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Probing interacting systems of cold atoms using interference experiments Harvard-MIT CUA Vladimir Gritsev Harvard Adilet Imambekov Harvard Anton Burkov.

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Presentation on theme: "Probing interacting systems of cold atoms using interference experiments Harvard-MIT CUA Vladimir Gritsev Harvard Adilet Imambekov Harvard Anton Burkov."— Presentation transcript:

1 Probing interacting systems of cold atoms using interference experiments Harvard-MIT CUA Vladimir Gritsev Harvard Adilet Imambekov Harvard Anton Burkov Harvard Robert Cherng Harvard Anatoli Polkovnikov Boston University Ehud Altman Weizmann Institute Mikhail Lukin Harvard Eugene Demler Harvard

2 Outline Measuring equilibrium correlation functions using interference experiments 1. Interference of independent condensates 2. Interference of interacting 1D systems 3. Interference of 2D systems. Observation of the BKT transition 4. Full distribution function of fringe visibility in intereference experiments. Connection to quantum impurity problem Studying non-equilibrium dynamics of interacting Bose systems in interference experiments

3 Interference of independent condensates Experiments: Andrews et al., Science 275:637 (1997) Theory: Javanainen, Yoo, PRL 76:161 (1996) Cirac, Zoller, et al. PRA 54:R3714 (1996) Castin, Dalibard, PRA 55:4330 (1997) and many more

4 Nature 4877:255 (1963)

5 Interference of one dimensional condensates Experiments: Schmiedmayer et al., Nature Physics (2005,2006) Transverse imaging long. imaging trans. imaging Longitudial imaging Figures courtesy of J. Schmiedmayer

6 x1x1 d Amplitude of interference fringes, Interference of one dimensional condensates For identical condensates Instantaneous correlation function For independent condensates A fr is finite but Df is random x2x2 Polkovnikov, Altman, Demler, PNAS 103:6125 (2006)

7 For impenetrable bosons and Interference between Luttinger liquids Luttinger liquid at T=0 K – Luttinger parameter Luttinger liquid at finite temperature For non-interacting bosons and Analysis of can be used for thermometry L

8 Interference of two dimensional condensates LyLy LxLx LxLx Experiments: Hadzibabic et al. Nature (2006) Probe beam parallel to the plane of the condensates Gati et al., PRL (2006)

9 Interference of two dimensional condensates. Quasi long range order and the KT transition LyLy LxLx Below KT transitionAbove KT transition

10 x z Time of flight Experiments with 2D Bose gas Hadzibabic, Dalibard et al., Nature 441:1118 (2006) integration distance D x (pixels) Contrast after integration 0.4 0.2 0 0 102030 middle T low T high T Exponent  central contrast 0.5 00.10.2 0.3 0.4 0.3 high Tlow T “Sudden” jump!?

11 Fundamental noise in interference experiments Amplitude of interference fringes is a quantum operator. The measured value of the amplitude will fluctuate from shot to shot. We want to characterize not only the average but the fluctuations as well.

12 Shot noise in interference experiments Interference with a finite number of atoms. How well can one measure the amplitude of interference fringes in a single shot? One atom: No Very many atoms: Exactly Finite number of atoms: ? Consider higher moments of the interference fringe amplitude,, and so on Obtain the entire distribution function of

13 Shot noise in interference experiments Interference of two condensates with 100 atoms in each cloud Coherent states Number states Polkovnikov, Europhys. Lett. 78:10006 (1997) Imambekov, Gritsev, Demler, 2006 Varenna lecture notes

14 Distribution function of fringe amplitudes for interference of fluctuating condensates L is a quantum operator. The measured value of will fluctuate from shot to shot. Higher moments reflect higher order correlation functions Gritsev, Altman, Demler, Polkovnikov, Nature Physics (2006) Imambekov, Gritsev, Demler, cond-mat/0612011 We need the full distribution function of

15 Interference of 1d condensates at T=0. Distribution function of the fringe contrast Narrow distribution for. Approaches Gumbel distribution. Width Wide Poissonian distribution for

16 Interference of 1d condensates at finite temperature. Distribution function of the fringe contrast Luttinger parameter K=5

17 Interference of 2d condensates at finite temperature. Distribution function of the fringe contrast T=T KT T=2/3 T KT T=2/5 T KT

18 From visibility of interference fringes to other problems in physics

19 Quantum impurity problem: interacting one dimensional electrons scattered on an impurity Conformal field theories with negative central charges: 2D quantum gravity, non-intersecting loop model, growth of random fractal stochastic interface, high energy limit of multicolor QCD, … Interference between interacting 1d Bose liquids. Distribution function of the interference amplitude is a quantum operator. The measured value of will fluctuate from shot to shot. How to predict the distribution function of Yang-Lee singularity 2D quantum gravity, non-intersecting loops

20 Fringe visibility and statistics of random surfaces Proof of the Gumbel distribution of interfernece fringe amplitude for 1d weakly interacting bosons relied on the known relation between 1/f Noise and Extreme Value Statistics T.Antal et al. Phys.Rev.Lett. 87, 240601(2001) Fringe visibility Roughness

21 Non-equilibrium coherent dynamics of low dimensional Bose gases probed in interference experiments

22 Studying dynamics using interference experiments. Thermal decoherence Prepare a system by splitting one condensate Take to the regime of zero tunneling Measure time evolution of fringe amplitudes

23 Relative phase dynamics Quantum regime 1D systems 2D systems Classical regime 1D systems 2D systems Burkov, Lukin, Demler, cond-mat/0701058 Different from the earlier theoretical work based on a single mode approximation, e.g. Gardiner and Zoller, Leggett

24 Quantum dynamics of coupled condensates. Studying Sine-Gordon model in interference experiments J Prepare a system by splitting one condensate Take to the regime of finite tunneling. System described by the quantum Sine-Gordon model Measure time evolution of fringe amplitudes

25 Dynamics of quantum sine-Gordon model Power spectrum Gritsev, Demler, Lukin, Polkovnikov, cond-mat/0702343 A combination of broad features and sharp peaks. Sharp peaks due to collective many-body excitations: breathers Gritsev, Polkovnikov, Demler, cond-mat/0701421

26 Conclusions Interference of extended condensates can be used to probe equilibrium correlation functions in one and two dimensional systems Interference experiments can be used to study non-equilibrium dynamics of low dimensional superfluids and do spectroscopy of the quantum sine-Gordon model

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