Interference experiments with ultracold atoms Collaborators: Ehud Altman, Anton Burkov, Robert Cherng, Adilet Imambekov, Serena Fagnocchi, Vladimir Gritsev,

Slides:

Advertisements

Similar presentations

Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA,

Advertisements

Superfluid insulator transition in a moving condensate Anatoli Polkovnikov Harvard University Ehud Altman, Eugene Demler, Bertrand Halperin, Misha Lukin.

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

Magnetism in systems of ultracold atoms: New problems of quantum many-body dynamics E. Altman (Weizmann), P. Barmettler (Frieburg), V. Gritsev (Harvard,

Nonequilibrium dynamics of ultracold atoms in optical lattices. Lattice modulation experiments and more Ehud Altman Weizmann Institute Peter Barmettler.

Nonequilibrium dynamics of ultracold fermions Theoretical work: Mehrtash Babadi, David Pekker, Rajdeep Sensarma, Ehud Altman, Eugene Demler $$ NSF, MURI,

Eugene Demler Harvard University

Lattice modulation experiments with fermions in optical lattice Dynamics of Hubbard model Ehud Altman Weizmann Institute David Pekker Harvard University.

Condensed Matter models for many-body systems of ultracold atoms Eugene Demler Harvard University Collaborators: Ehud Altman, Robert Cherng, Adilet Imambekov,

Breakdown of the adiabatic approximation in low-dimensional gapless systems Anatoli Polkovnikov, Boston University Vladimir Gritsev Harvard University.

Nonequilibrium spin dynamics in systems of ultracold atoms Funded by NSF, DARPA, MURI, AFOSR, Harvard-MIT CUA Collaborators: Ehud Altman, Robert Cherng,

Strongly correlated many-body systems: from electronic materials to ultracold atoms to photons Eugene Demler Harvard University Thanks to: E. Altman, I.

Conference on quantum fluids and strongly correlated systems Paris 2008.

Multicomponent systems of ultracold atoms Eugene Demler Harvard University Dynamical instability of spiral states In collaboration with Robert Cherng,

Measuring correlation functions in interacting systems of cold atoms Anatoli Polkovnikov Boston University Ehud Altman Weizmann Vladimir Gritsev Harvard.

Competing instabilities in ultracold Fermi gases $$ NSF, AFOSR MURI, DARPA ARO Harvard-MIT David Pekker (Harvard) Mehrtash Babadi (Harvard) Lode Pollet.

Spinor condensates beyond mean-field

Quantum noise studies of ultracold atoms Eugene Demler Harvard University Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA, MURI Collaborators: Ehud Altman,

Strongly Correlated Systems of Ultracold Atoms Theory work at CUA.

Interference between fluctuating condensates Anatoli Polkovnikov, Boston University Collaboration: Ehud Altman-Weizmann Eugene Demler - Harvard Vladimir.

Eugene Demler Harvard University Collaborators:

Fractional Quantum Hall states in optical lattices Anders Sorensen Ehud Altman Mikhail Lukin Eugene Demler Physics Department, Harvard University.

Measuring correlation functions in interacting systems of cold atoms

Superfluid insulator transition in a moving condensate Anatoli Polkovnikov Harvard University Ehud Altman, Eugene Demler, Bertrand Halperin, Misha Lukin.

Dipolar interactions and magnetoroton softening in spinor condensates Funded by NSF, DARPA, MURI, AFOSR, Harvard-MIT CUA Collaborators: Vladimir Gritsev.

Quantum simulator theory

Eugene Demler Harvard University Robert Cherng, Adilet Imambekov,

Nonequilibrium dynamics of ultracold atoms in optical lattices

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

Measuring correlation functions in interacting systems of cold atoms Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann Vladimir.

Probing many-body systems of ultracold atoms E. Altman (Weizmann), A. Aspect (CNRS, Paris), M. Greiner (Harvard), V. Gritsev (Freiburg), S. Hofferberth.

Strongly correlated systems: from electronic materials to cold atoms Collaborators: E. Altman, R. Barnett, I. Cirac, L. Duan, V. Gritsev, W. Hofstetter,

Non-equilibrium dynamics of cold atoms in optical lattices Vladimir Gritsev Harvard Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann.

