Relaxation towards negative temperatures in bosonic systems: Generalized Gibbs ensembles and beyond integrability

Abstract

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<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.

8 pages, 8 figures, published version

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• Generalized Thermalization in an Integrable Lattice System
• Negative Absolute Temperature for Motional Degrees of Freedom
• Control of Interaction-Induced Dephasing of Bloch Oscillations
• Equilibration rates and negative absolute temperatures for ultracold atoms in optical lattices
• Time evolution of one-dimensional Quantum Many Body Systems
• Finite-temperature properties of hard-core bosons confined on one-dimensional optical lattices
• Atomic Gases at Negative Kinetic Temperature
• Interacting Fermionic Atoms in Optical Lattices Diffuse Symmetrically Upwards and Downwards in a Gravitational Potential
• Mean-field dynamics to negative absolute temperatures in the Bose-Hubbard model

Cited by in corpus (5)

• Dynamical Quasicondensation of Hard-Core Bosons at Finite Momenta
• Statistical Mechanics of Systems with Negative Temperature
• Stochastic Differential Equations for Quantum Dynamics of Spin-Boson Networks
• Internal temperature of quantum chaotic systems at the nanoscale and its detection by a microscopic thermometer
• Absence of quasiclassical coherence in mean-field dynamics of bosons in a kinetically frustrated regime