principles of superconducting (josephson) electronics · sensitivity with feedback better than10-6...
TRANSCRIPT
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Principles of superconducting (Josephson)
electronics
Valeriy V. Ryazanov
Moscow Institute of Physics and Technology,
Dolgoprudny
Institute of Solid State Physics, Russian
Academy of Sciences, Chernogolovka
February 4, Skoltech
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Review of materials and devices for nano- and optoelectronics
Term 3, 2020 Tuesday Skoltech (16.00, R3-C2-2009)
February 4, Valeriy Ryazanov (Institute of Solid State Physics, Russian Academy of
Scienses, Chernogolovka). Principles of superconducting (Josephson) electronics
February 11, Nikolai Klenov (Lomonosov Moscow State University, Dukhov All-Russia
Research Institute of Automatics) Physical foundations of macroscopic quantum
effects in superconducting electronics and spintronics
February 18, Alexey Ustinov, (Karsruhe Institute of Technology, Germany, Russian
Quantum Center, MISIS). Dynamics of magnetic flux quanta
February 25, Valery Koshelets, (Kotel'nikov Institute of Radio Engineering and Electronics
RAS, Moscow) Superconducting Low-noise Terahertz Receivers
March 3. Igor Soloviev. (Lomonosov Moscow State University, Dukhov All-Russia Research
Institute of Automatics). Superconducting digital electronics
March 10/11. Jukka Pekola (Aalto University, Helsinki, Finland) Josephson current
standards, calorimetry and bolometry. (?)
March 17, 24 – Seminars...
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Superconductivity
Magnetic flux quantization
Josephson junctions
SQUIDs
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B
n0 C
Magnetic flux quantization in superconductors
The superconducting flux quantum was predicted by London (1948) using a phenomenological semiclasical model.
Superconductivity is a macroscopic quantum phenomenon.
= e i is the single superconducting wave function described all
condensed collective of Cooper electron pairs (2e, 2m). 2= nS / 2
p=2mvs+2eA is the gauge-invariant momentum of Cooper pairs
Meissner effect ħ =2mvs+2eA in bulk superconductor C C
ħ dl =2e A dl = B dS
2 n = (2e/ ħ) = 2 /0
= n0
Magnetic flux quantum
0 = h/ (2e) =2.067833636×10−15 Wb
(2.067833636×10−7 G cm2)
The phase running due to magnetic flux : =2 /0
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Magnetic flux quanta in type II superconductors and
Josephson junctions
Is () = Iс sin Josephson equation I
2eV= ħ= ħd/dt Josephson equations II
B B
L
d
J Meissner state destruction in
type II superconductors
+
1
2
Josephson vortex
J dm; dm =d+2
I
I
V ~ dn/dt ~ ~ d /dt
=2 -1
2eV= ħ= ħd/dt
V= [ħ /(2e)]d/dt = 0 /(2)d/dt
Is () = Iс sin
I>Ic B>Bc1
-
SC II Long Jos. junction
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0 1 2 3
0.5
1
I _______
Imax
/0
2Ic
Superconducting quantum interferometer
(dc-SQUID) 3 2
13+42 =3- 1 + 2- 4 =(2e/ħ)Adl + (2e/ħ) Adl
1 4
2- 1 + 3- 4 = a- b = (2e/ħ) Adl
a- b =2/0 a= 2- 1; b= 4-
2
Ia = Ic sin a; Ib = Ic sin b; I = Ic(sin a+ sinb)
sin a+ sinb=2sin[(a+ b)/2] cos[(a- b)/2]; a- b =2/0
I = 2Ic cos(/0)sin(b+ /0) a= b+2/0
Maximum of the current I is
Imax = 2Ic |cos(/0)|
3
4
1
2
I
Ib Ia
a b V
SQUID is analog
of light
interference on
double slit
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Resistive-Capacitive Shunted Junction (RCSJ-model)
IJ=Ic sin - “Josephson channel”
In=V/Rn= [0/(2Rn)]t - “resistive channel”
ID=CdV/dt =[0C/(2)]tt - “capacitive channel”
