arndt matter wave interferometry

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Matter wave interferometry with complex molecules Markus Arndt Quantum optics, Quantum nanophysics & Quantum information, University of Vienna

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The slide is about matter wave interferometry and discusses this subject first with regards to the following questions. 1. While quantum physics is a universally valid theory are there any mass, size or complexity limits ? 2. As quantum physics is a precise theory can we use quantum interferometry for particle metrology? 3. As there seems to be a limit of how far the quantum interferometry can be shown to exist how far can we extend the double slit interferometry to larger things ? The author's perspective is therefore to show that he can do double slit wave interferometry with quite large molecules. What is interesting to him is the velocity distribution or "velocity selection" as it is called in his poster. Then the author continues to discuss different interferometry techniques such as the Talbot-Lau interferometre and its extension, the Kapitza-Dirac Talbot-Lau interferometre. After this he starts mentioning quantum interferometry with "polyatomic strings" and continues to discuss a larger variety of techniques and molecules.

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Page 1: Arndt matter wave interferometry

Matter wave interferometrywith complex molecules 

Markus ArndtQuantum optics, Quantum nanophysics &

Quantum information, University of Vienna

Page 2: Arndt matter wave interferometry

The 2 Sides of Quantum Interferometry with large Molecules

Quantum physics is a universally valid theory

Are there any mass, size or complexity limits ?

Quantum physics is a precise theory

Can we use quantum interferometry for molecule metrology ?

Page 3: Arndt matter wave interferometry

Bohr‐Einstein Dialogue:  Can complementarity be tricked ?

Path–information in particle‘s recoil on the upper slit !Will interference still be seen ?

NO ! Because of the Δx/Δp uncertainty relation

p. 3

Page 4: Arndt matter wave interferometry

Can we extend double slit interferometry to larger things ?

What is philosophically debateable in this animation ?

Page 5: Arndt matter wave interferometry

How to test the quantum wave nature of clusters & molecules?1. Multi‐slit far‐field diffraction

C Sourc e60

Col limati on

5 µm 5 µm

1.3 3 m1.13 m

G ratin gVeloc itySelec tor Ioniz ation L aser

C Ofen60 5 µm5 µm

1 331.33 m1.13 m

S lt D t ktLGeschwindigkeitsselektor GitterSpalte DetektorLaserse e to Gitter

Page 6: Arndt matter wave interferometry

What are the basic coherence requirements ? 

Spectral (= longitudinal) coherence:

Different wavelengthsDifferent wavelengths 

⇒ different diffraction angles

⇒ averaging over minima and maxima

Coherence length: 

Coherence requirement for n‐th order interference:

Page 7: Arndt matter wave interferometry

Longitudinal coherence requirements: Velocity selection

2-slitλt d h d i ftowardsscreen

g Θ

n-th order interference: path length differenceand coherence length of n λ

λ

and coherence length of n λ⋅

1 0

1,2

1,4

rate

v- distribution:

( )−3 2 2m0f(v) ~ v exp (v v ) / v

0 4

0,6

0,8

1,0

lized

coun

tr

a )b )typical width (a):

( )m0f(v) v exp (v v ) / v

Δv / v ~ 0 6

0 100 200 300 400 500 600

0,0

0,2

0,4

norm

a

after selection (b):

Δv / v ~ 0.6

p. 7

0 100 200 300 400 500 600velocity (m/s)

( )Δv / v ~ 0.16

Page 8: Arndt matter wave interferometry

What are the other basic coherence requirements ? 

Spatial (= transverse) coherence:

Different emitter locations

⇒ transverse shift of interference patterns

⇒ averaging over minima and maxima

Can be avoided if 

Far‐field diffraction: Divergence angle    Θ div << diffraction angle Θ diff

Talbot Lau interferometry:  Transverse interferometry prepared by the setup

Page 9: Arndt matter wave interferometry

Reminder: How to test the quantum wave nature of clusters & molecules?

3000

4000

C60sin θ n λ/g ' 20μradC Sourc e60

Col limati on

5 µm 5 µm

1.3 3 m1.13 m

G ratin gVeloc itySelec tor Ioniz ation L aser ol

ecul

es

2000

3000sin θ = n · λ/g ' 20μrad

400dete

cted

mo

10002nd order inteference requirescoherence length

300

num

bero

fd

2nd order interference is an indication for van der Waals forces !

200

n

Molecule interference is a single‐particle phenomenon:

-150 -100 -50 0 50 100 150

100

particle phenomenon: 1. Average distance 100 µm = 

10000 van der Waals radii2 All molecules are in thermal

Nature 401, 680 (1999). Am. J. Phys. 71, 319 (2003).