Scaling and full counting statistics of interference between independent fluctuating condensates Anatoli Polkovnikov, Boston University Collaboration:

Quantum coherence and interactions in many body systems Collaborators: Ehud Altman, Anton Burkov, Derrick Chang, Adilet Imambekov, Vladimir Gritsev, Mikhail.

Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Collaborators: Takuya Kitagawa, Susanne Pielawa,

Nonequilibrium dynamics of ultracold atoms in optical lattices. Lattice modulation experiments and more Ehud Altman Weizmann Institute Peter Barmettler.

Using dynamics for optical lattice simulations. Anatoli Polkovnikov, Boston University AFOSR Ehud Altman -Weizmann Eugene Demler – Harvard Vladimir Gritsev.

Nonequilibrium dynamics of bosons in optical lattices $$ NSF, AFOSR MURI, DARPA, RFBR Harvard-MIT Eugene Demler Harvard University.

Vladimir Gritsev Harvard Adilet Imambekov Harvard Anton Burkov Harvard Robert Cherng Harvard Anatoli Polkovnikov Harvard/Boston University Ehud Altman.

Dipolar interactions in F=1 ferromagnetic spinor condensates. Roton instabilities and possible supersolid phase Eugene Demler Harvard University Funded.

Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Collaborators: Takuya Kitagawa, Susanne Pielawa,

Nonequilibrium dynamics of interacting systems of cold atoms Collaborators: Ehud Altman, Anton Burkov, Robert Cherng, Adilet Imambekov, Vladimir Gritsev,

Magnetism of spinor BEC in an optical lattice

Nonequilibrium dynamics of ultracold atoms in optical lattices David Pekker, Rajdeep Sensarma, Takuya Kitagawa, Susanne Pielawa, Vladmir Gritsev, Mikhail.

Probing phases and phase transitions in cold atoms using interference experiments. Anatoli Polkovnikov, Boston University Collaboration: Ehud Altman- The.

The Center for Ultracold Atoms at MIT and Harvard Quantum noise as probe of many-body systems Advisory Committee Visit, May 13-14, 2010.

Interference of fluctuating condensates Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann Vladimir Gritsev Harvard Mikhail Lukin.

Slow dynamics in gapless low-dimensional systems Anatoli Polkovnikov, Boston University AFOSR Vladimir Gritsev – Harvard Ehud Altman -Weizmann Eugene Demler.

Outline of these lectures Introduction. Systems of ultracold atoms. Cold atoms in optical lattices. Bose Hubbard model. Equilibrium and dynamics Bose mixtures.

T. Kitagawa (Harvard), S. Pielawa (Harvard), D. Pekker (Harvard), R. Sensarma (Harvard/JQI), V. Gritsev (Fribourg), M. Lukin (Harvard), Lode Pollet (Harvard)

Static and dynamic probes of strongly interacting low-dimensional atomic systems. Anatoli Polkovnikov, Boston University Collaboration: Ehud Altman- The.

Dynamics of repulsively bound pairs in fermionic Hubbard model David Pekker, Harvard University Rajdeep Sensarma, Harvard University Ehud Altman, Weizmann.

New physics with polar molecules Eugene Demler Harvard University Outline: Measurements of molecular wavefunctions using noise correlations Quantum critical.

Many-body quench dynamics in ultracold atoms Surprising applications to recent experiments $$ NSF, AFOSR MURI, DARPA Harvard-MIT Eugene Demler (Harvard)

Measuring correlation functions in interacting systems of cold atoms Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann Vladimir.

QUANTUM MANY-BODY SYSTEMS OF ULTRACOLD ATOMS Eugene Demler Harvard University Grad students: A. Imambekov (->Rice), Takuya Kitagawa Postdocs: E. Altman.

Atoms in optical lattices and the Quantum Hall effect Anders S. Sørensen Niels Bohr Institute, Copenhagen.

Optical lattices for ultracold atomic gases Sestri Levante, 9 June 2009 Andrea Trombettoni (SISSA, Trieste)

Optical lattice emulator Strongly correlated systems: from electronic materials to ultracold atoms.

Quantum magnetism of ultracold atoms $$ NSF, AFOSR MURI, DARPA Harvard-MIT Theory collaborators: Robert Cherng, Adilet Imambekov, Vladimir Gritsev, Takuya.