Ic sin + [0/(2Rn)]t + [0C/(2)]tt = Ie |*EJ/Iс
[ħ/(2e)]2C tt + [ħ /(2e)]2Rn-1t + EJ sin = EJ (Ie/Iс)
Tunnel Josephson junction B.D. Josephson, 1962
Ie
In IJ
ID
J Rn С
V= [ħ /(2e)]d/dt
= 0 /(2)d/dt
EJ=Ic0/2
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Josephson weak links
• Is () = Iс sin ; I<Iс;
• 2eV= ħ= ħd/dt ; I>Iс;
V= [ħ /(2e)]d/dt = (0/2)d/dt
J
I
2
1
=2 - 1
S S N S S I
N S
~ x
~ 2 nm ~ 1 m
a) b) c)
~
~20 nm
e) d)
S x
S
Different types of
Josepson weak links
Josephson weak link is a region of
suppressed superconductivity
F, TI…
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Sensitive SQUID-magnetometer
H
H
sample
Sensitivity with feedback
better than10-6 0/Hz
0=2x10-15 Wb (V c)
/0
Imax
2Ic
1
Sensitivity to magnetic field better than 10-11 G
/0 0.5 -0.5 1.0 -1.0
Magnetic flux – voltage
dependence (for I Ic )
V
0
0
Imax= 2Iccos( /0)
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Scanning SQUID-microscopy
x-y scan
jooint 10m 100m Spatial resolution ~10 m Magnetic flux resolution
~10-6 0
Different magnetic structure visualization
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Sensitive SQUID-picovoltmeter
SAMPLE (Rx)
Rst
Ix
Ist
R
Rst Ist = RxIx
Sensitivity better than 10-13 V
V, 10-13 V
100 200 I, 10-6 A
SNS (SFS) junction I-V characteristics
magnetic
flux
feedback
loop
output
amplifier current
source
current feedback loop
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Josephson junctions with
ferromagnetic barrier
Josephson magnetic switches
Superconducting phase inverters
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Problem of superconductivity/ferromagnetism
coexistence
B is Bohr magneton, is the energy gap of superconductor,
g is Lande giromagnetic factor
F
Orbital and magnetic depairing.
Paramagnetic limit Hp of superconductivity:
S
BHp=√2(/g)
Non-uniform superconductivity by
Larkin-Ovchinnikov-Fulde-Ferrel
in magnetic superconductor
LOFF-state
Paramagnetic limit
ErRh4B4,
HoMo6S8
etc
S
N
LOFF-state was not still observed
reliably in magnetic superconductors!
S and F have antagonistic
spin ordering ! Spin-triplet superconductivity
is possible too…
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Proximity effect in SF-structures
(x)=0 exp(-x/xF1) cos (x/xF2)
~ ħ/Eex (Eex >> kBT)
xF1 =1/k1~(ħD/ Eex)1/2
Buzdin, Bulaevskii, Panjukov JETP Lett. 35, 178 (1982)
Buzdin, Vujicic, Kupriyanov Sov. Phys. JETP 74, 124 (1992)
h – exchange field
(x)=0exp(-kx)=0exp(-x/xN)
Pair-breaking time ~ħ/kBT
xN ~(D)1/2~(ħD/ kBT)1/2
E ~ħ
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15
Spatial oscillations
of induced superconducting order parameter in
a ferromagnet in close proximity to a superconductor
Q ≠ 0 is the center of the pair
mass momentum
Clean limit
p'2/2m–p2/2m = pFQ/m = Eex ;
Q ~ Eex / vF
Ψ(x) = Ψ0 (ei2Qx+e-i2Qx)/2=
= Ψ 0Cos(2Qx)
Ψ(x)~exp(-k1x)cos(-k2x)
k=k1+ik2
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Recent fundamental observations on
superconductor/ferromagnet (SF-) structures
-Observation of the supercurrent through a
ferromagnet in superconductor-
ferromagnet-superconductor (SFS-)
junctions (LS ISSP 1999).
-Observation of nonuniform (“sign-
reversal”) superconductivity close to a
superconductor-ferromagnet (FS-)
interface, realization of Josephson SFS -
junctions with inversion of
superconducting phase. (LS ISSP 2001)
- Prediction and realization of FS-spin-
valves and spin-switches.
- Observation of superconducting long-
range spin-triplet component.
- Ferromagnetically assisted Cooper pair
splitting.
