typical ODMR data as function of magnetic field showing splitting tofour resonances. The dashed lines represent the theoretical predictionbased on Eq. (1.2) for the case where the magnetic field is appliedin the direction [cos θz sin θz 0], where θz = 21°. In general, thefour possible directions of the NV centers in a single crystal diamondgive rise to eight different resonance frequencies ν. For some fielddirections, the resonances are degenerate. The left inset shows thediamond unit cell projected along the [100] vector. If the magneticfield B is aligned in the [010] direction as depicted, the projection ofB on every possible NV direction is equal, and only two resonanceswill occur. The right inset shows a diamond unit cell projected along[cos θ′z sin θ

′z 0] for some arbitrary θ′z. As there are two possible values

for the B projection on the NV vectors, one of the degeneracies isremoved and four different resonances appear. . . . . . . . . . . . . . 5

vii

LIST OF FIGURES

1.3 (a) ODMR of a single camera pixel, arrow indicates the location on di-amond. (b) Locations and irradiation exposures scheme of the spots.(c) Per-pixel normalized ODMR dip magnitude in percents. The laserwas introduced with OF. Note the signal at the diamond edge andthe glue drop border, where photons scattered in the plane of thediamond change their direction. (d) Raw picture showing the spotsPL. Larger camera exposure would cause saturation of some spots butwould allow measurement of others. Background LED illuminationallows to see a current line on the sample that is close to contact withdiamond. The granulation is due to individual cores of the CFB. . . . 8

1.4 The cryogenic diamond magnetometer (a) The diamond disk (DD)containing NV centers is glued to the tip of a coherent fiber bundle(CFB) having 30,000 cores, and is brought to contact with the sil-icon (Si) wafer, which supports the superconducting niobium (Nb)film under study, using a 5-axis positioner. A room temperature op-tical setup allows optical imaging of the filtered ODMR signal usinga charge-coupled device (CCD) camera. An optical fiber (OF) is em-ployed for guiding the laser light into the CFB. Laser intensity iscontrolled using an acousto-optic modulator (AOM). A microwaveloop antenna (MLA) is employed for applying alternating signals tothe NV defects. (b) A photo of the magnetometer probing head anda sample under study. . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 (a) PL picture with the laser aligned to the diamond edge via CFB.Note that some of the spots are illuminated better than the others.(b) A scanning electron microscope picture of a tilted mirror fabri-cated with a focused ion beam in a 15µm thick diamond disk. Thelaser beam is to come from the bottom, enter the diamond and betotally reflected internally in the lateral direction. The location ofthis mirror in other insets marked with arrows. (c) An optical micro-scope image of the diamond with various crafted mirrors, oriented asin (d). (d) A PL image. The laser is introduced via the CFB onto theright bended mirror, that defuses the beam into the diamond plane.The bright spot on the left is the return of the laser beam into theCFB through the mirror shown in inset (a). The big PL spot in frontof it is made by a 2 hours 200KeV electron irradiation. The spot ispartially shadowed by the feature in the middle of the diamond. . . . 11

1.6 Transient simulation of the assembled PCB, showing a rather uni-form magnetic field at the CFB edge plane. In the inset there is acomparison of the stimuli current to the one measured through thebond connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

viii

LIST OF FIGURES

1.7 Noise sources analysis. (a) Comparison of SNR before and after theAOM for two different AOM MW drivers. (b) SNR of a camera asfunction of exposure time. The various plots correspond to pixels ofdifferent PL intensity. The two regions denote electron and photonnoise limited SNR. (c) Comparison of noise spectral density of theCFB input (laser) and output (PL) signals. No additional frequenciesare added, suggesting a good mechanical isolation of the fiber optics. 13

1.8 Correction of the NV− ODMR PL with the NV0 PL. In every graphthree lines are plotted: PL of the NV−, with an ODMR dip, PL of theNV0, without the ODMR dip and a division of the two. Three rowsare three different measurement locations. First and second columnare two separate frequency scan cycles, third column is an average of6 cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.9 Average NV− (top) and NV0 (bottom) PL as a function of the ontime and the duty cycle of a laser pulse train. The normalizationprocedure consists of (1) subtracting the bottom right data pointand (2) dividing by the duty cycle. Intensity peak of NV− is anti-correlated with the peak of NV0. The colorbars indicate that for bothcameras the measured spot was far from the saturation value of 255. 16

1.10 Two dimensional magnetic field imaging. (a,c) A photo taken withLED and laser on, showing the region where the magnetic field in-ducted by the current line is measured. (b,d) For every camera pixel,the maximum PL difference between the current on and off states forsome excitation frequency is plotted. (d) was measured with a biasfield, therefore different current directions may decrease or increasethe PL signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.11 Magnetic fields generated by the shielding currents in the Nb stripe(c)-(o) ODMR measurements for various values of the bias field Ha asa function of distance from the stripe edge, located at X = −850µm.The field Ha was gradually increased in (c)-(i) and decreased in (i)-(o). The white dashed lines represent the theoretical prediction thatis calculated with the following parameters: Z = 5µm, θz = −40°,θy = 2.85° and Jc = 16 × 109 Am−2 . The corresponding magneticfields are depicted in (a) for (c)-(i) and in (b) for (i)-(o). . . . . . . . 19

2.1 Nb/AlOx/Nb Josephson junction SEM image. The current is forcedto flow between the right and the left electrodes via the insulator inthe middle, that defines the JJ. In inset is the schematic cartoon ofthe JJ, with the current direction designated by the white arrow. . . 25

ix

LIST OF FIGURES

2.2 JJ anodization. (c) and (a) are dependency of the DC-SQUID onexternal flux before and after the anodization correspondingly, en-suring the JJ are operated in the quantum regime (see Sec. 2.3).(b) I-V characteristic before and after anodization. The critical cur-rent is decreased from 220µA to 100µA, corresponding to halvingthe initial JJ area of 400× 400 nm. The resulting anodization depthof 60 nm is beyond the estimated FIB Ga contamination depth of30 nm [21]. (d) An optical image of a trial sample after anodization,with a scratch that left some of the circuits electrically disconnectedduring the process. Anodization alters the Nb surface color, hencethe color contrast. (e) A sample during anodization. The bubblesvisible in the image are formed in time of the process. Fierce stirringpartially resolves the problem. . . . . . . . . . . . . . . . . . . . . . 26

2.3 DC-SQUID measurement. The junctions area is nominally 100 ×50 nm (possibly less due to Ga ions implantation). The oxidation wasproceeded for half an hour at a partial oxygen pressure of 160mTorr.(a) Schematic drawing of the four-probe measurement of the DC-SQUID. (b) Lock-in critical current measurement for zero bias flux.(c) Modulation of the critical current with applied flux. . . . . . . . . 28

2.4 RF-squid βL extraction. (a) Schematic drawing of the RF-SQUID.(b) Homodyne measurement of an RF-SQUID. Horizontal and verti-cal axes represent DC and AC modulation of the external flux corre-spondingly. A strong signal is measured along the dashed lines thatcorrespond to a bias flux causing a stability loss in the SQUID. Theratio between the depicted Φx,b and Φ0 results with βL = 9.8 (c) Acartoon depicting the Φx,b/Φ0 ratio for βL = 11. The charge stateof the system is approximated as a localized mass lying in a well.From top to bottom: for Φx = 0 the mass lies in the bottom well; forΦx = 1.5Φ0 the mass is still lying in the same well, corresponding tototal flux Φ = 0 in the loop; for Φx = Φx,b = 1.96Φ0 the well flattensand the mass slides to the next well, corresponding to Φ = 1 × Φ0

flux in the loop; rising the external flux Φx by another single fluxquantum to Φx = 2.96Φ0 causes to a slide to the next well of Φ = 2Φ0. 30

2.5 (a) Picture of the RF-SQUID measurement wafer inside a box. (b)Scanning electron microscope (SEM) image of the resonator area con-taining the SQUID and the adjacent flux line. (c) RF-SQUID. TheJJ is on the left. (d) The trilayer JJ. . . . . . . . . . . . . . . . . . . 31

