Decoherence Decoherence Measurements Measurements in Fullerene - - PowerPoint PPT Presentation
Uni Time And Matter 2007, Bled Time And Matter 2007, Bled Wien Decoherence Decoherence Measurements Measurements in Fullerene Fullerene Interferometry Interferometry in Lucia Hackermller Klaus Hornberger, Bjrn Brezger, Alexander
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Lucia Hackermüller Klaus Hornberger, Björn Brezger, Alexander Stibor, Stefan Gerlich, Hendrik Ulbricht and Markus Arndt Institute f. experimental physics, University of Vienna Institute for physics, Johannes-Gutenberg-University Mayence, Germany
Time And Matter 2007, Time And Matter 2007, Bled Bled
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Introduction Introduction
Coherence: : Nearfield Nearfield interferometry interferometry with with large large molecules molecules
Decoherence:
by collisions collisions with with restgas restgas atoms atoms
by emission emission of thermal
radiation
A new new interferometer interferometer: :
exploiting the the Kapitza Kapitza-
Dirac effect effect for for molecules molecules allows allows interference interference down to 100 down to 100 fm fm in in principle principle
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Coherence – Near-field interferometry with large molecules Coherence Coherence – – Near Near-
field interferometry interferometry with with large large molecules molecules
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Developement of matter wave interferometry
C C60
60 (1999)
(1999)
He & H He & H2
2
(1930 (1930)
)
Electron Electron
(1927) (1927)
Neutron (1936 Neutron (1936)
)
BEC, Atom BEC, Atom Lasers Lasers (1995 (1995 … …) ) Na Na2
2, I
, I2
2, K
, K2
2,
, He Heclusters
clusters
(mid (mid-
90‘ ‘s) s) BEC of BEC of Dimers Dimers… … (2003 (2003 … …) ) Porphyrins Porphyrins & & Fluorofullerenes Fluorofullerenes
(2003) (2003)
Atomic Atomic beams beams (1988) (1988) Cold Cold atoms atoms (1990 (1990´ ´s) s) Hemoglobin Hemoglobin ?? ??
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Farfield versus Nearfield diffraction
Farfield diffraction diffraction of
fullerenes
d
dB
λ θ = sin
d d… …grating grating constant constant λ λdB
dB…
…deBroglie deBroglie wave wave length length
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Pattern Formation in a Talbot-Lau Interferometer
Number of Molecules behind 3rd Grating
Interference generates a molecular pattern. Its period equals the period of the gratings.
Scanning Mask
Incoherent Molecular beam
Coherence Preparation
Diffraction
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Talbot-Lau-Interferometer: Theory
Talbot-effect:
illumination illumination with with a plane a plane wave wave
Lau-
effect: : spherical spherical waves waves. . Self Self images images occur
in distances distances behind behind the the second second grating grating
m,n m,n integers integers
λ
2
d n m LT =
) 2 ) ' ( exp( ) ' ( ' 2 ) (
2 2 1
L x x ik x t dx iL k e x
ikL L
− ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = Ψ
∫
π
∑
Ζ ∈
=
l l
d x il T x t ) ' 2 exp( ) ' ( π
) exp( ) 2 exp( ) (
2 2
d L l i d x il T e x
l l ikL L
λ π π − = Ψ
∑
Kirchhoff-Fresnel propagation:
Fourier series of grating: Integration leads to:
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Talbot-Lau interferometer: setup
T T
L L
= d = d
2 2
/ / l l
max min visibility 38.5 % max min
= +
Pos.3rd Pos.3rd grating grating ( (a.u a.u.) .) counts counts ( (a.u a.u.) .)
v [m/s] 240 180 140 120 107 90 80 10 20 30 40 50 visibility [%]
experiment
strong influence influence of VDW
interaction interaction! !
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Collisional – Decoherence Collisional Collisional – – Decoherence Decoherence
collisions with gas-particles
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(Decoherence)
1.
Spontaneous (Ghirardi/Rimini/Weber, Diosi)
2.
Gravity induced (Penrose)
Why is quantum interference (mostly) unobservable on the macro- scale ?