S
F
S
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Possible applications
- Josephson SFS (MJJ) junction like
a novel memory element for
superconducting and other digital
electronics
- Josephson SFS -junctions like
superconducting phase invertors
for superconducting digital and
quantum (qubit) logics
- FS-spin-valves and spin-switches
- Spin-polarized supercurrents for
spintronics
Magnetic Josephson
Junction (MJJ) S
F
S
F
F S
M
ds~xs
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Distributed Josephson junctions
Magnetic field penetration
(x,y) const at the junction plane. H 0
H
L>4J
w<<J
C contour: 1-2-3-4 (out of dm region, supercurrent = 0), (2-4) = dx.
ħ =2mvs+2eA Phase winding over path 1-3 + 4-2 is only due to magnetic field:
2e Adl =2e d, where d =Bdm dx
3-1+2-4 = (x+dx) - (x) = d =2 d /0d/dx=(2 /0)d/dx Magnetic induction in the junction: B(x)=(1/dm)d/dx =[0 /(2 dm)]d/dx
dm =2L+tox– “magnetic depth”
dm
dx
J >>dm ,L
3- 4 1-2 i.e. 3-1+2-4=3- 4 -1-2
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Critical current vs. magnetic flux
in the short junctions (L<4J)
Supercurrent Is through the junction can change only
due to the phase difference С: sin С1
B=[0 /(2 dm)]d/dx = const (uniformly at the short junctions)
i.e. (x) is linear d/dx=(2 dm/0)B =const
(x)=(2 dm/0)B x+С; where С is an integartion constant
Supercurrent distribution: js (x)= jс sin[(2 x /av)+ С], where av= 0/(B dm) Total current over the junction: Is= jс sin[(2 x /av)+ С] dx=-(av /2) jс cos [(2 x /av)+ С]|
cos (+) = cos cos - sin sin and cos(2 x /av)cosC | = 0
Is= jсL (av / L) sin( L/av) sin С = Iс[sin( L/av) /( L/av)] sin С
-L/2
L/2 L/2
-L/2
-L/2
L/2 x L/2 -L/2 0
I
Imax/Ic
/0
1.0
IсsinZ/Z,
where
Z=( /0)
Critical current Imax:
Imax = Iсsin( L/av) /(L/av)= Iсsin( /0) /( /0)
where Iс= jсL, L/av= /0 , = BLdm
per unit widths of the
junction Fraunhofer pattern
x
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Magneto-hysteretic behavior of the critical current
Si-substrate
SiO bottom Nb
Weak ferromagnetic alloys
Cu1-xNix, Pd1-xFex top Nb
(10-20 nm)
x=0.53-0.59,
TCurie=30-150 K;
Cu1-xNix,
-25 -20 -15 -10 -5 0 5 10 15
0,05
0,06
0,07
0,08
0,09
0,10
0,11
0,12
0,13
I c, m
A
H, Oe
M
H
Pd0.99Fe0.01
Cri
tic
al c
urr
en
t, m
A
Magnetic field, Oe
Very weak and soft ferromagnet
0
0max
/
)/sin(
=
cII
Pd1-xFex
x=0.01,
TCurie=15 K non-volatile switchable Magnetic
Josephson junctions (MJJs)
programmable using small field
Magnetic Josephson Memory with Fast Reading
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Josephson magnetometry
Nb - PdFe – Nb (10 x 10 m2, 30 nm)
Ic = Ic0 sin(πΦ/Φ0)/(πΦ/Φ0) ,
Φ=H(dF+2λL) +4πMdF ,
Φmin=Φ0n, Φmax=Φ0(n+1/2)
Msat~10-15 Am2
SFS without a tunnel layer
Vc~3nV
Switching
rate ~ 1MHz
f~Vc/Φ0
JETP Lett (2012)
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Magnetic Josephson Memory with Fast Reading
Nb
SIsFS junction
with thin s-layer
ds = 15 nm; ξS < ds << λ
SIs tunnel junction
“feels” F-layer
remagnetization
junction
Nb
tunnel layer PdFe
Si-substrate
Al/AlOx
SiO insulator
Nb wiring Top Nb electrode
Ferromagnetic layer
Nb interlayer
Bottom Nb electrode
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Theoretical model of SIsFS structures
S.V. Bakurskiy, N.V. Klenov, I.I. Soloviev, V.V. Bol'ginov, V.V. Ryazanov, I.V.
Vernik, O.A. Mukhanov, M.Yu. Kupriyanov, and A.A. Golubov.
Appl. Phys. Lett. 102, 192603 (2013).