The Center for Ultracold Atoms at MIT and Harvard Strongly Correlated Many-Body Systems Theoretical work in the CUA Advisory Committee Visit, May 13-14,

Exploring many-body physics with synthetic matter

Probing interacting systems of cold atoms using interference experiments Vladimir Gritsev, Adilet Imambekov, Anton Burkov, Robert Cherng, Anatoli Polkovnikov,

Analysis of quantum noise

Ehud Altman Anatoli Polkovnikov Bertrand Halperin Mikhail Lukin

Part II New challenges in quantum many-body theory:

Measuring correlation functions in interacting systems of cold atoms

Dynamics of spinor condensates: dipolar interactions and more

Strongly Correlated Systems of Cold Atoms Detection of many-body quantum phases by measuring correlation functions Anatoli Polkovnikov.

Presentation transcript:

Interference experiments with ultracold atoms Collaborators: Ehud Altman, Anton Burkov, Robert Cherng, Adilet Imambekov, Serena Fagnocchi, Vladimir Gritsev, Mikhail Lukin, David Pekker, Anatoli Polkovnikov Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA, MURI Eugene Demler Harvard University

Outline Introduction. Interference of fluctuating low dimensional condensates. Systems of mixed dimensionality Interference of fermions: probing paired states Detection of s-wave pairing Detection of FFLO Detection of d-wave pairing Interference experiments and non-equilibrium dynamics Decoherence of uniformly split condensates Ramsey interference of one dimensional systems Splitting condensates on Y-junctions

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

x z Time of flight Experiments with 2D Bose gas Hadzibabic, Dalibard et al., Nature 441:1118 (2006) Experiments with 1D Bose gas Hofferberth et al. arXiv

x1x1 Amplitude of interference fringes, Interference of fluctuating 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) L

Interference between fluctuating condensates 1d: Luttinger liquid, Hofferberth et al., 2007 x z L [pixels] middle T low T high T 2d: BKT transition, Hadzibabic et al, 2006 Time of flight low T high T BKT

Distribution function of interference fringe contrast Experiments: Hofferberth et al., arXiv Theory: Imambekov et al., cond-mat/ Comparison of theory and experiments: no free parameters Higher order correlation functions can be obtained Quantum fluctuations dominate : asymetric Gumbel distribution (low temp. T or short length L) Thermal fluctuations dominate: broad Poissonian distribution (high temp. T or long length L) Intermediate regime : double peak structure

Systems of mixed dimensionality Weakly coupled 2D condensates Experiments: M. Kasevich et al., Interplay of two dimensional physics of the BKT transition and coupling along the 3 rd direction Connection to quasi-2D and 1D condensed matter systems: quantum magnets, organic superconductors, high Tc cuprates, and many more

Berezinskii – Kosterlitz – Thouless transition T=T BKT temperature T=0 Fisher & Hohenberg, PRB 37, 4936 (1988)

Temperature scales for weakly coupled pancakes 3D XY 3D Phonons temperature T=0 T=T BKT T=T C T=2t

Interference of a stack of coupled pancakes Pekker, Gritsev, Demler

Interference experiments with fermions: probing paired states

Interference of fermionic systems Time of flight X Y Z 1 2 A pair of independent fermionic systems

Interference as a probe of fermionic pairing 1 2 W W Pairing correlations Time of flight Expectation value vanishes for independent systems due to random relative phase between D 1 and D 2

Interference as a probe of pairing 1 2 WIWI W II WIWI Experimental procedure Interfere two independent systems Measure and in the same shot Extract and from Fourier transforms in the z-direction Calculate and Find from averaging over many shots Polkovnikov, Gritsev, Demler

FFLO phase Pairing at finite center of mass momentum Theory: Fulde, Ferrell (1964); Larkin, Ovchinnikov (1965); Bowers, Rajagopal (2002); Liu, Wilczek (2003); Sheehy, Radzihovsky (2006); Combescot (2006); Yang, Sachdev (2006); Pieri, Srinati (2006); Parish et al., (2007); and many others Experiments: Zwierlein, Ketterle et al., (2006) Hulet et al., (2006)

Interference as a probe of FFLO phase 1 2 WIWI W II WIWI when q matches one of the wavevectors of D (r) of FFLO phase Integration by a laser beam Manual integration x y

d-wave pairing Fermionic Hubbard model Possible phase diagram of the Hubbard model D.J.Scalapino Phys. Rep. 250:329 (1995)

