Uni Time And Matter 2007, Bled Time And Matter 2007, Bled Wien Decoherence Decoherence Measurements Measurements in Fullerene Fullerene Interferometry Interferometry in 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
Uni Introduction Introduction Wien � Coherence Coherence: : Nearfield Nearfield interferometry interferometry with with large large � molecules molecules � Decoherence: Decoherence: � - by by collisions collisions with with restgas restgas atoms atoms - - by by emission emission of thermal of thermal radiation radiation - � A A new new interferometer interferometer: : � - exploiting exploiting the the Kapitza Kapitza- -Dirac Dirac effect effect for for molecules molecules - allows interference allows interference down to 100 down to 100 fm fm in in principle principle
Uni Wien Coherence – Coherence Coherence – – Near- -field field interferometry interferometry Near Near-field interferometry with large large molecules molecules with with large molecules
Developement of matter wave Uni interferometry Wien BEC of BEC of Dimers … Dimers … BEC, Atom BEC, Atom Porphyrins Porphyrins Lasers Lasers (2003 … ) (2003 … ) & Fluorofullerenes Fluorofullerenes & (1995 … ) (1995 … ) (2003) (2003) Hemoglobin ?? ?? Hemoglobin C 60 C 60 (1999) (1999) Na 2 Na 2 , I , I 2 2 , K , K 2 2 , , He He clusters clusters (mid- (mid -90 90 ‘ ‘ s) s) Atomic beams beams (1988) (1988) Atomic He & H 2 He & H Cold atoms atoms (1990 (1990´ ´s) s) Cold 2 (1930 ) (1930 ) Neutron (1936 ) Neutron (1936 ) Electron Electron (1927) (1927)
Farfield versus Nearfield Uni diffraction Wien � Farfield Farfield diffraction diffraction of of fullerenes fullerenes � λ θ = sin dB d d … … grating grating constant constant d λ dB deBroglie wave wave length length λ … deBroglie dB …
Pattern Formation in a Talbot-Lau Uni Interferometer Wien 1. Grating: 2. Grating: 3. Grating: Coherence Preparation Diffraction Scanning Mask Incoherent Molecular beam Number of Molecules behind 3 rd Grating Interference generates a molecular pattern. Its period equals the period of the gratings.
Uni Talbot-Lau-Interferometer: Theory Wien � Talbot-effect: illumination illumination with with a plane a plane wave wave 1 − 2 ⎛ ⎞ ( ' ) k 2 x x Kirchhoff-Fresnel propagation: ∫ Ψ = ⎜ ⎟ ( ) ' ( ' ) exp( ) ikL x e dx t x ik π L ⎝ 2 ⎠ 2 iL L ' x ∑ Fourier series of grating: = π ( ' ) exp( 2 ) t x T il l d ∈ Ζ l λ x L ∑ Integration leads to: Ψ = π − π 2 ( ) exp( 2 ) exp( ) ikL x e T il i l 2 L l d d l � Lau Lau- -effect effect: : spherical spherical waves waves. . � 2 Self images images occur occur in in distances distances m d behind the the second second Self behind L T = λ n grating grating m,n integers m,n integers
Uni Talbot-Lau interferometer: setup Wien .) a.u.) (a.u counts ( counts max min - visibility = = 38.5 % max min + Pos.3rd grating grating ( (a.u a.u.) .) Pos.3rd 50 experiment quant. w. van der Waals l l / / 2 2 d d quant. w. Casimir-Polder = = T T quant. w/o potential L L 40 class. w. van der Waals class. w/o potential visibility [%] 30 20 � strong strong influence influence of VDW of VDW 10 � interaction! ! interaction 0 80 90 107 120 140 180 240 v [m/s]
Uni Wien Collisional – – Decoherence Decoherence Collisional Collisional – Decoherence collisions with gas-particles
Why is quantum interference Uni (mostly) unobservable on the macro- Wien scale ? 1. Small de Broglie wavelength (Kinematics ) experiments wave experiments 2. Dephasing (Phase averaging without information transfer) matter wave for matter 3. Which-way information available (Bohr) relevant for Currently relevant Currently 4. Entanglement of quantum and environment (Decoherence) 5. „Objective“ collapse of the wave function Spontaneous (Ghirardi/Rimini/Weber, Diosi) 1. Gravity induced (Penrose) 2.