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Oscillating superconductivity and Josephson -junction
Nb-Cu0.47Ni0.53-Nb
-state
I=Icsin(+ )= - Icsin()
“0”-state
I=Icsin “0”-state
I=Icsin
h – exchange field
Qx=; Q ~ h/vF
-junction
Prediction: Buzdin, Bulaevskii, Panjukov JETP Lett. (1982)
Buzdin, Vujicic, Kupriyanov Sov. Phys. JETP (1992) Realization: V.R., Oboznov, Rusanov et al, Phys. Rev. Lett. (2001)
Oboznov, Bolginov, Feofanov, V.R., and Buzdin, Phys. Rev. Lett. (2006)
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Checkerboard
frustrated
Fully
frustrated
Imaging spontaneous flux in arrays of -junctions Frolov, Stoutimore, Crane, Van Harlingen, Oboznov, V.R. et al, Nature Physics 4, 32 (2008)
= =
= 2 /0
=0 /2
L 2LIc>0/2
I
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2. Demonstration of SFS π-shifters (Icπ>> IcJ)
-JJ
0-JJ
A.K. Feofanov, V.A. Oboznov, V.V. Bol’ginov, J. Lisenfeld, S. Poletto, V.R., V.P.
Koshelets, P.Dmitriev, A.V. Ustinov et al, Nature Physics 6, 593 (2010).
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Realization of the complementary cell-II
In collaboration with M.I. Khabipov, D.V. Balashov,
A B Zorin, PTB, Germany (2010)
Normal
RSFQ-cell
Complementary
-SFQ-cell
50 m
Physical compatibility of SFS and SIS JJs was proven
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Superconducting digital electronics
Based on storage of the magnetic flux quanta 0 = h/(2e) = 2.07×10−15 Вб
Started in Russia in 1985:
RSFQ –logic (Rapid Single Flux Quantum logic )
Fast digital electronics 20 GHz - 700 GHz (Nb)
Ultra-low power, can be used for reversible computing
- JJ-based memory for Random Access Memories (RAM)
exists, but it has low density, low capacity, cannot be easily
pipelined, not energy-efficient
- Large cell sizes needed to keep the flux quantum is the
second problem of the superconducting logic
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RSFQ- and -SFQ –Toggle Flip-Flop
RSFQ –Toggle
Flip-Flop
- large cell !
0 0
current bias
current bias
0
LIc >0
-SFQ –Toggle
Flip-Flop
The circuits demonstrated correct
functionality with the operation
parameter ranges of ± 20%
L 0
self-biased
in collaboration with
PTB, Braunschweig
proposed by Ustinov
& Kaplunenko
J. Appl. Phys. (2003).
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Integrated SFS+SFQ circuit of T-flip-flop
in collaboration with M. Khabipov, D. Balashov, A. B. Zorin,
Physikalisch-Technische Bundesanstalt, Braunschweig, Germany
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-SFQ –circuit with SFS -junction
combined Nb-AlOx-Nb, Nb-CuNi-Nb technology
in collobaration with M. Khabipov, D. Balashov, A. B. Zorin
In this cell, a large inductance required for the
fluxon storage is replaced by a -junction operated
as a passive phase shifter.
Nb-AlOx-Nb: 4x4 m2;
jc=100 A/сm2
Nb-CuNi-Nb: 8x8 m 2;
jc=500 A/сm2
Vи
нт (
отн
. ед
)
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Josephson junctions in “quantum
limit”
Superconducting qubits
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Nanotechnology at ISSP
shadow deposition at two angles
base pressure 10 -10 mbar
AFM image of Al/Cu/Al bridge
- Different technique of thin film
sputtering
- Optical and electron lithography
- Focused ion beam technique
- Chemical nanostructuring
- Ion and Reactive ion etching
~200 × 300 nm2
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Cu deposition
Al deposition
PMMA
MMA
PMMA
MMA
SiO
SiO
SiO
lift-off
shadow evaporation at two angles
base pressure 10 -10 mbar
Al1 evaporation
Al2
evaporation
Lift-off
PMMA
MMA
Shadow evaporation technique
0.1 m
spin-injection spin-injection S(Al) S(Al)
F(Fe) N(Cu)
spin-
injection
shadow evaporation at three angles
Sample fabrication by means of electron beam lithography and shadow evaporation
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35
)cos1(Ed sin2e
Idt
dt
dsinI
2eVdtIE J
0
c
t
0
c
t
0
s
-====
coup
Josephson junction energy
Is () = Iс sin Josephson equation I
2eV= ħ= ħd/dt Josephson equations II
=2 -1 ; V= [ħ /(2e)]d/dt =(2/0)d/dt
where
-4 -2 0 2 4
-8
-4
0
4
8
I< Ic
Eb Ecoup J
π2
I
2e
IE c0c
J
==
JE
E
2EJ
I=Ic
I=0.6 Ic
I=0
I
2πdt
dt
dI
2eVdtIE 0
t
0
t
0
b
===
-4 -2 - 0 2 3
]I
I)cos1[(EEEE
c
Jb --=-= coup
“Tilted washboard” potentials with
minima at satisfying I = Iс sin
(stationary states)
-
1
2
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36
“Equation of motion” for Josephson tunnel junction.