150 100 50 0 50 100 150

Detector position (µm) 2. All molecules are in thermal 

mixture. No molecule resemblesthe other!

Page 10: Arndt matter wave interferometry

Observing single molecules in scanning tunneling microscopy in Vienna

p. 10See poster by Stefan Truppe, Thomas Juffmann, Philipp Geyer

Page 11: Arndt matter wave interferometry

Observing single fullerenes on Si 111 (7x7) 

Page 12: Arndt matter wave interferometry

Towards higher mass and complexity:p y

Near field interferometry can cope with 

high masses small diffraction angleshigh masses, small diffraction angles & dilute moleculear beams

Page 13: Arndt matter wave interferometry

Mathematical background to the Talbot‐Effect: Self‐imaging without a lens

Fresnel diffraction at a  grating of transmission function t(x) (Summation over Huygens spherical wavelets)

dGrating is a periodic structure: Fourier expansion

L

Insertion into ψ yields:

t(x)=⇒ ψL

2d

t(x)⇒ ψL

= ≡λ

⋅ ⋅ ⋅ ⋅TalbotL 2 m 2d L mSelf imaging if L= multiple of the Talbot‐Length:

Page 14: Arndt matter wave interferometry

Extension of near‐field interferometry to spatially incoherent sources:Talbot‐Lau Interferometry

1. grating:  2. grating:  3. grating: 

prepares coherence diffraction scanning mask

incoherent

molecular beam

2

λ

2pLTalbot =

Page 15: Arndt matter wave interferometry

First realization of Talbot Lau interferometry for molecules

Def. Visibility:

max min

i

I IVI I

−=

+

Def. Visibility:

max minI I+

IImax

Imin

g = 990 nm (period)

d = 450 nm (slit opening)

b = 500 nm (membrane thicknes)

Page 16: Arndt matter wave interferometry

Distinguish Quantum interference from Moiré shadow fringes

V = 0 % V = 20 %V = 100 %Intensity V = 0 % V = 20 %V = 100 %Intensity

Screen

2. Grating

1. Gratinggf = 1/5 f = 1/2 f = 2/3

At our opening ratio d/g=f = 0.48: classical contrast nearly vanishing

Page 17: Arndt matter wave interferometry

Proving the wave nature of large moleculesin the presence of VdW forces …

50Quantum with Van der WaalsQuantum without grating potential

Quantum with Casimir-Polder

40

g g pClassical with van der WaalsClassical without grating potential

30

bilit

y [%

]

20visi

24018014012010790800

10

24018014012010790 80 v [m/s]

Phys. Rev. Lett. 88, 100404 (2002).

Page 18: Arndt matter wave interferometry

Avoid van der Waals: Far‐field diffraction of C60 at an optical phase grating

800 experim enttheory ohne Laser

400

y

P 5 5 W

n 1

50 s

200

400 P=5.5 W

cou

nts

in

150

300 P=7.5 W

200

50

P=9.5 W

-65 -43 -22 0 22 43 65 0

100

detector position x [µm]D k i i ( )

Phys. Rev. Lett. 87, 160401 (2001) 

detector position x [µm]Detektorposition (µm)

Page 19: Arndt matter wave interferometry

A new type of interferometerA new type of interferometer

Kapitza‐Dirac‐Talbot‐LauKapitza Dirac Talbot Lau

Interferometerf

Page 20: Arndt matter wave interferometry

An interferometer without van der Waals dephasing  Kapitza‐Dirac‐Talbot‐Lau Interferometer   

Advantage: 

g=266 nm

16 x higher masses underconditions similar toconditions similar toprevious TLI

Generally scalable to muchhigher masses (1.000.000 u…)

Page 21: Arndt matter wave interferometry

Kapitza‐Dirac Talbot‐Lau Interferometer

1st Grating 2nd G ti 3rd G ti1st GratingCoherence preparation

2nd GratingDiffraction

3rd GratingDetection Mask

2pLλpLTalbot =

Page 22: Arndt matter wave interferometry

Precision requirementsGratings by Tim Savas, Massachusetts Institute of Technology  & nm2

Photo‐lithographical manufacturing

Supportstructure: 1.5µm

Period: 266.38nm

Required accuracy : Δg < 0.5 Å <  H‐atom !!