2.6 Homodyne measurement setup. (see text) . . . . . . . . . . . . . . . 322.7 Comparison of lock-in versus DC signal for the same resonance. DC

and AC bias where applied by different sources in this experiment. . . 33

x

LIST OF FIGURES

3.1 The calculated ring current and magnetic field in the center for oneflux quantum trapped inside, as a function of the ring radius. . . . . 35

xi

Abstract

Optical detection of magnetic resonances of nitrogen-vacancy (NV) defects in a dia-mond lattice via a fiber bundle is applied to measure the Meissner shielding magneticfields in a thin film type II superconductor at 4K. The electronic spin 1 structureof the NV center is sensitive to magnetic field, temperature, and strain. The spinstate may be polarized with laser excitation, altered by standard electron spin res-onance protocols and optically measured, as the photoluminescence of the centerdepends on the spin state. The long coherence and relaxation times make the NVcenter rather a sensitive sensor. In this work, an NV magnetometer was designed,constructed and tested on a superconducting sample at 4K, without a noticeableimpact on the sample temperature. The experimental results are compared withtheoretical predictions based on the macroscopic critical state model with an ac-ceptable agreement. Reducing the operation temperature by an order of magnitudemay allow quantum computation applications. The second topic of this thesis isdesign and fabrication of superconducting integrated circuits, that allow to engi-neer quantum Hamiltonians with macroscopic degrees of freedom like capacitanceor inductance, compactly describing the joint dynamics of an Avogadro number ofelectrons. Basic building blocks of a quantum circuit, including a superconductingmicrowave resonator, coupled to a superconducting loop with a Josephson junctionwere prepared and measured towards the integration with NV magnetometry.

1

1

Magnetometry withNitrogen-Vacancy Centers

2

1. MAGNETOMETRY WITH NITROGEN-VACANCY CENTERS

3A2

3E

1E2E

1A1

4A2

2A

C.B.

ms=-1ms=0

ms=1

ms=-1ms=0

ms=1

NV-NV0

NV -

NV0

PL[a.u.]

λ[nm]

[100][010]

[001] V

N

C

a)

b)

c)

Figure 1.1: NV center (a) Diamond unit cell, with an NV center aligned along the[111] direction. (b) Scheme of the NV center PL spectrum in arbitrary units (a.u.).Denoted from left to right are the excitation frequency used in this work and theZPLs of NV0 and NV−. Distinguished ZPL peaks are typical for cryogenic temper-atures. (c) Energy level diagram of the NV center, NV0 on the left and NV− onthe right. Solid (Dashed) lines indicate radiative (non-radiative) transitions. Themore common transitions 3E(mS = ±1) →1A1 and 1E →3A2(mS = 0) are depicted,though the 3E(mS = 0) →1 A1 and 1E →3 A2(mS = ±1) occur. Photoconversiontransitions via the conductance band necessarily modify the charge state. Sponta-neous electron trapping of the NV0 is depicted by the 2E →3A2 transition.

1.1 Introduction

The nitrogen-vacancy (NV) center in diamond consists of a substitutional nitrogenatom (N) adjacent to a vacancy (V) in the diamond lattice [see Fig. 1.1(a)] [1]. Thethree carbon atoms (C) around the vacancy contribute one electron each, one of themremaining unpaired. Upon trapping an electron, the zero charged NV0 changes intoa stable negatively-charged NV−. The NV center has a C3v symmetry - namely, itmay be rotated by an angle of 120° about the N-V vector, or reflected through aplane defined by the N-V and any of the N-C vectors, having the atoms return to theinitial positions. This symmetry predicts certain structure of the electronic quantumstates, partially confirmed, giving rise to the naming convention of the energy levels.Though yet a subject of active research, both computationally and experimentally,the current understanding of the electronic level structure is depicted in Fig. 1.1(c).

3


The NV− center electronic structure contains triplet ground and excited states,with optical zero phonon line (ZPL) energy separation of 1.945 eV (wavelength of637 nm). The sub-levels mS = 0 and mS = ±1 of the ground state triplet 3A2 areseparated by D = 2.87GHz in the absence of magnetic field. Note that mS denotesthe spin along the NV axis [see Fig. 1.1(a)]. The excited state 3E is a triplet as well,with zero-field splitting of Des = 1.42GHz.

After being optically excited with a green photon into the 3E state, the NV−

defect can relax either through the same radiative transition, which gives rise to redphotoluminescence (PL), or through a secondary path involving non-radiative inter-system crossing to the dark singlet states 1A1 and

1E, as can be seen in Fig. 1.1(b,c).While optical transitions are spin conserving, these non-radiative crossings are stronglyspin selective, as the shelving rate from mS = 0 sublevel of the 3E is much slowerthan those from mS = ±1. In addition, the NV defect decays preferentially fromthe lowest singlet state 1A1 towards the mS = 0 sublevel of the ground triplet 3A2.These spin selective processes allow spin polarization into mS = 0 through opticalpumping. Furthermore, since intersystem crossings are non-radiative, the NV de-fect PL is significantly higher when the mS = 0 state is populated, thus allowing anoptical measurement of the spin state [2]. Notably, the 1E lifetime (approximately300 ns) is by an order of magnitude longer than the one of 3E.

The ground state spin Hamiltonian of the NV− defect in diamond is given by

H = H∥ +H⊥ + hE(S2x′ − S2

y′), (1.1)

where the z′ direction is taken to be parallel to the NV axis, the parallel part H∥is given by H∥ = hDS2

z′ + gµBBz′Sz′ , the transverse part H⊥ is given by H⊥ =gµB(Bx′Sx′ + By′Sy′), Bi is the magnetic field in the i direction (i = x′, y′, z′), Si

is the corresponding 3 × 3 spin S = 1 matrix, E ∼ 5MHz and D are axial andoff-axial zero-field splitting parameters, respectively, g ≃ 2 is Lande g-factor, h isPlanck constant and µB is Bohr magneton [1]. By evaluating the eigenvalues of Husing perturbation theory, one finds for the case where E ≪ γgBz′ ≪ D that theresonance frequencies ν± corresponding to the transitions mS = 0 ↔ mS = ±1 aregiven by [3]

ν± = D ±√

(γgB∥)2 + E2 +3γ2

gB2⊥

2D, (1.2)

where γg = gµB/h ≃ 28.024GHz/T is the electron spin gyromagnetic ratio, B∥ = Bz′

and B2⊥ = B2

x′ +B2y′ .

The continuous wave (CW) optical detection of magnetic resonances (ODMR)in NV− centers may be understood as a measurement of the spin polarization re-duction. Upon a CW laser excitation, the population of mS = 0 subsets of 3A2 and3E increases as compared to the thermal equilibrium. A resonant CW microwave(MW) excitation repopulates the mS = ±1 substates of 3A2, causing a reduced PL.

4


B B

Figure 1.2: Typical ODMR data as function of magnetic field showing splittingto four resonances. The dashed lines represent the theoretical prediction basedon Eq. (1.2) for the case where the magnetic field is applied in the direction[cos θz sin θz 0], where θz = 21°. In general, the four possible directions of theNV centers in a single crystal diamond give rise to eight different resonance fre-quencies ν. For some field directions, the resonances are degenerate. The left insetshows the diamond unit cell projected along the [100] vector. If the magnetic fieldB is aligned in the [010] direction as depicted, the projection of B on every possibleNV direction is equal, and only two resonances will occur. The right inset shows adiamond unit cell projected along [cos θ′z sin θ

′z 0] for some arbitrary θ′z. As there are

two possible values for the B projection on the NV vectors, one of the degeneraciesis removed and four different resonances appear.

5


Typically a few percent reduction is measured. Sensitivity of the spin state mea-surement may be increased with pulsed ESR techniques, however only by an orderof magnitude [4].

The NV defects in a single crystal diamond are oriented along the four latticevectors [111],[111],[111],[111]. The ODMR data seen in Fig. 1.2 has been obtainedwith externally applied magnetic field having a vanishing component in the [001]direction, and consequently only 4 resonances are obtained. The dashed lines rep-resent the frequencies ν± calculated according to Eq. (1.2). For low fields, the termproportional to B2

⊥ in Eq. (1.2) can be disregarded when B⊥ ≪ D/γg ≃ 0.1T. Note,however, that the comparison between the ODMR data seen in Fig. 1.2 and theoryyields poor agreement when this term is disregarded.