Currently Currently relevant relevant for for matter matter wave wave experiments experiments
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Decoherence Experiments Decoherence Experiments
Interaction with environment (position measurement) generates entanglement
Collisions
Emission of thermal radiation radiation Evolution of Evolution of density density matrix matrix: :
Decoherence Decoherence function function
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Experimental Experimental setup setup
Various gases can be added with a well controlled pressure
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Fringe Fringe visibility visibility: : Exponential Exponential pressure pressure dependence dependence
51 52 53 54 51 52 53 54 50 100 150 200 250 300 350 400 countrate (s
Position 3rd grating(µm) Position 3rd grating (µm)
10 10-
8 mbar
mbar 5*10 5*10-
7 mbar
mbar
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Collisional Collisional decoherence: decoherence: Calculation Calculation of
reduced visibility visibility
(z T T
l l
η →
) )] ( 1 [ exp(
2
dz z R T T
L l l
∫
− − → η
Single decoherence Single decoherence event event: :
with rate R in ( rate R in (z,z+dz z,z+dz) )
Integrate differential equation: : Decoherence Decoherence function function for for collisions collisions: : Interference contrast:
) 2 exp( ' LR V V − =
PRA 70, 053608 (2004) PRA 70, 053608 (2004)
l l
T z R dz z dT )) ( 1 ( ) ( η − − =
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Fringe Fringe visibility visibility: : Exponential Exponential pressure pressure dependence dependence
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 4.0 6.0 8.0 10.0 20.0 30.0
visibility (%) pressure (in 10
collisional cross section gratings distance pressure “ “decoherence decoherence pressure pressure“ “
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Decoherence pressures for various gases
40 50 60 70 80 90 100 110 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
H2 D2 He CH4 Ne Ar Kr Xe N2 Air
p0 (10−6 mbar) σeff (nm2)
experiment theory
weak mass dependence due to near cancellation of (i) increasing polarizability and (ii) decreasing mean gas velocity
eff B
L T k p σ 2
0 =
PRL 90, 160401 (2003) PRL 90, 160401 (2003)
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Decoherence by collision as a principle limit for interference experiments ?
Buckyballs C70
p0= 1 x 10-6 mbar m= 840 amu = 3 pm
Insulin
m = 5734 amu = 0.35 pm p0 = 9 x 10-7 mbar
Rhinovirus
M = 5 x 107 amu
v = 10 m/s = 8 x 10-16 m
p0=2.7x10-10 mbar
Appl
. Phys. B 77, 781 (2003)
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Thermal – Decoherence Decoherence through emission
Thermal Thermal – – Decoherence Decoherence Decoherence Decoherence through through emission emission
photons
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“ “Self Self-
Localization“ “ due due to thermal to thermal radiation radiation
with up to 10 heating beams.
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The The interference interference contrast contrast is is reduced reduced with with increasing increasing temperature temperature ... ...
Ar-Laser
488 nm Dichroitischer Spiegel Detektion PBS λ/2 Ofen D1 D2 514 nm Fenster NR
Setup Setup
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Remaining problem: How to measure the temperature
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Finding Finding a a model model for for photon photon absorption absorption and and emission emission
2.
Find model model for for photon photon absorption absorption and and emission emission (Klaus Hornberger) (Klaus Hornberger) velocity velocity (m/s) (m/s) Normalized Normalized ion ion rate ( rate (a.u a.u.) .) Measure Measure ionization ionization rate rate
dependent ion rate in heating region in front of interferometer
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change in countrate behind interferometer and compare with measured countrate
emitted photon rate and expected loss of coherence and compare calculation with experiment Laser Laser heating heating power power (W) (W) rel.
change in in count count rate rate
1 1 heating heating beam beam 2 2 heating heating beams beams 4 4 heating heating beams beams 10 10 heating heating beams beams
check check model model
How How to to determine determine the the temperature temperature
the molecules molecules? ?
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Calculated distribution
200 300 400 500 600 700 800 900 1000 2000 2250 2500 2750 3000 2 4 6 8 10 12 14 16 18 20
photon wave length (nm) temperature (K) spectral emission rate Rλ (sec−1nm−1)
stimulated emission
capacity
Deviation from Planck’s law:
Hansen et al. (1997) Coheur et al. (1996)
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Thermal decoherence of C Thermal decoherence of C70
70
Comparison Comparison between between Experiment & Experiment & Theory Theory
1 2 3 4 5 6 7 8 9 10 0.0 0.2 0.4 0.6 0.8 1.0 mean temperature (K) 1360 2270 2850 3070 3140
normalized visibility Laser heating power (W)
v = 200 m/s, 16 heating beams
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Thermal decoherence of C Thermal decoherence of C70
70
Comparison Comparison between between Experiment & Experiment & Theory Theory
1 2 3 4 5 6 7 8 9 10 0.0 0.2 0.4 0.6 0.8 1.0
mean temperature (K)
1540 2580 2880 2930 2940
normalized visibility Laser heating power (W)
v = 100 m/s, 10 heating beams
calculated decoherence curve without fit:
data
Nature 427, 711–714 (2004).
rate of rate of emitted emitted photons photons
⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − =
∫ ∫
∞
)) ' ( 2 ( sinc
)) ( , ( exp
/ 2
r r t T R d dt V V
v L
λ π λ λ
Coherence Coherence function function of
photons
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Can themal photons limit interferometry ?