Analogy with a pendulum.
Resistive-Capacitive Shunted Junction (RCSJ-model)
IJ=Ic sin - “Josephson channel”
In=V/Rn= [0/(2Rn)]t - “resistive channel”
ID=CdV/dt =[0C/(2)]tt - “capacitive channel” Ic sin + [0/(2Rn)]t + [0C/(2)]tt = Ie |*EJ/Iс
[ħ/(2e)]2C tt + [ħ /(2e)]2Rn-1t + EJ sin = EJ (Ie/Iс)
The pendulum motion equation
J tt + t + m g l sin = M
Phase angle Phase difference Moment of inertia J=m l
2 [ħ /(2e)]2C
Viscosity coefficient [ħ /(2e)]2Rn-1
Restoring moment (m g sin ) l EJ sin Applied torque moment T EJ (I/Iс)
Ie
In IJ
ID
J Rn C
m
l
(mg sin)l
mg
T
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Submicron-scale tunnel junction with small enough capacitance C.
Single electron Coulomb (charging) energy EC =e2/(2C) is large.
Q is charge and Ec=Q2/(2C)=CV2/2 is energy of this capacitor.
Discharge of the capacitor is not favorable for some value Q:
new energy E'c=(Q-|e|)2/(2C) becomes larger for 0<Q<|e|/2 !
Coulomb blockade of tunneling for V: (V=Q/C)
0<V<|e|/(2C)
The increase of the differential resistance
around zero bias is called the Coulomb blockade.
Limitation on T and R:
Ec>kT (thermal fluctuations), C<10-15 F,T>1 K
1/RT+1/Re<1/RQ (quantum fluctuations)
RQ=h/ (4e2)~6 k is the quantum resistance
37
Submicron tunnel junctions in normal state
N I N
E'c-Ec>0
Q/e=
VC/e
Region of
Coulomb
blockade
Tunneling is
prohibited
E Ec E'c
Q/e
1/2 -1/2
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38
Josephson junction in quantum limit
“Quantum Josephson junction” is a submicron-scale tunnel junction with small
enough capacitance C0.
By analogy with “Quantum pendulum”: when m0 null oscillations arise,
because M ~ ħ. (=0 и M=0 without oscillations!)
M= J t is angular momentum.
