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arXiv:1211.4350 · Physical Review A

Mean-field dynamics to negative absolute temperatures in the Bose-Hubbard model

Ákos Rapp

Published Apr 9, 2013• 12 citations
arXivHTMLPDF

Abstract

We apply time-dependent Gutzwiller mean-field theory to provide a qualitative understanding for bosons in optical lattices that approach states corresponding to negative absolute temperatures. We perform the dynamical simulations to relate to the recent experiments by Braun et al. [S. Braun, J. P. Ronzheimer, M. Schreiber, S. S. Hodgman, T. Rom, I. Bloch, and U. Schneider, Science 339, 52 (2013)]. Time-of-flight images calculated from the two-dimensional numerical simulations reproduce characteristics of the experimental observations, in particular the emergence of the four peaks at the corners of the Brillouin zone.

DOI
10.1103/physreva.87.043611

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We apply time-dependent Gutzwiller mean-field theory to provide a qualitative understanding for bosons in optical lattices that approach states corresponding to negative absolute temperatures. We perform the dynamical simulations to relate to the recent experiments by Braun et al. [S. Braun, J. P. Ronzheimer, M. Schreiber, S. S. Hodgman, T. Rom, I. Bloch, and U. Schneider, Science 339, 52 (2013)]. Time-of-flight images calculated from the two-dimensional numerical simulations reproduce characteristics of the experimental observations, in particular the emergence of the four peaks at the corners of the Brillouin zone.
Motivated by the recent experimental observation of negative absolute temperature states in systems of ultracold atomic gases in optical lattices [Braun et al., Science 339, 52 (2013)], we investigate theoretically the formation of these states. More specifically, we consider the relaxation after a sudden inversion of the external parabolic confining potential in the one-dimensional inhomogeneous Bose-Hubbard model. First, we focus on the integrable hard-core boson limit, which allows us to treat large systems and arbitrarily long times, providing convincing numerical evidence for relaxation to a generalized Gibbs ensemble at negative temperature T<0T<0T<0, a notion we define in this context. Second, going beyond one dimension, we demonstrate that the emergence of negative temperature states can be understood in a dual way in terms of positive temperatures, which relies on a dynamic symmetry of the Hubbard model. We complement the study by exact diagonalization simulations at finite values of the on-site interaction.
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambureal-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory andstrong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory capturesnot only dynamical transitions but also damping and thermalization effects at finite temperature. We applythe formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamicalproperties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well aslong-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium“phase diagrams” that map out the different dynamical regimes.
We investigate a bosonic quantum gas consisting of two interacting species in an optical lattice at zero and finite temperature. The equilibrium properties and dynamics of this system are obtained by means of the Gutzwiller mean-field method. In particular we model recent experiments where the ramp-up of the optical lattice occurs on a time scale comparable to the tunneling time of the bosons. We demonstrate the violation of adiabaticity of this process with respect to the many-body quantum states, and we reproduce and explain the oscillations of the visibility as a function of ramp-up time, as seen in experiments.
Ultracold atoms in optical lattices offer an important tool for studying dynamics in many-body interacting systems in a pristine environment. This thesis focuses on three theoretical works motivated by recent optical lattice experiments. In the first, we theoretically study the center of mass dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center of mass motion even with insulating states in the center. We identify short and long-time mechanisms for edge state transport in insulating phases. We also argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our zero temperature results offer important insights into mechanisms of transport of atoms in trapped optical lattices while putting bounds on center of mass dynamics expected at non-zero temperature. In the second work, we study the domain wall expansion dynamics of strongly interacting bosons in 2D optical lattices with disorder in a recent experiment {[}J.-y. Choi et al., Science 352, 1547 (2016)]. We show that Gutzwiller mean-field theory (GMFT) captures the main experimental observations, which are a result of the competition between disorder and interactions. Our findings highlight the difficulty in distinguishing glassy dynamics, which can be captured by GMFT, and many-body localization, which cannot be captured by GMFT, and indicate the need for further experimental studies of this system. The last work features our study of phase diagrams of the 2D Bose-Hubbard model in an optical lattice with synthetic spin-orbit coupling. We investigate the transitions between superfluids with different phase patterns, which may be detected by measuring the spin-dependent momentum distribution.
We present a cluster Gutzwiller mean-field study for ground states and time-evolution dynamics in the Bose-Hubbard ladder (BHL), which can be realized by loading Bose atoms in double-well optical lattices. In our cluster mean-field approach, we treat each double-well unit of two lattice sites as a coherent whole for composing the cluster Gutzwiller ansatz, which may remain some residual correlations in each two-site unit. For an unbiased BHL, in addition to conventional superfluid phase and integer Mott insulator phases, we find that there are exotic fractional insulator phases if the interchain tunneling is much stronger than the intrachain one. The fractional insulator phases cannot be found by using a conventional mean-field treatment based upon the single-site Gutzwiller ansatz. For a biased BHL, we find there appear single-atom tunneling and interaction blockade if the system is dominated by the interplay between the on-site interaction and the interchain bias. In the many-body Landau-Zener process, in which the interchain bias is linearly swept from negative to positive or vice versa, our numerical results are qualitatively consistent with the experimental observation [Nat. Phys. 7, 61 (2011)]. Our cluster bosonic Gutzwiller treatment is of promising perspectives in exploring exotic quantum phases and time-evolution dynamics of bosonic particles in superlattices.
We consider a mixture of interacting bosons and fermions in optical lattices described by the Bose–Fermi Hubbard Hamiltonian. To treat bosonic degrees of freedom, we use a generalized dynamical mean field theory (GDMFT). By combining the GDMFT with the numerical renormalization group method, we revisit the zero-temperature phase diagram with particular emphasis on many-body effects in a supersolid state and discuss the origin of an anomalous peak structure emerging in the density of states for fermions.