Thermally ‚activated‘ vibrational radiation in „viruses“ # of vibrations = 3N – 6 = ca. 105
…106 modes
T=300 K: all modes excited with p ~ 1-5 % Emission rates Γ ~ 10 s-1 Decoherence very likely !!! Consequence: Large things will have to be cooled to the vibrational ground state feasible using for example supersonic sources Decoherence very unlikely !!
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Even more sensitive: An interferometer using a standing light wave Even Even more more sensitive: sensitive: An An interferometer interferometer using using a a standing standing light light wave wave
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How to show interference of wavelengths in the fm range?
2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 0.0 0.2 0.4 0.6 0.8 1.0
Visibility Wavelength [pm] VdW Laser 3W Laser Abs
Small grating period:
strong influence of VDW interaction ! extreme velocity selection required
Solution: optical grating
typical velocity spread of Δv/v=10 % : → up to 30% contrast for material-optical-material grating → 1% contrast for 3 material gratings Visibility Visibility predictions predictions: :
PRA 71, 023601 (2005) PRA 71, 023601 (2005)
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Kapitza-Dirac-Talbot-Lau- Interferometer
SiN SiNx
x gratings
gratings in in collaboration collaboration with with T.
Savas MIT MIT
Minimal wavelength wavelength: 100 : 100 fm fm ► ► 7000 7000 amu amu @ 300m/s @ 300m/s ► ► 20000 20000 amu amu @ 100m/s @ 100m/s
Light grating grating: : green green, , single single mode mode laser laser g= g=l l/2=266.14nm /2=266.14nm focused focused to w to wz
z=20
=20µ µm m
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Results for Fullerene and Azabenzene
Interference of C70:
:
corrensponds to 4-8th Talbot order
Interference of Azabenzene
250 500 750 1000 1250 100 200 300 400 500 600
Counts / 3s Position of 3
rd grating (nm)
C30H12F30N2O4
32 Å
100 200 300 400 500 600 700 800
Counts / 4s
C70
8 Å
a) b)
print) )
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Power dependence of the interference contrast
Good agreement agreement between between experiment experiment and and theory theory
For a given given vel vel., ., visibilty visibilty can can be be adjusted adjusted to to maximum maximum by by changing changing the the light light power power
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More More candidates candidates for interferometry for interferometry … …
Thermal Thermal sources
sources Fluorinated Fluorinated particles particles
N,N N,N-
Bis[3-
[tris(2-
perfluorooctylethyl)silyl]propyl]-
trifluoroacetamide
C C60
60[(CF
[(CF2
2)
)11
11CF
CF3
3]
]10
10
m = 2900 amu ☺ ☺ low low velocity velocity → → v= v=√ √(2m/kT) (2m/kT) ☺ ☺ high high density density m ~ 7000 amu
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Supersonic sources: biomolecules
Polypeptide: Gramicidin Polypeptide: Gramicidin Amino acid: Tryptophan Amino acid: Tryptophan m=204 m=204 amu amu m=1800 m=1800 amu amu
400 800 1200 1600 2000 0.0 0.5 1.0 1.5 2.0
Carrier gas: Argon @ 3.8 bar Signal / Noise: 1.5V / 0.006V = 250
Polypeptide: Gramicidin ~ 1800 u
Signal (V) m/z (u/e)
Signal (V)
m/z (u/e)
50 100 150 200 1 2 3 4 5 6
Carrier gas: Argon @ 2.8 bar Signal/Noise: 5.9V/0.012V = 490
Signal (V) m/z (u/e)
Signal (V)
m/z (u/e) TOF TOF mass mass spetra spetra
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The ‚molecular quantum optics‘ team 2007
Funding: FWF: STARTY177, SFB F1505 EU: RTN New: EUROQUAM COMPA
by Anton Zeilinger
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collisional decoherence: modelling the fullerene experiment
Collisions outside of the interferometer disturb the velocity selection. Accounted for by a Monte Carlo simulation of the classical phase space dynamics using semiclassical differential cross sections.
between non-polar molecules (London dispersion force) the unpleasant part ...