The NV0 electronic structure contains two doublets in the ground 2E and theexcited 2A states, with a ZPL of 2.156 eV (575 nm). The NV0, like the NV−, maybe excited with a green photon into the 2A state and may relax either via the sameradiative path, or non radiatively via the 4A2 quartet. Despite the doublet structure,no electron spin resonance (ESR) signal is detected from the 2A and 2E states. The4A2 quartet does present an ESR signal, however it is yet to be measured by opticalmeans. The absorption and PL spectrum of the NV− and NV0 overlap significantly,yet are distinguishable in the tails and ZPL peaks, as can be seen in Fig. 1.1(b).

The NV0 would be of no interest to spin related applications, contributing mostlyto the background signal of the NV− PL, however recently a photoconversion mech-anism between the two charge states of the NV center was studied. In a two pho-ton process, the NV−(NV0) is first excited into the 3E(2A) state, and then ionized(recombined) to a NV0(NV

−) [5]. Hence the NV−/NV0 ratio changes during themeasurement, as it was observed in our setup.

The photoconversion effect was successfully used [6] to improve the sensitivity ofan NV− spin state measurement by applying the following protocol: first the NV−

was selectively shelved in the 1A1 state, depending upon the spin substate of the 3A2

ground triplet, then converted into an NV0 with an energetic laser pulse. The NV−

in the 1A1 state was protected from the conversion pulse, hence the photoconversiondepended on the spin state of the NV−. As determining the charge state of the NVcenter is easier than the relative PL intensity of the NV−, the overall sensitivitywas increased by an order of magnitude. Moreover, the magnetic field is no longerrequired to remain constant during the measurement, as it was effectively measuredin the moment of photoconversion. The last might be important for measuringtransient or quantum fields.

6


1.2 Experimental Setup

1.2.1 Diamond Preparation

In this work a single crystal type Ib diamonds from Element-six had been used, facescut along {100} crystal planes with accuracy of 3°. Type Ib diamonds are rich withnitrogen (≈ 200 ppm), thus eliminating the need in nitrogen implantation. Large(3 × 3 × 0.1mm) polished plates had been studied. Additionally, a 1mm diameterand 15µm thickness disk was laser cut for on-chip magnetometry. The large samplespresented better ODMR contrast than the disks (7% versus 3%).

The vacancies were introduced by means of electron irradiation at a 200KeV (FEITecnai T20) and 300KeV (FEI Titan) Tunneling Electron Microscopes (TEMs) [7].Unfortunately, the exact doze remained unknown, as no Faraday cup was avail-able. The beam was focused into a ≈ 30µm spot at an approximate surface ofthe diamond. The irradiation was performed in arrays of spots with different ex-posure time (see Fig. 1.3). In general, spots with larger doze produced greater PL.Spots exposed for more than 10′ resulted with poor ODMR signal. On the otherhand, the area between spots, exposed only during stage movements, produced adetectable ODMR. Similar PL intensities obtained for spots made with the 200KeVand 300KeV TEMs, despite the different electron sources (field emission gun andlanthanum hexaboride, respectively). Spots irradiated during in-situ annealing of900C showed reduced PL. TEM beam might be focused to only a few nanometersin diameter. Combined with nanometer precision stage movement it allows highlateral resolution patterning of NV centers. Covering the whole 1mm disk with adoze corresponding to a 1′ exposure of a 30µm spot would take 18 hours.

One sample was irradiated with 120KeV argon ions with a doze of 3×1019 cm−2,resulting with a rather poor ODMR, possibly due to a bad measurement. The maindifference between electron and ion irradiation is the density profile of the vacanciescreated. While the electrons cause damage along their path, with an exponentiallydecaying energy (typical decay distance of 10µm for the energies used), the ions areimplanted at a well defined depth (≈ 100 nm for our sample), where most of thevacancies will be concentrated. Going beyond a certain concentration of damageswill result in poor ODMR and then a graphitisation of the diamond. Larger volumescontaining NV centers will provide a stronger PL signal. However, for fields close tothe diamond surface, e.g created by sub-micron resolution circuitry, it is preferredto limit the NV depth, in order to avoid background signal.

Following vacancies creation, the diamonds were annealed to allow N-V recom-binations. The annealing was mostly done in quartz tube heaters, in argon en-vironment for one hour at a temperature of 900C.The annealing was followed bycleaning in boiling acids (1:1:1 perchloric,sulfuric,fuming nitric) and solvents (ace-tone, methanol, isopropanol and deionized water).

7


100 m

100 m

Glue border

Broken

edge

Hz

PL[a.u.] c)a)

b)

d)

Figure 1.3: (a) ODMR of a single camera pixel, arrow indicates the location ondiamond. (b) Locations and irradiation exposures scheme of the spots. (c) Per-pixel normalized ODMR dip magnitude in percents. The laser was introduced withOF. Note the signal at the diamond edge and the glue drop border, where photonsscattered in the plane of the diamond change their direction. (d) Raw pictureshowing the spots PL. Larger camera exposure would cause saturation of some spotsbut would allow measurement of others. Background LED illumination allows to seea current line on the sample that is close to contact with diamond. The granulationis due to individual cores of the CFB.

8


1.2.2 Cryogenic Setup

In our prototype cryogenic magnetometer design, the thin diamond disk is gluedwith an optical adhesive to the edge of a coherent fiber bundle (CFB) having 30, 000cores, ≈ 4µm in diameter, allowing optical imaging. The excitation laser may beintroduced by two means: with a separate multimode optical fiber (OF) or throughCFB. In the first case, the OF is illuminating the CFB from a side [see Fig. 1.4(a)],with an angle ensuring total internal reflection of the laser light from the diamondbottom, and at a distance ensuring full diamond coverage. In the second option ofillumination, the laser was guided through the CFB fibers close to the diamond edge,scattered from it, guided through the thin diamond and reached NV centers spotsat a distance of ≈ 0.5mm. This technique had allowed concentrating the laser atspecific spots. In order to improve the method, tilted mirrors and guides were etchedin the thin diamond with focused ion beam (FIB), successfully bending light (seeFig. 1.5 (a)), however resulting with poor ODMR, possibly due to contamination inthe FIB chamber.

The MW excitation was introduced by means of microwave loop antenna (MLA).The MLA is formed by a two side photolithography on a high frequency Rogersprinted circuit board (PCB) with a manually soldered wire bond to close the loopbetween the two sides of the PCB. Holes to guide the CFB and OF were drilledin the lateral plane of the PCB. ’CST studio’ simulations predict good magneticfield concentration and low return coefficient (see Fig. 1.6). High powered MWirradiation caused a significant sample heating (≈ 1K), thus a semi-CW techniquewas applied: long (≈ 10ms) MW and laser pulses, followed by long relaxationperiods. The heating problem might be addressed by making use of MW resonatorsfor NV excitation, reducing the injected amplitude by the resonator quality factor.For superconducting resonators, quality factors of million are reasonable.

The sample under study is fixed in a chip holder allowing DC electrical connec-tion, mounted on a 5-axis piezoelectric positioner with sub nanometer resolution,which allows to bring the sample in contact with the diamond. After a few cryo-cycles the optical glue had broken and the diamond had fallen. We had found thatthe diamond with equal probability sticks to the CFB or the wafer, probably due toelectrostatic forces. Hence in the following experiments the diamond was carried tothe proper position and put upon the sample, ensuring maximal contact. In futurework, samples may be designed with alignment current lines so that their ODMRpatterns will provide the measurement of relative angles between the diamond andsample.

The sample and PCB ground plane are thermally sinked to the cold plate (≈ 3K)of an insert, immersed into the liquid helium cup of a closed loop cryostat. The insertis hung from an optical table, and hermetically attached to the cryostat via a flexiblebellow, to isolate it from compressor vibrations. A home-made persistent-current

9


Figure 1.4: The cryogenic diamond magnetometer (a) The diamond disk (DD) con-taining NV centers is glued to the tip of a coherent fiber bundle (CFB) having30,000 cores, and is brought to contact with the silicon (Si) wafer, which supportsthe superconducting niobium (Nb) film under study, using a 5-axis positioner. Aroom temperature optical setup allows optical imaging of the filtered ODMR signalusing a charge-coupled device (CCD) camera. An optical fiber (OF) is employed forguiding the laser light into the CFB. Laser intensity is controlled using an acousto-optic modulator (AOM). A microwave loop antenna (MLA) is employed for applyingalternating signals to the NV defects. (b) A photo of the magnetometer probinghead and a sample under study.

