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Register a new userQuench dynamics of 1D Bose gas in an optical lattice: does the system relax?
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Understanding the relaxation process is the most important unsolved problem in non-equilibrium quantum physics. Current understanding primarily concerns on if and how an isolated quantum many-body system thermalize. However, there is no clear understanding of what conditions and on which time-scale do thermalization occurs. In this article, we simulate the quench dynamics of one-dimensional Bose gas in an optical lattice from an{it {ab initio}} perspective by solving the time-dependent many-boson Schrodinger equation using the multi-configurational time-dependent Hartree method for bosons (MCTDHB). We direct a superfluid (SF) to Mott-insulator (MI) transition by performing two independent quenches: an interaction quench when the interaction strength is changed instantaneously, and a lattice depth quench where the depth of the lattice is altered suddenly. We show that although the Bose-Hubbard model predicts identical physics, the general many-body treatment shows significant differences between the two cases. We observe that lattice depth quench exhibits a large time-scale to reach the MI state and shows an oscillatory phase collapse-revival dynamics and a complete absence of thermalization that reveals through the analysis of the time-evolution of the reduced one-body density matrix, two-body density, and entropy production. In contrast, the interaction quench shows a swift transition to the MI state and shows a clear signature of thermalization for strong quench values. We provide a physical explanation for these differences and prescribe an analytical fitting formula for the time required for thermalization.
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Statistical mechanics is one of the most comprehensive theories in physics. From a boiling pot of water to the complex dynamics of quantum many-body systems it provides a successful connection between the microscopic dynamics of atoms and molecules and the macroscopic properties of matter. However, statistical mechanics only describes the thermal equilibrium situation of a system, and there is no general framework to describe how equilibrium is reached or under which circumstances it can be reached at all. This problem is particularly challenging in quantum mechanics, where unitarity appears to render the very concept of thermalization counterintuitive. With the rapid experimental progress in the control and probing of ultracold quantum gases this question has become within reach of detailed experimental investigations. In these notes we present a series of experiments with ultracold one-dimensional Bose gases, which provide novel insights into this fundamental question.
Two-component coupled Bose gas in a 1D optical lattice is examined. In addition to the postulated Mott insulator and Superfluid phases, multiple bosonic components manifest spin degrees of freedom. Coupling of the components in the Bose gas within same site and neighboring sites leads to substantial change in the previously observed spin phases revealing fascinating remarkable spin correlations. In the presence of strong interactions it gives rise to unconventional effective ordering of the spins leading to unprecedented spin phases: site-dependent $ztextsf{-}x$ spin configuration with tunable (by hopping parameter) proclivity of spin alignment along $z$. Exact analysis and Variational Monte Carlo (VMC) along with stochastic minimization on Entangled Plaquette State (EPS) bestow a unique and enhanced perspective into the system beyond the scope of mean-field treatment. The physics of complex intra-component tunneling and inter-component coupling and filling factor greater than unity are discussed.
We create supercurrents in annular two-dimensional Bose gases through a temperature quench of the normal-to-superfluid phase transition. We detect the amplitude and the chirality of these supercurrents by measuring spiral patterns resulting from the interference of the cloud with a central reference disk. These measurements demonstrate the stochastic nature of the supercurrents. We further measure their distribution for different quench times and compare it with the predictions based on the Kibble-Zurek mechanism.
Using a species-selective dipole potential, we create initially localized impurities and investigate their interactions with a majority species of bosonic atoms in a one-dimensional configuration during expansion. We find an interaction-dependent amplitude reduction of the oscillation of the impurities size with no measurable frequency shift, and study it as a function of the interaction strength. We discuss possible theoretical interpretations of the data. We compare, in particular, with a polaronic mass shift model derived following Feynman variational approach.
We investigate the response of a one-dimensional Bose gas to a slow increase of its interaction strength. We focus on the rich dynamics of equal-time single-particle correlations treating the Lieb-Liniger model within a bosonization approach and the Bose-Hubbard model using the time-dependent density-matrix renormalization group method. For short distances, correlations follow a power-law with distance with an exponent given by the adiabatic approximation. In contrast, for long distances, correlations decay algebraically with an exponent understood within the sudden quench approximation. This long distance regime is separated from an intermediate distance one by a generalized Lieb-Robinson criterion. At long times, in this intermediate regime, bosonization predicts that single-particle correlations decay following a stretched exponential. This latter regime is unconventional as, for one-dimensional interacting systems, the decay of single-particle correlations is usually algebraic within the Luttinger liquid picture. We develop here an intuitive understanding for the propagation of correlations, in terms of a generalized light-cone, applicable to a large variety of systems and quench forms.
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