Josephson junction angular momentum is
M= J t =[ħ /(2e)]2Ct = [ħ /(2e)]C V=Q[ħ /(2e)]
Q ~ 2e or n ~ 1
where Q is the junction (capacitor) charge, n= Q/(2e) is excess Cooper pairs. Quantum Josephson junctions have large Coulomb energy EC ~ EJ due to
small capacitance: EC =(2e)2/(2C)
(Tunnel junctions with sizes smaller than 0.3x0.3 m2
, C~10-15F)
Thus total energy of the quantum Josephson junction is
E= (2e)2/(2C) + EJ (1- cos ) - [0/(2)]I
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39
Thermal and quantum fluctuations of the critical
current
The resistive state is observed at Iс* < Iс= (2e/ħ)EJ
due to thermal activation through the barrier U0(I) The rate of the thermo-activated decay is
where (I) = p[1- (I/Iс)
2]1/4; p=(LJC)-
1/2
and U0(I)=(42/3) EJ[1- (I/Iс)]
3/2
Quantum decay for “quantum” Josephson junctions
(from ground state)
kT ħ (I), the null oscillation energy
U0(I)
(I)
T
)kT
)I(Uexp(ω(I)ω 0
T -=
)ω(I)
)I(Uexp(ω(I)aω 0
-=
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L -parameter, energy of superconducting ring
with Josephson junction
Dimensionless potential
(normalized to EJ):
U(φ) = 1−cosφ + li2/2 = 1−cosφ + (φ−φe)2/2l,
where dimensionless ring inductance:
0
2
== c
L
LIl
π2
IE c0
J
=
=2 Φ/Φ0 ; e =2 Φe/Φ0
LI2/2=(Φ-Φe) 2/2L
Φ = Φe − LI L I
Φ
Φe
L >1, barriers exist
L <1, no barriers
Φe =0
Φe = Φ0/2
, i=I/Ic
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Superconducting flux
qubit
ток в
кольце
по
часовой
против
часовой
0
1
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Qubit states on Bloch sphere
Microwave manipulations on qubit states
Classical bit
0
Qubit
Superposition
of these two states
10 =
wave function
x
y
z
0
Bloch
sphere 1AWG
к образцу
Microwave pulses
with controlled amplitude,
duration and phase
Qubit is an artificial atom
4
1
qubit spectrum
0.45 0.5 0.550
10
20
ext
/ 0
E
frequ
en
cy,
GH
z magnetic flux
01f
0
1
Two-level atom
Qubit controlled by magnetic field
is a superconducting ring with
several Josephson junctions.
An artificial 2-level atom with
and states 0 1ħq
Ф=Ф0/2
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Phase qubit: Rabi flopping
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Phase qubit with integrated SFS -junction
SIS – junction and readout
dc-SQUID fabricated by
VTT, Finland
– junction integrated
afterwards in
Chernogolovka
-JJ
0-JJ
Here the -junction
always remains at the
zero-voltage state.
in collobaration with Alexey Ustinov´s group, Karlsruhe Inst. of Technology,
Germany
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Experimental data: Rabi oscillations
phase qubit with a -junction conventional phase qubit
0/ 2
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Flux qubit with SFS -junction
Ip
/
4
A.V. Shcherbakova et al, Supercond. Sci. Tech. 28, 025009 (2015).
- the resonator dispersive
shift due to coupling to a
qubit
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28
© Martinis lab, 2015
line
capacitance
shunted a
Josephson
junction
емкостью ~ 20
фФ
resonator
qubit 100 мкм
Csh~20 fF; =0.52;
jc=0.5 кА/сm2; Ic=0.4
А
T2=1.3 мкс
Проект «Лиман» - 1 этап Flux qubit shunted by large capacitance
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3D-transmons
The coherence
time
T2=5 μs
3D-transmon
in cavity
resonator
Devoret &
Schoelkopf,
Science 339,
1169 (2013)
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PLANAR QUBITS (XMONS)
The coherence
time
T1=11.5 μs
The coherence time T2=7 μs
delay of readout (μs) delay of readout (μs)
delay of readout
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MULTIQUBIT SPECTRA (2-XMON-QUBIT SYSTEM)
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Q1 freq “z” Q1“xy”
Q2 freq “z”
Q2
“xy”
Q3 freq
“z”
Q3 “xy”
ro
f = 6.85 GHz
Q = 6000
f = 7.15 GHz
Q = 6000
f = 7.00 GHz
Q = 6000
1-qubit spectrum
𝐻int = 𝐽𝜎 𝑥1𝜎 𝑥
2
J ~20-30 MHz
2𝐽
The coherence time for each qubit T2 ~ 3 мкс
THREE-QUBIT SYSTEM (2 XMONS AND ‘COUPLER’)
2-qubit spectrum
coupling
energy
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РЕЗУЛЬТАТЫGrover search algorithm
initialization Oracle
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РЕЗУЛЬТАТЫ РЕАЛИЗАЦИИ АЛГОРИТМА
ГРОВЕРА
1
3
The blue columns is statistics of the states at 10000 launches for sequential storage
in each of the "cells“:
|0>=|00>, |1>=|01>, |2>=|10> и |3>=|11>.
The red columns is a hypothetical result for an ideal (error-free) quantum computer.
Еhe black dotted line is a 50% probability (the limit for a classic computer with a
single access to the “Oracle”). Measured probabilities of correct state search: |00> –
58%, |01> – 57%, |10> – 53%, I / 11> - 57%.
Grover search algorithm realization
search of |0> state search of |1> state
search of |2> state search of |3> state