U(r) = -C6/r6
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Dephasing by gravitational space-time deformations
Brahim Lamine et al, + Eur. Phys. J. D 20 (2002), 165 + PhD thesis, ENS (2003)
Gravitational Waves induce as phase shift, formally similar to the Sagnac effect Deformations of the metric in time determine the size of the effect The Interferometer output is phase modulated The visibility is influenced by an average over time
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C3000 @ 5000 m/s λdB = 2.2 x 10-15 m Tobacco mosaic virus (2 x 107 amu) @ 200 m/s λdB = 1.0 x 10-16 m Au cluster (r=27 nm, 109 amu) @ 30 m/s λdB = 1.3 x 10-17 m
Influence of Gravitational Waves
would need :
Freely falling beam splitters (satellite experiment)
& priv. comm. & Lamine PhD thesis, ENS
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The formal basis of complementarity: Entanglement & decoherence
Measurement on a superposition state: Density matrix after the measurment: A measurement correlates the ‚system‘ and the ‚meter‘
n n n n n
c n c n Φ Φ ⎛ ⎞ ⊗ → ⎜ ⎟ ⎝ ⎠
∑ ∑
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Ignoring the environment = Trace over environment Reduced state has lost all coherences if the environmental states are orthogonal No fringe visibility iff „Unambiguos Wich-Way information“ (Correspondence Principle) iff „All ‚meter‘ states are orthogonal“ (Decoherence Theory)
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New New molecular molecular beam beam methods methods: Laser Desorption : Laser Desorption
Molecules are are desorbed desorbed by by a ns a ns laser laser beam beam
Instantaneously cooled cooled in a in a supersonic supersonic gas gas beam beam How to transfer big molecules into the gas phase ? How How to to transfer transfer big big molecules molecules into into the the gas gas phase phase ? ?
Provides Provides: :
☺ ☺ Shown Shown for for: : peptides peptides ( (Gramicidin Gramicidin), ), proteins proteins (Insulin, (Insulin, Insulin B), Insulin B), metall metall cluster cluster
☺ ☺ Neutral & Neutral & directed directed beam beam of
particles
☺ ☺ Excellent Excellent velocity velocity selection selection (1/1000) (1/1000) ☺ ☺ Supersonic Supersonic expansion expansion provides provides cold cold beam beam ☺ ☺ Velocities
Velocities between between 200 200-
400 m/s depending depending on
cooling gas gas
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Nanostructuring of surfaces
SPM C60 Si(111)
Interferometer generates generates regular regular pattern pattern
Instead of a
scanning grating grating the the molecules molecules are are deposited deposited on a
surface surface, , e.g e.g reconstructed reconstructed Si Si
Fractional Talbot Talbot-
effect can can produce produce periodes periodes down to 30 nm down to 30 nm
Talbot-
effect works works for for any any periodical periodical pattern pattern
Detection with with scanning scanning probe probe microscopy microscopy Fullerenes Fullerenes on
surfaces
Experiments Experiments done done by by A. Major & S.
Deachapunya
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Metrology Metrology: : Measuring Measuring polarisabilities polarisabilities of
molecules… … Deflector Deflector Electrodes Electrodes Forceplot Forceplot
fringes shift shift due due additional additional phase phase
resolution < 10 nm < 10 nm
Experiment Experiment done done by by M. Berninger
& A. & A. Stefanov Stefanov
Accuracy: Literature (theory & exp.) : 10% Vienna experiment (now) : < 10% Vienna experiment (target) : < 1%
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Metrology Metrology: : Measuring Measuring the the polarisability polarisability of
molecules… …
Accuracy: Literature (theory & exp.) : 10% Vienna experiment (now) : < 10% Vienna experiment (target) : < 1%
Gain in Talbot-Lau Interferometry: High count rates by massively parallel sampling (shown) < 10 nm resolution for shift of molecular beam (shown) Devices suitable for molecular sorting (still to be demonstrated) Quantum contrast may be higher than classical contrast (true for C70)
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Earth‘s rotation
τ L v L x
z 2
2 Ω = Ω = Δ
z
v L / 2 = τ η ρ ρ / 2
Sagnac
A m Ω = Φ rad/s 10 55 . 5
5 −
× = Ω
⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Ω − =
2 2 2
8 exp
z v c
v d L V V σ π 99 . V V ≤
Averaging over
velocities ( (Gaussian Gaussian v v-
distrib.) .) reduces reduces visibility visibility
Rotation causes causes fringe fringe shift shift ( (Sagnac Sagnac phase) phase)
Fullerenes (720 u): (720 u): 100 m/s, d=990 nm, 100 m/s, d=990 nm, σ σ=0.1 =0.1 v vz
z
Hemoglobin (62.000 u): (62.000 u): L=0.5 m, v= 50 m/s, s=0.1 L=0.5 m, v= 50 m/s, s=0.1 (0.2) (0.2) v vz
z, d=257 nm
, d=257 nm
) 015 . ( 35 . V V ≤
( (Vienna Vienna) )
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Earth‘s gravity
2 2
sin
z G v
L g x θ = Δ ) , ( A g
G
ρ ρ ∠ = θ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − =
2 3 2
sin 2 exp
z v G
v d L g V V σ θ π
99 . V V ≤
Fullerenes (720 u): (720 u): 100 m/s, d=990 nm, 100 m/s, d=990 nm, σ σ=0.1 =0.1 v vz
z
Hemoglobin (62.000 u): (62.000 u): L=0.5 m, v= 50 m/s, s=0.1 L=0.5 m, v= 50 m/s, s=0.1 (0.2) (0.2) v vz
z, d=257 nm
, d=257 nm
) 025 . ( 39 . V V ≤
Averaging over
velocities ( (Gaussian Gaussian v v-
distrib.) .) reduces reduces visibility visibility For For θ θ = 0.5 mrad: = 0.5 mrad:
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Remedies…
Possible measures against Sagnac - dephasing
Possible Possible measures measures against against Sagnac Sagnac -
dephasing
Good v v-
selection ( (sources sources with with Δ Δv v/v < 1%) /v < 1%)
Vertical orientation
(with with special special azimuthal azimuthal alignment alignment) )
Counter-
rotating platform platform ( (telescope telescope base base) )
Equator or
satellite based based experiment experiment Possible measures against gravitational dephasing
Possible Possible measures measures against against gravitational gravitational dephasing dephasing
Very good good v v-
selection ( (sources sources with with Δ Δv v/v < 1%) /v < 1%)
Precise alignment alignment ( (better better than than 100 100 µ µrad) rad)
Vertical orientation
Satellite based based experiment experiment Do these processes impose a fundamental limit ?
Do Do these these processes processes impose impose a fundamental a fundamental limit limit ? ?
No !
But technolgy technolgy may may get get rather rather demanding demanding beyond beyond hemoglobin hemoglobin … …
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Phase averaging in the lab Floor (pumps) & laser (water cooling)
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Sensitivity of the TL- interferometer to floor vibrations
37000 38000 39000 40000 41000 42000 250 300 350 400 450 500 550 600 37000 38000 39000 40000 41000 42000 180 200 220 240 260 280
position of 3
rd grating (nm)
position of 3
rd grating (nm)
Vibration isolation active! Optical table: down
: a < 5x10-4 g laser on „eraser“ rubber reduces vibrations to : a < 5x10-5 g
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The „really real“ Quantum Eraser
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Stretched TLI: vibration of laser water supply
400 420 440 460 480 10 20 30 40 50
Visibility in % source position / 10
= velocity from ~240 m/s to ~70 m/s
damping of table + laser damping of table only
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The interferometer as a pendulum
0.2 0.4 0.6 A
200 400 600 f Hz 0.25 0.5 0.75 1 RP 0.2 0.4 A
(comoving gratings)
(counter moving gratings, pivot at „z“)
2 1 1 2 z0
200 400 600 f Hz 0.25 0.5 0.75 1 RT 2 1 1 z0
Amplitude =0.5 x grating Amplitude =0.5 x grating const const. .
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Dephasing due to external vibrations
50 100 150 200 5 10 15 20 25 30 35 40 45 Visibility (%) Frequency (Hz)
Amplitude of one
vacuum flange flange excited excited with with „ „15 nm 15 nm“ “. .
The peak peak structure structure is is determined determined by by the the mechanical mechanical resonance resonance of
the vacuum vacuum container container. .
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What happens during the heating ?
τs ~ 0.7 ns
ΦΤ > 90 %
τT ~ 13 µs - 50 ms
S0 S1 S3 S2 T3 T2 T1
non- radiative
514 nm 1.7 eV E
ion7.6 eV 514 nm
non- radiative
Fullerenes heat up side-wise: Heating of vibrational modes Delayed climbing on the ionization-ladder