Quantum coherence and interactions in many body systems

1. Quantum coherence and interactions in many body systems Eugene Demler Harvard University Collaborators: Ehud Altman, Anton Burkov, Derrick Chang, Adilet Imambekov, Vladimir Gritsev , Mikhail Lukin, Giovanna Morigi, Anatoli Polkonikov Funded by NSF, AFOSR, Harvard-MIT CUA

2. Condensed matter physics Atomic physics Quantum coherence Quantum optics Quantum information

3. Quantum Optics with atoms andCondensed Matter Physics with photons Interference of fluctuating condensates From reduced contrast of fringes to correlation functions Distribution function of fringe contrast Non-equilibrium dynamics probed in interference experiments Luttinger liquid of photons Can we get “fermionization” of photons? Non-equilibrium coherent dynamics of strongly interacting photons

4. Interference experimentswith cold atoms

5. 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

6. Interference of two independent condensates r’ r 1 r+d d 2 Clouds 1 and 2 do not have a well defined phase difference. However each individual measurement shows an interference pattern

7. Nature 4877:255 (1963)

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

9. Amplitude of interference fringes, For identical condensates Interference of one dimensional condensates Polkovnikov, Altman, Demler,PNAS 103:6125 (2006) d x1 For independent condensates Afr is finite but Df is random x2 Instantaneous correlation function

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

11. Ly Lx Below KT transition Above KT transition Interference of two dimensional condensates.Quasi long range order and the KT transition

12. Experiments with 2D Bose gas low temperature higher temperature Hadzibabic, Dalibard et al., Nature 441:1118 (2006) Time of flight z x Typical interference patterns

13. Contrast after integration integration over x axis z 0.4 low T z middle T 0.2 integration over x axis high T z 0 0 Dx 10 20 30 integration distance Dx (pixels) Experiments with 2D Bose gas Hadzibabic et al., Nature 441:1118 (2006) x integration over x axis z

14. 0.4 low T 0.2 Exponent a middle T 0 0 10 20 30 high T if g1(r) decays exponentially with : high T low T 0.5 0.4 if g1(r) decays algebraically or exponentially with a large : central contrast 0.3 “Sudden” jump!? 0 0.1 0.2 0.3 Experiments with 2D Bose gas Hadzibabic et al., Nature 441:1118 (2006) fit by: Integrated contrast integration distance Dx

15. 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.

16. , , and so on 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 Obtain the entire distribution function of

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

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

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

20. Interference of 1d condensates at finite temperature. Distribution function of the fringe contrast Experiments: Schmiedmayer et al. Luttinger parameter K=5

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

22. From visibility of interference fringes to other problems in physics

23. is a quantum operator. The measured value of will fluctuate from shot to shot. How to predict the distribution function of 2D quantum gravity, non-intersecting loops Yang-Lee singularity Interference between interacting 1d Bose liquids. Distribution function of the interference amplitude 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, …

24. Fringe visibility Roughness 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 StatisticsT.Antal et al. Phys.Rev.Lett. 87, 240601(2001)

25. Non-equilibrium coherentdynamics of low dimensional Bose gases probed in interference experiments

26. 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

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

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

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

30. Condensed matter physics with photons

31. Luttinger liquid of photons Tonks gas of photons: photon “fermionization” Chang, Demler, Gritsev, Lukin, Morigi, unpublished

32. w w0 k0 k Self-interaction effects for one-dimensional optical waves Nonlinear polarization for isotropic medium Envelope function

33. Self-interaction effects for one-dimensional optical waves Frame of reference moving with the group velocity Gross-Pitaevskii type equation for light propagation Nonlinear Optics, Mills Competition of dispersion and non-linearity

34. Self-interaction effects for one-dimensional optical waves BEFORE: two level systems and insufficient mode confinement NOW: EIT and tight mode confinement Interaction corresponds to attraction. Physics of solitons (e.g. Drummond) Sign of the interaction can be tuned Tight confinement of the electromagnetic mode enhances nonlinearity Weak non-linearity due to insufficient mode confining Limit on non-linearity due to photon decay Strong non-linearity without losses can be achieved using EIT

35. Controlling self-interaction effects for photons D w w Wc w Imamoglu et al., PRL 79:1467 (1997) describes photons. We need to normalize to polaritons

36. Tonks gas of photons Photon fermionization Crystal of photons Is it realistic? Experimental signatures

37. Tonks gas of atoms Small g– weakly interacting Bose gas Large g– Tonks gas. Fermionized bosons Additional effects for for photons: Photons are moving with the group velocity Limit on the cross section of photon interacting with one atom

38. Tonks gas of photons Limit on strongly interacting 1d photon liquid due to finite group velocity Concrete example: atoms in a hollow fiber Theory: photonic crystal and non-linear medium Deutsch et al., PRA 52:1394 (2005); Pritchard et al., cond-mat/0607277 Experiments: Cornell et al. PRL 75:3253 (1995); Lukin, Vuletic, Zibrov et.al.

39. w k Atoms in a hollow fiber A – cross section of e-m mode Typical numbers l=1mm A=10mm2 Ltot=1cm Without using the “slow light” points

40. c Experimental detection of the Luttinger liquid of photons Control beam off. Coherent pulse of non-interacting photons enters the fiber. Control beam switched on adiabatically. Converts the pulse into a Luttinger liquid of photons. “Fermionization” of photons detected by observing oscillations in g2 K – Luttinger parameter

41. Non-equilibrium dynamics of strongly correlated many-body systems g2 for expanding Tonks gas with adiabatic switching of interactions 100 photons after expansion

42. Outlook Next challenge in studying quantum coherence: understand non-equilibrium coherent quantum dynamics of strongly correlated many-body systems Atomic physics and quantum optics traditionally study non-equilibrium coherent quantum dynamics of relatively simple systems. Condensed matter physics analyzes complicated electron system but focuses on the ground state and small excitations around it. We will need the expertise of both fields “…The primary objective of the JQI is to develop a world class research institute that will explore coherent quantum phenomena and thereby lay the foundation for engineering and controlling complex quantum systems…” From the JQI web page http://jqi.umd.edu/