Page 23: Arndt matter wave interferometry

Alignment conditions for the KDTLI : needed to avoid geometrical dephasing

Roll (each grating ) ΔΘ < 500 µrad

Pitch (each grating ) Δθ < 1 mrad

Yaw (each grating ) Δφ < 200 µradYaw (each grating ) Δφ < 200 µrad

Relative grating positioning ΔL / L < 10- 4

Grating mismatch 0.05 nm

Laser waist Δw0 ~ 5 µm

Laser beam pointing ΔΘdi < 1mradLaser beam pointing ΔΘdiv< 1mrad

non-stationary accelerations Δa < 0.001 g

Page 24: Arndt matter wave interferometry

Quantum interferometry with „polyatomic strings“perfluoralkyl‐functionalized diazobenzenes

700

600

650

500

550

600

Cou

nts

400

450

500

50,0 50,2 50,4 50,6 50,8 51,0 51,2400

Position of 3rd grating (µm)

Gerlich et al., Nature Physics 3, 711 (2007) Interference in very good agreement

with quantum expectations!

Page 25: Arndt matter wave interferometry

High‐contrast quantum interference has been observed in Vienna with  ….

Fullerene C60& C7060  70  

Fluoro‐Fullerene  C60F36 & C60F48

Porphyrins & derivatives

Perfluoroalkyl‐functionalized molecules

Page 26: Arndt matter wave interferometry

Towards higher mass & complexity

1. Chemical approach

p. 26

Page 27: Arndt matter wave interferometry

Slow beams of very large moleculesA molecular "octupus" 

Eur. Phys. J. D 46, 307 (2008).

Perfluoralkylated Buckyball

C60[(CF2)11CF3]1060[( 2)11 3]10

8 fluoro‐carbon chains6910m = 6910 amu

N = 430 atoms

Very low thermal velocity

Page 28: Arndt matter wave interferometry

Overcoming the "ionization limit for organic molecules": Dye‐tagged perfluoroalkyl‐functionalized dendrimers …  

I ti bIn preparation by our

ESF MIME partners in Basel

Prof. Marcel Mayor & coworkers

Page 29: Arndt matter wave interferometry

Towards higher mass & complexity

2. Cluster approach

p. 29

Page 30: Arndt matter wave interferometry

Cluster sources for biomolecules: Laser desoprtion into cold mixing channel  

Source: version 1

• Straight channel

• 266 nm ionization

Source: version 2

• U‐shaped channel

• UV (157 nm) ionization• UV (157 nm)  ionization

• Admixture of CaCO3

⇒ large cIusters detected!g

Page 31: Arndt matter wave interferometry

Neutral biomolecular clusters & metal complexes

n

CaTrp10CaTrp10

Cluster formation up to Trp30 is triggeredCluster formation up to Trp30 is triggeredby the presence of a single Calcium ion

M. Marksteiner, P. Haslinger,  et al... 

J. Am. Soc. Mass. Spectrom. 19, 1021 (2008)

Page 32: Arndt matter wave interferometry

Similarly : other neutral biocluster‐metal complexes with up tom>6000 amu

(Gramidin D)n ‐ clusters with n=1..5 

Tryptophan‐Gramicidin clusters

Trp Clusters seeded with Ba, Sr, Cu, Na, …

Nucleotide‐cluster (Guanine)n with n=1..50Nucleotide cluster (Guanine)n with n 1..50

Pure Polypeptide‐Cluster  (Trp‐Trp‐Gly)n  with n=1..5

1. There is an entire zoo of clusters we still need to understand

2 Interferometry will be a valuable tool as soon as we are able to2. Interferometry will be a valuable tool as soon as we are able to

a. Slow these clusters

b Cool also their internal degrees of freedomb. Cool also their internal degrees of freedom

Page 33: Arndt matter wave interferometry

New perspectives for supermassive interferometry

Towards interfereometry with m= 1,000,000 u ...

Cryogenically cold metal clustersCryogenically cold metal clusters

Laser ionization gratings

Compact setupi d fcm‐sized even for 

MDa –particles ?

Reiger, Hackermüller, Arndt

Opt. Comm.  264, 326‐332 (2006).

Page 34: Arndt matter wave interferometry

M l l M t lMolecule Metrology1. Static polarizability1. Static polarizability  

2. Optical polarizability  

3 Susceptibilities and structure analysis3. Susceptibilities and structure analysis

p. 34

Page 35: Arndt matter wave interferometry

Interferometric deflectometry:Nanoimprint on the molecular beam ⇒ high resolution for forces !  

Laser gratingQuadrupole mass detector

( t 9000 )

Mechanicalgrating

(up to 9000 amu)

Source

grating

Mechanicaligrating

The laser interacts through optical polarizability 

p. 35

The static field gradient (homogeneous force field) interacts throughstatic polarizability & permanent electric dipole moment

Page 36: Arndt matter wave interferometry

1. Interferometric deflectometry  for static polarizabilities

Phys. Rev. A. 76, 013607 (2007).

