Session B10: Invited Session: Equilibration and Relaxation in Cold Atoms

Timescales for equilibration and adiabaticity in optical lattices

What are the timescales governing local and global dynamics in strongly correlated systems? How do we probe this dynamics in an isolated quantum system without coupling the system to leads? High in-situ resolved experiments on bosons in optical lattices are answering precisely these questions by imaging the gas following a sudden change of the lattice potential. The results are striking. Experiments have revealed a disparity as large as two orders of magnitude between fast equilibration of local number fluctuations and slow global mass redistribution. In this talk, I will provide a simple model which captures all the relevant physics. Additionally, I will show that the fast timescales for local dynamics challenge the accepted notions of adiabaticity times, invalidating routinely used techniques such as band-mapping as useful probes of quantum many body systems. References: S. S. Natu, K. R. A. Hazzard and E. J. Mueller, Phys. Rev. Lett. 106 125301 (2011).   

Pomeranchuk effect and spin-gradient cooling of Bose-Bose mixtures in an optical lattice

We theoretically investigate finite-temperature thermodynamics and demagnetization cooling of two-component Bose-Bose mixtures in a cubic optical lattice, by using bosonic dynamical mean-field theory (BDMFT). We calculate the finite-temperature phase diagram, and remarkably find that the system can be heated from the superfluid into the Mott insulator at low temperature, analogous to the Pomeranchuk effect in $^3$He. This provides a promising many-body cooling technique. We examine the entropy distribution in the trapped system and discuss its dependence on temperature and an applied magnetic field gradient. Our numerical simulations quantitatively validate the spin- gradient demagnetization cooling scheme proposed in recent experiments.   

The amplitude mode at the superfluid-mott insulator transition

We study a two dimensional gas of repulsively interacting bosons in the presence of both an optical lattice and a trap using optical lattice modulation spectroscopy. The strongly interacting superfluid supports two types of low energy modes associated with the symmetry breaking at the phase transition: gapless phase (Goldstone) modes and gapped amplitude (Anderson-Higgs) modes. Both experimentally and in theoretical simulations lattice modulation spectroscopy shows an onset of absorption at a frequency associated with the amplitude mode gap, followed by a broad absorption peak at higher frequencies. From the simulations, we learn that energy is being absorbed by various amplitude modes, which inside a trap resemble the modes of a (gapped) drum. Our main results are: (1) despite coupling to the phase modes, modulation spectroscopy shows a sharp absorption onset at the frequency associated with the amplitude mode gap; (2) as we approach the Mott transition the gap softens and finally disappears at the transition point; (3) in the weak coupling regime, deep in the superfluid phase, the amplitude mode disappears.   

Two-dimensional Fermi gases

Pairing of fermions is ubiquitous in nature and it is responsible for a large variety of fascinating phenomena like superconductivity, superfluidity of 3He, the anomalous rotation of neutron stars, and the BEC-BCS crossover in strongly interacting Fermi gases. When confined to two dimensions, interacting many-body systems bear even more subtle effects, many of which lack understanding at a fundamental level. Most striking is the, yet unexplained, effect of high-temperature superconductivity in cuprates, which is intimately related to the two-dimensional geometry of the crystal structure. In particular, the question how many-body pairing is established at high temperature and whether it precedes superconductivity are crucial questions to be answered. We will report on recent experiments of pairing in a two-dimensional atomic Fermi gas in the regime of strong coupling. We perform angle-resolved photoemission spectroscopy to measure the spectral function of the gas and we observe a many-body pairing gap even above the predicted superfluid transition temperature.   

Relaxation Dynamics and Pre-thermalization in an isolated Quantum System

Understanding non-equilibrium dynamics of many-body quantum systems is crucial for understanding many fundamental and applied physics problems ranging from decoherence and equilibration to the development of future quantum technologies such as quantum computers which are inherently non-equilibrium quantum systems. One of the biggest challenges is that there is no general approach to characterize the resulting quantum states. In this talk I will present how to use the full distribution functions of a quantum observable to study the relaxation dynamics in one-dimensional quantum systems and to characterize the underlying many body states. Interfering two 1 dimensional quantum gases allows to study how the coherence created between the two many body systems by the splitting process [1] slowly dies by coupling to the many internal degrees of freedom available [2]. To reveal the nature of the quantum states behind this de-coherence we analyze the interference of the two evolving quantum systems. The full distribution function of the shot to shot variations of the interference patterns [3,4], especially its higher moments, allows characterizing the underlying physical processes [5]. Two distinct regimes are clearly visible in the experiment: for short length scales the system is characterized by spin diffusion, for long length scales by spin decay [6]. After a rapid evolution the distributions approach a steady state which can be characterized by thermal distribution functions. Interestingly, its (effective) temperature is over five times lower than the kinetic temperature of the initial system. Our system, being a weakly-interacting Bosons in one dimension, is nearly integrable and the dynamics is constrained by constants of motion which leads to the establishment of a generalized Gibbs ensemble and pre-thermalization. We therefore interpret our observations as an illustration of the fast relaxation of a nearly integrable many-body system to a quasi-steady state through de-phasing. The observation of an effective temperature significant different from the expected kinetic temperature supports the observation of the generalized Gibbs state [6]. \\[4pt] [1] T. Schumm \emph{et al.} Nature Physics, {\bf 1}, 57 (2005).\\[0pt] [2] S. Hofferberth \emph{et al.} Nature {\bf 449}, 324 (2007).\\[0pt] [3] A. Polkovnikov, \emph{et al.} Proc. Natl. Acad. Sci. {\bf 103}, 6125 (2006); V. Gritsev, \emph{et al.}, Nature Phys. {\bf 2}, 705 (2006); \\[0pt] [4] S. Hofferberth \emph{et al.} Nature Physics {\bf 4}, 489 (2008); \\[0pt] [5] T. Kitagawa, \emph{et al.}, Phys. Rev. Lett. {\bf 104}, 255302 (2010); New Journal of Physcs, {\bf 13} 073018 (2011)\\[0pt] [6] Gring \emph{et al.}, to be published