Uni Decoherence Experiments Decoherence Experiments Wien Collisions Collisions � � Emission of thermal Emission of thermal � � radiation radiation Interaction with environment (position measurement) generates entanglement Evolution of density density matrix matrix: : Evolution of Decoherence function function Decoherence
Uni Experimental setup setup Experimental Wien Various gases can be added with a well controlled pressure
Fringe visibility visibility: : Fringe Uni Exponential pressure pressure dependence dependence Exponential Wien 7 mbar 8 mbar 5*10 - mbar 5*10 -7 10 - -8 mbar 10 400 350 300 -1 ) 250 countrate (s 200 150 100 50 0 51 52 53 54 51 52 53 54 Position 3rd grating (µm) Position 3rd grating(µm)
Collisional decoherence: decoherence: Collisional Uni Calculation of of reduced reduced visibility visibility Calculation Wien Decoherence Decoherence function function for for collisions collisions: : � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � �� �� � � � ��� ��� � � � � � � � � � � � � � Single decoherence event Single decoherence event: : ( ) dT z → η ( z ) = − − η T T ( 1 ( )) l R z T l l l dz occurs with with rate R in ( rate R in (z,z+dz z,z+dz) ) occurs Interference contrast: Integrate differential equation: : 2 L = − ∫ ' exp( 2 ) → − − η exp( [ 1 ( )] ) V V LR T T R z dz 0 l l 0 PRA 70, 053608 (2004) PRA 70, 053608 (2004)
Fringe visibility visibility: : Fringe Uni Exponential pressure pressure dependence dependence Exponential Wien 30.0 20.0 visibility (%) 10.0 8.0 6.0 “ decoherence decoherence pressure pressure “ “ “ 4.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 -6 mbar) pressure (in 10 collisional cross section gratings distance pressure
Decoherence pressures for Uni various gases Wien 2 k T experiment 0 = B p theory σ 1.8 2 L eff 1.6 1.4 p 0 (10 −6 mbar) 1.2 weak mass dependence due to near cancellation of 1 ( i ) increasing polarizability and ( ii ) decreasing mean gas velocity 0.8 Ne He Kr Ar Xe Air 0.6 N 2 D 2 CH 4 0.4 H 2 0.2 0 40 50 60 70 80 90 100 110 σ eff (nm 2 ) PRL 90, 160401 (2003) PRL 90, 160401 (2003)
Decoherence by collision as a principle Uni limit for Wien interference experiments ? � Buckyballs C 70 p 0 = 1 x 10 -6 mbar m= 840 amu � = 3 pm p 0 = 9 x 10 -7 mbar � Insulin m = 5734 amu � = 0.35 pm � Rhinovirus p 0 =2.7x10 -10 mbar M = 5 x 10 7 amu v = 10 m/s � = 8 x 10 -16 m Appl Appl. Phys. B 77, 781 (2003) . Phys. B 77, 781 (2003)
Uni Wien Thermal – – Decoherence Decoherence Thermal Thermal – Decoherence Decoherence through through emission emission Decoherence Decoherence through emission of thermal photons photons of thermal of thermal photons
“Self Self- -Localization Localization“ “ due due to thermal to thermal “ Uni radiation radiation Wien Heating of C 70 before it enters the interferometer (up to ~ 3000 K) � with up to 10 heating beams. Hot fullerenes emit visible light (see Mitzner& Campbell). � The path difference d = 1 µ m can be resolved. � The interference contrast decreases, with increasing temperature. �
The interference interference contrast contrast is is reduced reduced The Uni with increasing increasing temperature temperature ... ... with Wien Setup Setup Dichroitischer Spiegel Detektion Ar-Laser 488 nm max. 28 W λ/2 PBS 514 nm Fenster Ofen D2 NR D1
Remaining problem: Uni How to measure the temperature Wien of C 70 ? measure the emitted blackbody photons � T-dependence of ionization rate in heating stage � T-dependence of count rate in detector �
Finding a a model model for for photon photon Finding Uni absorption and and emission emission absorption Wien Measure ionization Measure ionization rate rate 1. Detect velocity dependent ion rate in heating region in front of .) a.u.) interferometer rate (a.u ion rate ( Normalized ion 2. Find Find model model for for photon photon 2. Normalized absorption and and absorption emission emission (Klaus Hornberger) (Klaus Hornberger) velocity (m/s) (m/s) velocity
How to to determine determine the the temperature temperature How Uni of the the molecules molecules? ? of Wien check model model check 3. Use model to predict change in countrate behind interferometer and compare with measured rate count rate countrate in count 1 heating heating beam beam 2 heating heating beams beams 1 2 change in 4. Use model to calculate rel. change emitted photon rate and expected loss of rel. coherence and compare calculation with experiment 4 heating heating beams beams 4 10 heating 10 heating beams beams Laser heating heating power power (W) (W) Laser
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