ZählrateZählrate

ecto

rde

fle8

VerschiebungVerschiebung

10 12.5

15

7.5

55678

µm]

(E )Eα ∇r r r

02.5

15

17.520

HV1234

shift

[

d 2

(E )Exm vα ∇

∝r

HV –Power Supply [kV]

5 10 15voltage [kV]00

120

Page 37: Arndt matter wave interferometry

Static polarizabilities:  More precise values for C60

shiftshift

∂∂ UU²²/v/v²²∂∂ UU²²/v/v²²

α(C60) = 86.2 ± 3.5 ± 3.5 ų Relative Polarizability:

α(C70) = 106.6 ± 2.7 ± 4.3 ųα(C70) / α(C60) = 1.24 ± 0.06

p. 37Phys. Rev. A. 76, 013607 (2007)

Page 38: Arndt matter wave interferometry

Quantum interference of the fluorinated catalyst: C96H48Cl2F102P2Pd (3378 amu)Detection using EI‐QMS on the fragment m = 1597 amu

Where does the l l d ?moelcule decay?

In the source or

p. 38

in the detector ?

Page 39: Arndt matter wave interferometry

The power dependence of the  fringe visibility gives the answer !

G Cl i l thGreen: Classical theory

Red: Quantum theory intact molecule

Blue: Quantum theory 1600 amu fragmentBlue: Quantum theory 1600 amu fragment

p. 39Angew. Chem. Int. Ed. 47, 6195 (2008).

Page 40: Arndt matter wave interferometry

Proposed interferometric sorting of polypeptidesY = Tyrosine

Polypeptides = chains of amin acids

Diff diff l i ibili iDifferent sequences ⇒ different electric susceptibilities

G = Glycine

W = Tryptophan

p. 40

LSIM, Lyon & INRA Montpellier &Indiana UniversityAnal. Chem. 75, 5512 (2003)

Page 41: Arndt matter wave interferometry

Proposed interferometric sorting of polypeptides (2)

Talbot‐Lau deflectometry can selectivelytransmit one peptide sequence and block YWG = redtransmit one peptide sequence and block another one. YGW = blue

Quantum simulations show better contrastthan classical fringes !than classical fringes !

p. 41Gas phase sorting of nanoparticlesNanotechnology 19, 045502 (2008). 

Page 42: Arndt matter wave interferometry

Proposed: Absolute cross section measurements using single photon recoil

Absorption of a single photon is sufficient tophoton is sufficient to create a clearly discernible side‐peak

Relative height of the peaks measure the cross‐sectionsection

Advantage:

Absolute values

Ever for absorption lengths 

> 10.000 km

Page 43: Arndt matter wave interferometry

Summary: Molecular Quantum Optics  

p. 43

Page 44: Arndt matter wave interferometry

The 2008 team in Molecular Quantum Optics

Stefan  Gerlich

HendrikUlbricht

Markus Marksteiner

Stefan Nimmrichter

Tarik Berrada

MicheleSclafani

Philipp Haslinger

Michael Gring

Thomas Juffmann

StefanTruppe

Philipp Geyer

Peter Asenbaum

International collaborations on these projectsProf. Marcel Mayor, Univ. Basel

Coworkers 2005‐2007Mag. Martin Berninger ⇒ Univ. Innsbruck

Dr. Klaus Hornberger, LMU Munich

Prof. H. Gleiter, FZ Karlsruhe

Prof. Helmut Ritsch, Univ. Innsbruck

Dr. Sarayut Deachapunya, ⇒ Burapha Univ.

Dr. Fabienne Goldfarb ⇒ LAC, Orsay

Dr. Lucia Hackermüller ⇒ Mainz / Wien 

Dr. Tim Savas, MIT Cambridge

Dr. Nikos Doltsinis, King‘s College, London

Prof. Christoph Dellago, Univ. Wien 

Mag. Gregor Kiesewetter ⇒ Univ. Bremen

Dr. Elisabeth Reiger ⇒ Regensburg

Dr. Alexander Stibor ⇒ Univ. Tübingen

Page 45: Arndt matter wave interferometry

Thank youThank you

for your attention!yLiterature:

Markus Arndt, Klaus Hornberger, and Anton ZeilingerP bi h li i f h ldProbing the limits of the quantum worldPhysics World 18, 35 ‐40 (2005).

M. Arndt & K. Hornberger in  a chapter on Molecule interference in the book “Proceedings of the international school of physics “Enrico Fermi”book  Proceedings of the international school of physics   Enrico Fermi , Course CLXXI ‐ "Quantum Coherence in Solid State Systems", Ed P. Schwendimann, Societa Italiana di Fisica (2008).

Atom interferometry:Atom interferometry: Rev. Mod. Phys. Cronin, Schmiedmayer, Pritchard (2008)