10


b)

a)

d)

c)

Figure 1.5: (a) PL picture with the laser aligned to the diamond edge via CFB.Note that some of the spots are illuminated better than the others. (b) A scanningelectron microscope picture of a tilted mirror fabricated with a focused ion beam ina 15µm thick diamond disk. The laser beam is to come from the bottom, enter thediamond and be totally reflected internally in the lateral direction. The location ofthis mirror in other insets marked with arrows. (c) An optical microscope image ofthe diamond with various crafted mirrors, oriented as in (d). (d) A PL image. Thelaser is introduced via the CFB onto the right bended mirror, that defuses the beaminto the diamond plane. The bright spot on the left is the return of the laser beaminto the CFB through the mirror shown in inset (a). The big PL spot in front of itis made by a 2 hours 200KeV electron irradiation. The spot is partially shadowedby the feature in the middle of the diamond.

11


Figure 1.6: Transient simulation of the assembled PCB, showing a rather uniformmagnetic field at the CFB edge plane. In the inset there is a comparison of thestimuli current to the one measured through the bond connection.

superconducting solenoid magnet is attached to the cryostat, encircling the samplelocation. The insert is kept in vacuum to avoid diffusive heating of the sample byMLA and avoid moisture condensation (though a thin ice layer was considered as anobstacle for a full contact). Home-made vacuum feed-through were required for theCFB and OF. The basic MW setup consists only of a synthesizer and an amplifier.The estimated delivered power was between −15 dBm and 0 dBm.

1.2.3 Optical Table Setup

The laser beam is modulated by an acousto-optical modulator (AOM) and eitheris directly coupled to the OF or is reflected by a dichroic 550 nm mirror througha ×10 objective onto the CFB surface. Return signal is collected by the sameobjective, split in two by a beam splitter (BS) and collected by two room temperaturecommercial cameras, after being filtered to contain only NV− or NV0 spectrum witha 593 nm long pass and a 575 nm band pass filters, respectively. The cameras wheresynchronized by an external trigger, their joint exposure and individual gain valuesadjusted for the PL intensity of the NV center spots of interest. Light emittingdiode (LED) and photo-detector (PD) were introduced to the setup with additionalBSs for alignment purposes (imaging the pattern on sample) and monitoring thelaser intensity.

To measure the cameras’ noise level for a given exposure time, the followingmethodology was applied. First a long exposure image of a constant diamond PLwas taken multiple times and averaged, to receive a picture of mean values. Next,multiple frames of short exposure were taken and a per pixel standard deviation wascalculated, using the values of the different short frames. The signal to noise SNR =

12


a)

b)

c)

Electron

noise

Photon

noise

Figure 1.7: Noise sources analysis. (a) Comparison of SNR before and after theAOM for two different AOM MW drivers. (b) SNR of a camera as function ofexposure time. The various plots correspond to pixels of different PL intensity. Thetwo regions denote electron and photon noise limited SNR. (c) Comparison of noisespectral density of the CFB input (laser) and output (PL) signals. No additionalfrequencies are added, suggesting a good mechanical isolation of the fiber optics.

13


µ/σ ratio, where µ and σ are here the brightness mean and standard deviation wascomputed per pixel. The SNR of pixels differs by the brightness of the input signal.In order to present the data on a single graph, the pixels were sorted by percentilesof mean brightness, and their SNR values averaged. The SNR differs, but reachesa plateau at an exposure of 100ms (see Fig. 1.7(b)). For shorter frames, SNR islimited by the electron noise of the camera. For bright pixels, the plateau level is atSNR = 10. To measure ODMR PL changes of 1%, an SNR = 1000 is required, thatcorresponds to n = (1000/10)2 = 10, 000 samplings. This is achieved by averagingacross large lateral areas and/or taking multiple frames. The PL is non uniformacross the diamond due to different NV concentration and light conditions, henceeven larger areas are required.

The laser source and the AOM are unstable on the scale of minutes and secondscorrespondingly, in the range of one percent. The inverse of their SNR is depicted inFig. 1.7(a). The measured effect (ODMR PL) is two orders of magnitude grater thanthe input signal noise. The noise spectral density added by the fiber optics is ratheruniform, suggesting it is mostly due to signal weakening, despite the sensitivity ofoptical fibers to mechanical vibrations (see Fig. 1.7(c)). About 200 frequency pointsare required for resonances reconstruction. Usually about 10 frequency scans arerequired to compensate for slow drifts. The resulting scanning time is about 10minutes for a 30µm spot of strong PL.

1.3 Results

1.3.1 NV0 Correction

The optical table setup includes a second camera, with an NV0 ZPL bandpass filter,that provides a reference PL picture unaffected by the MW. Practically, the gainedsensitivity did not justify the alignment and calibration efforts, required for everymeasurement. The correction results are presented in Fig. 1.8. Note the peak in NV0

ODMR when NV− is in resonance. One could expect a dip in the NV0 correlatedwith the NV− dip, if a photoconversion limited by singlet shelving was taking place,hence the effect remains unexplained and a subject of further study.

The pattern of anti-correlation was registered in an another experiment, wherean attempt was made to measure the spin polarization and relaxation times withan open camera by modifying parameters of a laser pulses train (without MW). Noreliable fit to a NV transition rates model was achieved, however the two recordedsignals present anti-correlation patterns (see Fig. 1.9).

14


0.94

0.96

0.98

1

Spo

t 9

Cycle 1 Cycle 2

Average 6 Cycles

0.96

0.98

1

Spo

t 10

2.7 2.8 2.9 30.96

0.98

1

Spo

t 11

GHz2.7 2.8 2.9 3

GHz2.7 2.8 2.9 3

GHz

NV−

NV0

NV−/NV0

Figure 1.8: Correction of the NV− ODMR PL with the NV0 PL. In every graph threelines are plotted: PL of the NV−, with an ODMR dip, PL of the NV0, without theODMR dip and a division of the two. Three rows are three different measurementlocations. First and second column are two separate frequency scan cycles, thirdcolumn is an average of 6 cycles.

15


9.1e−2 4.6e−2 1.8e−2 6.9e−3 2.6e−3 1.0e−31.0e−7

5.2e−7

3.5e−6

2.3e−5

1.5e−4

1.0e−3NV−

Ton

/(Ton

+Toff

)

Ton

0

20

40

60

80

100

9.1e−2 4.6e−2 1.8e−2 6.9e−3 2.6e−3 1.0e−31.0e−7

5.2e−7

3.5e−6

2.3e−5

1.5e−4

1.0e−3NV0

Ton

/(Ton

+Toff

)

Ton

0

20

40

60

Figure 1.9: Average NV− (top) and NV0 (bottom) PL as a function of the on timeand the duty cycle of a laser pulse train. The normalization procedure consists of (1)subtracting the bottom right data point and (2) dividing by the duty cycle. Intensitypeak of NV− is anti-correlated with the peak of NV0. The colorbars indicate thatfor both cameras the measured spot was far from the saturation value of 255.

16


c) d)

a) b)

Figure 1.10: Two dimensional magnetic field imaging. (a,c) A photo taken withLED and laser on, showing the region where the magnetic field inducted by thecurrent line is measured. (b,d) For every camera pixel, the maximum PL differencebetween the current on and off states for some excitation frequency is plotted. (d)was measured with a bias field, therefore different current directions may decreaseor increase the PL signal.

17


1.3.2 2D Imaging

Our magnetometer allows an imaging of 2D magnetic fields, a feature that mightbe useful when scanning magnetometry is too slow to capture the dynamics orwhen the interaction with a scanning probe might influence the sample. Anothermotivation is a simultaneous collapse of the quantum state across the chip, whenthe magnetic fields encode a logic state of quantum computation. To demonstratethis ability, an Nb circuit was fabricated with standard photolithography methodson a silicon substrate. DC current was applied through the thin film lines. In orderto avoid heating effects contribution, the measurement was performed in a pseudoCW protocol (similar to section 1.2.2), with an addition of a current pulses throughthe chip. Measuring PL when the current pulses were set out of phase with the MWand laser had confirmed that the PL signal is not due to local heating.

1.3.3 Measuring Shielding Currents in Superconductors

An important milestone for this project and the main result of current thesis ismeasurement of a superconducting effect, ensuring that the magnetometer is com-patible with cryogenic temperatures. For this purpose a 500 nm thick niobium filmhaving a rectangular shape and an area of 5.25mm× 1.7mm has been deposited ona high resistivity Si/SiN substrate through a mechanical mask using DC-magnetronsputtering. Bias perpendicular magnetic field caused formation of complex shield-ing currents inside the superconductor (see section 1.4.2). The ODMR was averagedalong the axis parallel to the niobium edge. Measured ODMR signal is presented inFig. 1.11 for various values of the externally applied magnetic field.

1.4 Analysis

1.4.1 Reconstruction of NV-center Resonances

Reconstructing the magnetic field from an ODMR data is possible [8], but in thiswork we solve a simpler task of reconstructing the resonance frequencies when thesheet currents distribution is given. The induced magnetic field in the whole space iscomputed by integrating the current density with the Biot-Savart kernel. The biasfield Ha is assumed to be applied perpendicularly to the sample. Perpendicularity tothe diamond was independently verified during the magnet calibration, when onlytwo resonances appeared (see also caption of Fig. 1.2).

Diamond disk is modeled parallel to the sample at a distance Z from it. Thespatial orientation of the diamond crystal with respect to the cartesian coordinatesystem that is defined in Fig. 1.4 is specified in terms of the unitary transformationu (θz, θy) = Rz (θz)Ry (θy), where Ry (θy) (Rz (θz)) represents a rotation around the

18


f [G

Hz]

(c)

3.15mT

2.8

3

f [G

Hz]

(d)

0.00mT

2.8

3

f [G

Hz]

(e)

0.53mT

2.8

3

f [G

Hz]

(f)

1.05mT

2.8

3

f [G

Hz]

(g)

1.58mT

2.8

3

f [G

Hz]

(h)

2.10mT

2.8

3

f [G

Hz]

(i)

2.63mT

2.8

3

f [G

Hz]

(j)

3.15mT

2.8

3

0.99

0.995

1

(k)

2.63mT

(l)

2.10mT

(m)

1.58mT

(n)

1.05mT

(o)

0.53mT

(p)

0.00mT

−900 −800 −700 −600−5

0

5

10

X [µm]

H [m

T]

(a)

Hx Hz

−900 −800 −700 −600−5

0

5

10

X [µm]

(b)

Hx Hz

Figure 1.11: Magnetic fields generated by the shielding currents in the Nb stripe(c)-(o) ODMR measurements for various values of the bias field Ha as a function ofdistance from the stripe edge, located at X = −850µm. The field Ha was graduallyincreased in (c)-(i) and decreased in (i)-(o). The white dashed lines represent thetheoretical prediction that is calculated with the following parameters: Z = 5µm,θz = −40°, θy = 2.85° and Jc = 16× 109Am−2 . The corresponding magnetic fieldsare depicted in (a) for (c)-(i) and in (b) for (i)-(o).

19


y (z) axis with the rotation angle θy (θz). First, the transformation is applied to theinitial orientation, for which the lattice vectors [100],[010] and [001] are taken to beparallel to the unit vectors x, y and z, respectively, allowing thus the calculation ofthe 4 unit vectors pointing in the directions of NV defects in the diamond disk. Thesmall value of θz may be due to polishing mismatch. Next, the resonance frequenciesν± are calculated for each unit vector using Eq. (1.2) (see the red dashed lines inFig. 1.11(c)-(o), which represent the calculated values of ν+).

1.4.2 Type II Superconductors in Bias Magnetic Field

The current distribution in a thin long film of a type-II superconductor under anapplied bias magnetic fieldHa is theoretically predicted by the critical state model [9,10]. In this model the density of shielding currents is only allowed to be as high asthe critical value Jc. For the case of a constant Jc, the current distribution is foundto be given by [11, 12]:

J(x,Ha, Jc) =

{2Jcπ

arctan cx√x2p−x2

|x| < xp

Jcx/|x| xp < |x| < w/2, (1.3)

where w = 1.7mm is the width of the stripe, c = tanh(Ha/Hc), xp = w/ cosh(Ha/Hc)and Hc = Jc/π is the critical field. The bias field Ha is applied along the z axis, andthe currents J(x) are along the y axis, as defined in Fig. 1.4.

In general, due to flux trapping the current distribution J is history dependent.For the case where the bias magnetic field is first risen from zero to a maximumvalue of H↑, and then decreased to H↓, the resulting current distribution is found tobe given by [11]

J↓(x,H↓, Jc) = J(x,H↑, Jc)− J(x,H↓, 2Jc). (1.4)

Comparison between the experimental results and theory is presented in Fig.1.11, for both cases of increasing Ha [panels (d)-(j)] and decreasing Ha [panels (j)-(p)]. Good agreement is obtained for relatively small values of Ha. However forHa & 2.5 mT a significant discrepancy is observed. For that range a good fittingcan be obtained by reducing the assumed value of Jc by a factor of about 1.5,however, good agreement cannot be achieved for the entire range when a fixed valueof Jc is being used .

One of the simplifying assumptions that have been made in the derivation of Eqs.(1.3) and (1.4) is that Jc is independent on the local magnetic induction B [11, 12].More recently, however, various types of dependencies Jc(B) have been assumed,and the calculation of the current density has been generalized accordingly [10, 13–

20


15]. One of the popular models is the so called Kim’s model [16]:

Jc(B(x)) =Jc0

1 + |B(x)|/B0

, (1.5)

where B0 is a constant and Jc0 is the sheet critical current in the low magnetic fieldlimit. The model was applied to fit the data in Fig. 1.11 (c), utilizing numericalmethods that have been presented [17](see Appendix A).

1.5 Discussion

A low temperature optical spacial magnetometer is demonstrated, by measuringthe magnetic fields created by shielding currents in a superconducting film. Thedesign is compatible with even lower temperatures, commonly used for supercon-ducting quantum circuits operation. The required sensitivity is roughly of 1mTwith a spacial resolution of 1µm (see Ch. 3). Several approaches exist to increasethe sensitivity, so that a 1000 decrease in area will not cause a 1000 increase inmeasurement time.

On the optical table side, a stabilized laser and a cooled camera or a singlephoton counter might provide the necessary sensitivity increase. As it was shownin section 1.2.3, a measurable signal is received with 1ms exposure, however onlyfor 100ms the sensitivity is no longer limited by the electronic noise of the camera,hence the sensitivity may be increased by a factor of 100 with a more sensitivecamera.

Concentrating the laser beam on the region of measurement with mirrors andguides, as shown in Fig. 1.5 would increase the PL signal proportionally. In thecurrent setup with side illumination we can measure across the whole 1mm of thediamond simultaneously. If we are interested in a much smaller area of 5µm radiusfor example, and be able to concentrate the laser on that spot, the PL would increaseby a factor of 104. This approach might eliminate the need in more sensitive cameras.

Fabrication of the superconducting circuit directly on diamond would minimizethe contact distance, increasing the magnetic field amplitude at the NV ensemblevicinity. Companioned by an ion irradiation through masks, the NV ensembles(spots) might be aligned with a sub-micron accuracy in all three dimensions to themagnetic field generating currents [18]. In this approach the ODMR peak broadeningdue to magnetic field inhomogeneity is minimized, resulting with a higher achievableresolution of magnetic field detection. One expected challenge is isolation of thelaser beam from the superconductor. A possible solution is introducing a silica layerbetween diamond and metal, serving as a mirror for in plane photons due to a totalinternal reflection from a lower refractive index surface.

21


One particularly interesting approach for sensitivity increase is the protocol uti-lizing NV charge state photoconversion, described in section 1.1, as it suits our opencameras setup. The charge conversion may occur before the frame is taken, andthe relatively long exposure time of the camera is then used for acquiring statis-tics regarding the NV−/NV0 ratio. The photoconversion pulse may be deliveredthrough the imaging core of the CFB, while the weaker measurement and shelvingexcitations would be delivered via a distant core, or an optical fiber.

To increase the spacial resolution, currently limited by the core size of the bundlefiber, gradient-index (GRIN) on fiber optics may be used. GRIN lenses are glassrods in the fiber diameter, with a refractive index modified along the radial direction,that effectively correspond to the thickness modification of the conventional lenses.GRIN telescopes are routinely used with fiber bundles in endoscopic applicationsfor ten times increase of the field of view. Here the requirement is opposite, thefield of view needs to be decreased, therefore a GRIN microscope is to be designedaccordingly.

22

2

Superconducting Circuits

23

2. SUPERCONDUCTING CIRCUITS

2.1 Introduction

Superconducting integrated circuits allow to engineer quantum Hamiltonians withmacroscopic degrees of freedom like capacitance or inductance, compactly describingthe joint dynamics of an Avogadro number of electrons. The various designs ofsuperconducting qubits are based on the Josephson tunnel junction (JJ), the onlynon-dissipative, strongly non-linear circuit element available at low temperature [19].In this chapter design, fabrication and measurement of circuits with JJs will bedemonstrated.

2.2 Josephson Junctions

The JJ consists of two superconducting electrodes, typically separated by a thininsulator. The basic equations governing Josephson effect dynamics are [20]

V (t) = Φτ∂θ

∂t(2.1)

I(t) = Ic sin(θ(t)) (2.2)

where V ,I are the voltage and the current across the JJ, Φτ = Φ0/2π, Φ0 = h/2e isthe magnetic flux quantum, h is Planck constant, e is electron charge, Ic is the criticalcurrent of the JJ and θ is the gauge-invariant phase difference of the superconductingorder parameter function across the JJ. Ic scales proportionally to the insulator layerarea, and diminishes exponentially with its thickness. JJ dissipates energy, if biasedby current greater than Ic. The energy stored in the junction is

E(t) =

∫ t

−∞V (t′)I(t′)dt′ = −EJ cos θ (2.3)

where EJ = ΦτIc is the Josephson energy of the junction.The Josephson junctions are fabricated by side ion milling in Nb/AlOx/Nb tri-

layer. First, the niobium is DC-magnetron sputtered on a high resistivity silicon sub-strate. Next, 5 nm of aluminum are sputtered in the same chamber without breakingthe vacuum, and oxidized in pure oxygen atmosphere. A second Nb sputter finishesthe trilayer. Micrometer sized features are patterned by standard photolithographymethods. The JJs are narrowed by Focused Ion Beam (FIB) to ≈ 300 × 300 nm.The sample is rotated, adjusting the beam to be parallel to the surface, and twoholes are made in the trilayer wall, that will force the current to go from the top tobottom Nb electrode through the aluminum oxide (AlOx) layer, thus forming thejunction (Fig. 2.1). Low gallium (Ga) ion current of 1.5 pA is used do minimizeGa implantation. Image recognition scripts are used for drifts compensation. It is

24


Figure 2.1: Nb/AlOx/Nb Josephson junction SEM image. The current is forced toflow between the right and the left electrodes via the insulator in the middle, thatdefines the JJ. In inset is the schematic cartoon of the JJ, with the current directiondesignated by the white arrow.

25


d) e)

0 50 100 150 200 250

15

20

25

30

35

40

45

50

I[μA]

V[μ

V]

I-V

after

before

0 0.5 1

4

5

6

7

8

x 10-5

Vflux

V

0 0.5 1

4

5

6

7

8

x 10-5

Vflux

V

a) b) c)

Figure 2.2: JJ anodization. (c) and (a) are dependency of the DC-SQUID onexternal flux before and after the anodization correspondingly, ensuring the JJ areoperated in the quantum regime (see Sec. 2.3). (b) I-V characteristic before and afteranodization. The critical current is decreased from 220µA to 100µA, correspondingto halving the initial JJ area of 400 × 400 nm. The resulting anodization depth of60 nm is beyond the estimated FIB Ga contamination depth of 30 nm [21]. (d)An optical image of a trial sample after anodization, with a scratch that left someof the circuits electrically disconnected during the process. Anodization alters theNb surface color, hence the color contrast. (e) A sample during anodization. Thebubbles visible in the image are formed in time of the process. Fierce stirringpartially resolves the problem.

26


assumed that the top and bottom Nb layers are connected via a pinhole in the AlOxlayer somewhere in a distance from the JJ.

Some of the samples were anodized at a constant potential of 5V for 20 s inan electrolytic solution containing 165 g ammonium pentaborate, 1120ml ethyleneglycol and 760ml deionized water. The purpose of anodization is to decrease thejunction area and eliminate the niobium layer contaminated by Ga ions in FIB [22].The anodized junctions presented a decrease in critical current, in correspondenceto the expected decrease in the junction area (see Fig. 2.2).

Our original [22] method is attractive for two reasons. First, it allows to makesmall junctions with niobium, rather than with the commonly used aluminum, whilekeeping the oxide layer free of contamination. Nb superconducting devices may betested in liquid helium, while aluminum requires the more expensive and troublesomeoperation of dilution refrigerators. Second, our technology easily allows a formationof stacked junctions array, by introducing additional Nb/AlOx layers. The stackedjunctions lack the parasitic capacitance to the substrate, thus relaxing some of theconstrains in the design of multiple junctions qubits [23].

2.3 DC-SQUIDs

The direct current superconducting interference device (DC-SQUID) is essentiallya superconducting line with a hole. In each of the branches formed by the hole, aJJ is inserted. Direct current (DC) is applied across the whole structure, and anexternal magnetic flux Φx is applied through the hole. For the case of small loopinductance, the phase jumps θ1 and θ2 on the junctions must obey

θ1 − θ2 = Φx/Φτ . (2.4)

Eq. (2.4) presents the connection between the phase of the order parameter and themagnetic flux by requiring a continuity and utilizing the normalization coefficientΦτ . In the limit of small loop inductance, the current through the device is givenby [24] (p.21-17):

I = Ic(sin θ1 + sin θ2) (2.5)

= 2Ic cos(1

2

Φx

Φτ

) sin(θ1 + θ2

2). (2.6)

By comparing to Eq. (2.2), it can be seen that the overall behavior of a singlejunction is reconstructed, but with the critical current periodically modulated byΦx. To ensure that the fabricated junctions are indeed operated at the quantumregime, we measure the voltage drop across the DC-SQUID as a function of theapplied flux (see Fig. 2.3).

27


Figure 2.3: DC-SQUID measurement. The junctions area is nominally 100× 50 nm(possibly less due to Ga ions implantation). The oxidation was proceeded for half anhour at a partial oxygen pressure of 160mTorr. (a) Schematic drawing of the four-probe measurement of the DC-SQUID. (b) Lock-in critical current measurement forzero bias flux. (c) Modulation of the critical current with applied flux.

28


2.4 RF-SQUIDs

The radio frequency superconducting quantum interference device (RF-SQUID) iscomposed of a superconducting ring interrupted by a single Josephson junction,threaded by an externally applied bias flux Φx (see Fig. 2.4). The Hamiltonian ofthe system is [19]:

H =Q2

2CJ

+Φτ

2L

[(Φ

Φτ

− Φx

Φτ

)2

− 2βL cosΦ

Φτ

], (2.7)

where Φ is the total magnetic flux through the loop (or, equivalently, −Φ/Φτ is thephase jump on the junction), Q is the charge on the junction leads, a conjugatevariable to Φ ([Φ, Q] = i~), CJ is the capacitance of the JJ, L is the loop inductanceand βL = LIc/2Φτ is a unitless parameter. The Hamiltonian consists of a kineticpart analogous to a particle of mass (2e)2/2C in a parabolic potential part related tothe loop inductance L, superimposed by a cosine potential of the SQUID. For βL > 1local wells will appear in the potential shape, corresponding to a different numberof flux quanta trapped in the loop. By modifying the external flux it is possible todrive the system state between the wells. The external flux Φx,b required to flattenthe zeroth well is calculated by comparing the second derivative of the potential tozero and results with [25] Φx,b/Φτ = π − arccos(β−1

L ) +√

β2L − 1. Increasing the

external flux further will induce additional intra-well transitions with a period ofΦ0, as depicted in Fig. 2.4 [c].

In order to measure the inter-well transitions, the RF-SQUID is inductivelycoupled to a λ/2 microwave resonator with a first mode of a few GHz, that consistsof a finite length of a microstrip transmission line. The zero current boundaryconditions impose standing wave solutions, with the first mode wavelength λ equalto twice the resonator length, giving rise to its name. The energy relaxation of theSQUID due to an inter-well transition causes changes in the resonance frequencyand shape. A single transition is harder to measure, hence an alternating current(AC) external flux modulation at a KHz frequency is applied in order to ’recharge’the SQUID.

The resonators are fabricated by standard photolithography means and the RF-SQUID loops and junctions are defined with FIB, similarly to the process describedin Sec. 2.3 (see Fig. 2.5). The continuous wave radio frequency signal is transmit-ted along the microstrip transmission line, and the bias magnetic flux is appliedvia a separate line. At a resonant frequency more energy is transmitted into theresonators, and dissipated into the surroundings, resulting with an amplitude dip(reflection measurement). This scheme allows to measure several resonators of dif-ferent lengths on the same sample.

29


Φ0

Φx,b

a)

b)

Φ JJ

Φxc)

Figure 2.4: RF-squid βL extraction. (a) Schematic drawing of the RF-SQUID. (b)Homodyne measurement of an RF-SQUID. Horizontal and vertical axes representDC and AC modulation of the external flux correspondingly. A strong signal ismeasured along the dashed lines that correspond to a bias flux causing a stabilityloss in the SQUID. The ratio between the depicted Φx,b and Φ0 results with βL = 9.8(c) A cartoon depicting the Φx,b/Φ0 ratio for βL = 11. The charge state of the systemis approximated as a localized mass lying in a well. From top to bottom: for Φx = 0the mass lies in the bottom well; for Φx = 1.5Φ0 the mass is still lying in the samewell, corresponding to total flux Φ = 0 in the loop; for Φx = Φx,b = 1.96Φ0 the wellflattens and the mass slides to the next well, corresponding to Φ = 1 × Φ0 flux inthe loop; rising the external flux Φx by another single flux quantum to Φx = 2.96Φ0

causes to a slide to the next well of Φ = 2Φ0.

30


Figure 2.5: (a) Picture of the RF-SQUID measurement wafer inside a box. (b)Scanning electron microscope (SEM) image of the resonator area containing theSQUID and the adjacent flux line. (c) RF-SQUID. The JJ is on the left. (d) Thetrilayer JJ.

31


SynthesizerLock-in

Func on

Generator

3GHz

10dBm

lo if

50KHz

1V

DC+AC

4K

rf ref

ref

-20dB -60dB

-50dB

Figure 2.6: Homodyne measurement setup. (see text)

The Homodyne measurement scheme (see Fig. 2.6) uses the same MW synthe-sizer signal at a λ/2 resonator resonance frequency to feed the radio frequency (rf)and the local oscillator (lo) ports of a mixer, hence the signal amplitude is down-converted to DC at the mixer intermediate frequency (if) port. The signal is pickedup by a lock-in amplifier, that uses as a reference the same AC frequency that isused to modulate the SQUIDs flux. The results are depicted in Fig. 2.4 (b). Lock-inmeasurement is more sensitive, as the low frequency noise is filtered out, however itis more difficult to interpret. At higher modulation frequencies a DC signal from theif port of the mixer was measurable (see Fig. 2.7). Qualitatively, the resonance peakdeformation increases with the number of inter-well transitions in a single Φx swing,hence the colors of the different zones correspond to a different integer number ofwells for the given Φx.

32


−2 0 2

x 10−3

0.005

0.01

0.015

0.02

0.025

0.03

0.035

VDC

VA

C/2

Lock−in 100KHz

−2 0 2

x 10−3

0.005

0.01

0.015

0.02

0.025

0.03

0.035

VDC

VA

C/2

DC 80MHz

Figure 2.7: Comparison of lock-in versus DC signal for the same resonance. DC andAC bias where applied by different sources in this experiment.

33

3

Outlook

34

3. OUTLOOK

10−7

10−6

10−4

10−3

10−2

I(r),Bc(r)

Radius[m]

I[A]

10−7

10−6

10−3

10−2

10−1

100

101

Bc[T

]

IB

Figure 3.1: The calculated ring current and magnetic field in the center for one fluxquantum trapped inside, as a function of the ring radius.

In the previous chapters, design and measurement of superconducting quantumcircuits and a diamond magnetometer were described. In the route towards mea-surement of a qubit state, the next milestone may be measurement of magnetic fluxquantization by a superconducting ring, or more practically, by a SQUID, as a ringrequires temperature manipulation to modify the trapped magnetic flux. With anincrease of the bias field, the integer number of flux quanta in the ring will increaseas well, but by quantum steps. In Fig. 3.1 the shielding Meissner current and themagnetic field in the ring center are calculated [26] as a function of the ring radius.In this work, fields of 1mT and currents of 1mA were measured, that correspondto a radius of 100 nm− 1µm, that presents no difficulty in fabrication.

In this work, Josephson junctions with critical current of hundreds of micro-ampere were made. To increase the critical current larger junctions and/or shorteroxidation times might be applied. Another approach might be utilizing nano-bridgesas Josephson elements [25], as they support larger currents. The optical readoutsensitivity is to be increased by means discussed in Section 1.5.

Yet another research direction lies in the field of hybrid systems. NV centers

35

3. OUTLOOK

ensemble had been shown to be used as a quantum memory for a superconductingqubit [27], and a scheme of increasing the coherence times of the ensemble wasproposed [28]. Introducing our optical magnetometer to these hybrid designs mightsimplify the readout scheme and provide an increased decoupling of the quantummemory from the environment.

36

Appendix A

Critical State Model for Jc(B)

37

APPENDIX A. CRITICAL STATE MODEL FOR JC(B)

In Section 1.4.2 a correction to the critical state model is discussed, where thecritical current density Jc is dependent upon the local magnetic field B. The Jc(B)dependency models vary in various sources [10]:

Jc(B) = Jc0/(B0 + |B|), (A.1)

Jc(B) =

{Jc0(1− |B|/B0), |B| < B0,0, |B| > B0,

) (A.2)

Jc(B) = k|B|−q, (A.3)

Jc(B) = Jc0 exp(−|B|/B0), (A.4)

where B0,Jc0,k,q are positive constants. Eq. (A.1) is the model used in this work.For a general Jc(B) dependence, implicit equations are available for an infinite thinstripe, beginning at a virgin (no trapped flux) state, after a perpendicular biasmagnetic field Ha is applied (Eqs. 10-12 in [17]):

J(x) =

− 2πx√

x2p − x2

∫ w/2

xp

Jc(Bz(x′))

(x′2 − x2)√x′2 − x2

p

dx′, |x| < xp,

− |x|xJc(Bz(x)), xp < |x| < w/2,

(A.5)

Bz(x) = Bf|x|√

x2 − x2p

∫ w/2

xp

Jc(Bz(x′))/Jc0

(x′2 − x2)√x′2 − x2

p

dx′, xp < |x| = w/2, (A.6)

µ0Ha = Bf

∫ w/2

xp

Jc(Bz(x′))/Jc0√

x′2 − x2p

dx′. (A.7)

where Bz = B is the local magnetic induction at the superconducting film plane inthe perpendicular direction, Bf = µ0Jc0t/π is a scaling field, µ0 = 4π × 10−7H/mis the vacuum permeability constant. For Jc = Jc0, Eq. (1.3) is restored. Fora given Jc(B) model, first Eq (A.6) is solved for various values of xp by meansof a numerical solver, and a library of Bz(xp, x) is created. The solver input isthe function F (Bz(x)) = Bz(x) − r.h.s. where the r.h.s. is the right hand side ofEq. (A.6), and the output is the Bz(x) vector that minimizes F . For numericalstability integration by parts was used, as∫

dx′

(x′2 − x2)√

x′2 − x2p

=1

x√x2 − x2

p

atanh

(x′

x

√x2 − x2

p

x′2 − x2p

)(A.8)

does not diverge inside the integration limits. A derivative of Jc(Bz(x)) is takennumerically. Ha(xp) is then computed with Eq. (A.7), and the appropriate value ofxp is chosen. Finally J(x) is found with Eq. (A.5) for the whole stripe.

38

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41

עגל חשמלי מ -. הדגם CFB-הדגם הנמדד. אנטנת מיקרוגל בצורת לולאה ממוקמת מסביב לזואלקטרים אמובא עד כדי נגיעה ביהלום על ידי חמישה מנועים פי -מודפס על פיסת סיליקון

הליום נוזלי במעגל סגור ומקורר מקררדיוק ננומטרי. ההתקן המתואר לעיל מוכנס לתוך עלי ב

על, הממוקם במישור היהלום -מותקן סליל של מגנט מוליך מקרר. בתוך ה4ºKרטורה של לטמפת מערכת עירור ומערכת קריאה. מערכת העירור מורכבת ול השולחן האופטי מותקנעומסביב לו.

אופטי, ואילו מערכת הקריאה מורכבת מעצמית, מערכת מלייזר מאופנן על ידי מודולטור אקוסטו למקור מיקרוגל דרך מגבר. מסננים ומצלמה דיגיטאלית. אנטנת המיקרוגל מחוברת

על מן הסוג השני. הדגם עשוי מפיסת -חיצוני במוליךהמגנטי השדה המיסוך ואהאפקט הנמדד הדרך מסכה מכנית. ננומטר 500 שעליה הותזה שכבת ניוביום בצורת פס ארוך בעובי שלסיליקון

מוליך אשר קורר ללא שדה מגנטי מאונך למישור הדגם. הופעל יהלום, וה לאהדגם קורר, הוצמד בשלב מאוחר יותר, ויפתח זרמים ם אליו של קווי השדה המגנטישדה מגנטי יתנגד להכנסת

ות זרמים עולה, עד על מן הסוג השני יתמוך בצפיפ-. מוליך(התאם לאפקט מייזנר)בשיימנעו זאת בצורה של מערבולות כן יאפשר חדירה של קווי שדהולאחר מ -שזו שתגיע לערך מקסימלי כלשהו

רוחב אזור הזרם הרווי ילך וגדל בהדרגה. באם השדה החיצוני יגיע זרם מהשוליים אל הפנים. (. כרוןיזבפנים )תופעת ה לכודיםלערך מקסימלי כלשהו ויורד בהדרגה, חלק מקווי השדה יישארו

בו צפיפות הזרם שמקרה עבור ה. (CSMמובא במודל המצב הקריטי )קרוסקופי אהתיאור המהמתאר את צפיפות קיים מודל אנליטי קבועה עבור חומר ועובי שכבה מסוימים,המקסימלי היא

הילייה לתוצאות ניסיוניות, משתמשים בק המודל , על מנת להתאיםברםפס אינסופי. בהזרמים אמפיריים שונים אשר בהם צפיפות הזרם המקסימלי תלויה בשדה המגנטי המדעית בתיקונים

מרחק מקצה הפס, והצלחנו להתאים בניסוי כפונקציה של ODMRהלוקאלי. ביצענו מדידות התאמה של דו מימדיות )ציר תדר וציר מרחק( בשדה מגנטי עולה ויורד על ידי מדידות 15בודד

. יתרה מכך, הראנו כי התיקון האמפירי למודל הוא הכרחי, צפיפות הזרם הקריטית –פרמטר בודד ולכן המגנטומטר יכול לשמש ככלי מחקר לתיקונים אלו.

במעגלים אלו על.-בניין למעגלים קוונטיים במוליכי של אבני תםנושא המחקר השני הוא הנדסמאקרוסקופי של אלקטרונים מתוארת באופרטורים קוונטיים תנועתם המשותפת של מספר

של המילטוניאנים קוונטים את הנדסתםהגישה מאפשרת מאקרוסקופיים כגון השראות וקיבול. על עושים שימוש -ם רבים של ביטים קוונטים במוליכיתכנוניבאמצעים של מיקרואלקטרוניקה.

יאריות מובהקת עם חוסר דיסיפציה )אינו מפזר לינ-בצומת ג'וזפסון, ההתקן היחידי אשר משלב איאנרגיה בצורה לא קוהרנטית(. בעבודה זו תוכננו ואופיינו מעגלים המשלבים צמתי ג'וזפסון

ייחודיים, פרי פיתוח הקבוצה.

למדוד מצבים קוונטים אשר הוכנו במעגלים אחדו, וניתן יהיהתבמבט לעתיד שני נושאי המחקר י

.NV-באמצעות מגנטומטר העל -מוליכישל

תקציר

( בסריג היהלום דרך סיב אופטי מרובה NVחור )-תהודה מגנטית במרכזי חנקןגילוי אופטי של

על -למדוד את זרמי המיסוך של מייזנר בשכבה דקה של מוליך בכדי( מיושם bundle fiberליבות )

, 1כולל מערכת ספין NV-. המבנה האלקטרוני של מרכז ה4ºKמן הסוג השני בטמפרטורה של סובבדרך עירור בלייזר, ל ניתן לקטב ספיןמצב האת שדה מגנטי, טמפרטורה ולחץ. ל הרגישה

בזכות זאת -מדוד באמצעים אופטיים בפרוטוקולים סטנדרטיים של תהודת ספין אלקטרון ולהופכים את מרכז תלות הפוטולומיניסנציה במצב הספין. זמני הקוהרנציה והרלקסציה הארוכים

לחיישן רגיש למדי. NV-ה

השפעה ניכרת , ללא4ºKתוכנן, נבנה ונבדק בטמפרטורות נמוכות של NVבעבודה זו, מגנטומטר

(, ונמצא כי CSMעל טמפרטורת הדגם. תוצאות המדידה הושוו לתיאורית מודל המצב הקריטי )תאפשר יישומים של אחד ההתאמה מניחה את הדעת. הורדת טמפרטורת ההפעלה בסדר גודל

מצומדהעל, -טי, הכוללים מהוד מיקרוגלי מוליךחישובים קוונטיים. אבני בניין של מעגל קוונ-על עם צומת ג'וזפסון הוכנו ונמדדו כשלשב מקדים למדידה עם מגנטומטר ה-לטבעת מוליכת

NV.

צמוד לחור ונמצא ( אשר תופס את מקומו של אטום הפחמן, Nמורכב מאטום חנקן ) NV-מרכז ה

(Vב )כל אחד משלושת אטומי הפחמן מסביב לחור תורמים אלקטרון ריג הגבישי של היהלום.ס

ממצב מטען NV-טרון אחד נשאר לא מצומד. מכשנלכד אלקטרון, עובר מרכז האחד, כך שאלק

י ספינכולל טריפלט NV--(. המבנה האלקטרוני של הNV-( למצב טעון שלילית )0NVניטראלי )בניסוי זה העירור מבוצע על ידי פוטון י במצב המעורר.ספינבמצב היסוד האופטי וכן טריפלט

637-ננומטר(, והפליטה היא של פוטון אדום, באורך גל שיכול להתחיל מ 532אורך גל של בירוק )ננומטר. המעברים הקרינתיים משמרים את הספין של הטריפלט. כמו כן, מותרת רלקסציה לא

טריפלט התחתון דרך שני מצבי סינגלט. המעבר החשוך אל קרינתית )חשוכה( מהטריפלט העליון

של הטריפלט העליון, ב. עדיפות ±1ים ספינא. עדיפות למעבר מתת המצבים המאופיין על ידי: יחסית של הסינגלט. ארוך ג. אורך חיים -בטריפלט התחתון, ו 0י ספינלמעבר לתת המצב ה

ירידה ברמת , מהותה מדידת הNV( במרכזי ODMRגילוי אופטי של תהודה מגנטית )הספין. בהינתן ערור לייזר ומיקרוגל קבועים, קיטובטולומיניסנציה בעקבות ירידת רמת הפו

הספין בזכות השאיבה האופטית והרלקסציה דרך המעבר החשוך, ואילו קיטובהלייזר גורם ל

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כמעט 1--ו 1+תתי המצבים . יופיע בור ODMR-בספקטרום ה כתוצאה מכך, ו1-או 1+המצב

. שדה מגנטי בכיוון המקביל 0מתת המצב 2.8GHz -מנוונים בהעדר שדה מגנטי, ומרוחקים ב

הבור ODMR-בספקטרום היסיר את הניוון )פיצול זימן(, NV-חור של מרכז ה-לווקטור חנקןהמרחק בין הבורות יציין את עוצמת הרכיב המקביל של והבודד יפוצל לשני בורות בהתאמה,

בגביש, ארבעה כיוונים של ווקטורי גביש יניבו באופן NVהשדה המגנטי. עבור צבר של מרכזי

ים, מסובכיוון מגנטי עבור שדה ,ODMR-כללי ארבעה זוגות של בורות תהודה בספקטרום הבצורה זו, מדידת עוצמת הפוטולומיניסנציה כתלות .וג ימדוד את הרכיב המקביל אליוכאשר כל ז

הכיוון של השדה המגנטי.אודות בתדר מיקרוגל תניב מידע אודות העוצמה ו

מלאכותי מיקרון נחתכה מגביש 15ל במערכת שלנו, דיסקת יהלום בקוטר של מילימטר ועובי ש

( 200KeVהקרנת אלקטרונים אנרגטיים ) ועברה צהוב(,בעל זיהום חנקן גבוה )יהלום

מאפשר 1000ºС-ריג. איחוי של שעה בחורים בס במיקרוסקופ מנהור אלקטרוני על מנת ליצור

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