Phase sensitive probe of d-wave pairing in high Tc superconductors Superconducting quantum interference device (SQUID) F Van Harlingen, Leggett et al, PRL 71:2134 (93)

Other signatures of d-wave pairing: dispersion of quasiparticles Quasiparticle energies Superconducting gap Normal state dispersion of quasiparticles Low energy quasiparticles correspond to four Dirac nodes Observed in: Photoemission Raman spectroscopy T-dependence of thermodynamic and transport properties, c V, k, l L STM and many other probes

Phase sensitive probe of d-wave pairing in high Tc superconductors Superconducting quantum interference device (SQUID) F Van Harlingen, Leggett et al, PRL 71:2134 (93)

Interference as a probe of d-wave pairing 2 W II 1 WIWI W III WIWI W II W III System 1 is an s-wave superfluid System 2 is a d-wave superfluid Regions II and III differ only by 90 o rotation Phase sensitive probe of d-wave pairing d-wave superfluid s-wave superfluid

Interference experiments and non-equilibrium dynamics

Uniform splitting of the condensates Prepare a system by splitting one condensate Take to the regime of zero tunneling Measure time evolution of fringe amplitudes

Long phase coherence implies squeezing factor of 10. Squeezing due to finite time of splitting. Leggett, Sols, PRL (1998) Burkov et al., PRL (2007) Squeezing factor

1d BEC: Decay of coherence Experiments: Hofferberth, Schumm, Schmiedmayer, Nature (2007) double logarithmic plot of the coherence factor slopes: 0.64 ± ± ± 0.06 get t 0 from fit with fixed slope 2/3 and calculate T from T 5 = 110 ± 21 nK T 10 = 130 ± 25 nK T 15 = 170 ± 22 nK

Relative phase dynamics beyond single mode approximation Conjugate variables Hamiltonian can be diagonalized in momentum space A collection of harmonic oscillators with Need to solve dynamics of harmonic oscillators at finite T Coherence Initial state f q = 0

Quantum regime 1D systems 2D systems Classical regime 1D systems 2D systems Relative phase dynamics beyond single mode approximation Bistritzer, Altman, PNAS (2007) Burkov, Lukin, Demler, PRL (2007)

Dynamics of condensate splitting and Ramsey interference

Working with N atoms improves the precision of frequency spectroscopy by. Ramsey interference t 0 1

Interaction induced collapse of Ramsey fringes Experiments in 1d tubes: A. Widera, et al. arXiv 0709:2094

Spin echo. Time reversal experiments Single mode approximation predicts full revival Experiments in 1d tubes : A.Widera, et al. arXiv 0709:2094. Need to analyze multi-mode model in 1d Only q=0 mode shows complete spin echo Finite q modes continue decay The net visibility is a result of competition between q=0 and other modes

Splitting condensates on Y-junctions: quantum zipper problem

Splitting condensates on Y-junctions Partial splitting stage: new physics Full splitting stage: same as before Earlier work: Non-interacting atoms: Scully and Dowling, PRA (1993) Analysis of transverse modes: Jaasekelatnen and Stenholm, PRA (2003) Tonks-Girardeau regime: Girardeau et al. PRA (2002)

Splitting condensates on Y-junctions: beyond mean-field x Wave equation in both arms of the interferometer. c is the speed of sound Relative phase Time dependent boundary conditions in the frame of the condensate. v is the condensate velocity 1 st arm 2 nd arm

Moving mirror problem in optics Moore, J. Math. Phys. 9:2679 (1970) Exciting photons in a cavity with a moving mirror Experimentally always in the adiabatic regime c is the speed of light

Splitting condensate on Y-junction: beyond mean-field K – Luttinger parameter v is the condensate velocity d This is similar to the usual 1d condensates Extra suppression due to finite velocity of splitting

Splitting with acceleration: Unruh like effect Fagnocchi, Altman, Demler Splitting condensates with relativistic acceleration gives rise to thermal correlations. This is analogous to the Unruh effect in field theory and quantum gravity Unruh (1974), Fulling and Davies (1976)

Summary Interference experiments with ultracold atoms provide a powerful tool for analyzing equilibrium properties and dynamics of many-body systems. Analysis beyond mean-field and single mode approximation is needed important Thanks to: