Equilibrium and off-equilibrium trap-size scaling in 1D ultracold bosonic gases

Abstract

We study some aspects of equilibrium and off equilibrium quantum dynamics of dilute bosonic gases in the presence of a trapping potential. We consider systems with a fixed number of particles N and study their scaling behavior with increasing the trap size. We focus on one-dimensional (1D) bosonic systems, such as gases described by the Lieb-Liniger model and its Tonks-Girardeau limit of impenetrable bosons, and gases constrained in optical lattices as described by the Bose-Hubbard model. We study their quantum (zero-temperature) behavior at equilibrium and off equilibrium during the unitary time evolution arising from changes of the trapping potential, which may be instantaneous or described by a power-law time dependence, starting from the equilibrium ground state for a initial trap size. Renormalization-group scaling arguments, analytical and numerical calculations show that the trap-size dependence of the equilibrium and off-equilibrium dynamics can be cast in the form of a trap-size scaling in the low-density regime, characterized by universal power laws of the trap size, in dilute gases with repulsive contact interactions and lattice systems described by the Bose-Hubbard model. The scaling functions corresponding to several physically interesting observables are computed. Our results are of experimental relevance for systems of cold atomic gases trapped by tunable confining potentials.

24 pages

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Cited by in corpus (37)

• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
• Equilibration of a Tonks-Girardeau gas following a trap release
• The entanglement entropy of one-dimensional gases
• Universality in the full counting statistics of trapped fermions
• Exact relations between particle fluctuations and entanglement in Fermi gases
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems
• Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations
• Coherent and dissipative dynamics at quantum phase transitions
• Phase transitions and edge scaling of number variance in Gaussian random matrices
• Finite temperature free fermions and the Kardar-Parisi-Zhang equation at finite time
• Random matrices and entanglement entropy of trapped Fermi gases
• Entanglement Entropy of Quantum Wire Junctions
• Entanglement and particle correlations of Fermi gases in harmonic traps
• The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases
• Number statistics for $\beta$-ensembles of random matrices: applications to trapped fermions at zero temperature
• Universal ground state properties of free fermions in a $d$-dimensional trap
• Dynamic finite-size scaling after a quench at quantum transitions
• Quantum dynamics and entanglement of a 1D Fermi gas released from a trap
• Entanglement evolution across defects in critical anisotropic Heisenberg chains
• Scaling properties of work fluctuations after quenches at quantum transitions
• Universal quantum behaviors of interacting fermions in 1D traps: from few particles to the trap thermodynamic limit
• Spectral order statistics of Gaussian random matrices: large deviations for trapped fermions and associated phase transitions
• Critical parameters from trap-size scaling in trapped particle systems
• Dynamical off-equilibrium scaling across magnetic first-order phase transitions
• Interplay between temperature and trap effects in one-dimensional lattice systems of bosonic particles
• Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps
• Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap
• Quasi-long-range order in trapped systems
• Scaling behaviour of trapped bosonic particles in two dimensions at finite temperature
• One-dimensional Bose gas driven by a slow time-dependent harmonic trap
• Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions
• Trap effects and continuum limit of the Hubbard model in the presence of a harmonic potential
• Critical behavior at the spatial boundary of a trapped inhomogeneous Bose-Einstein condensate
• Critical dynamics in trapped particle systems
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• Quench Dynamics in Confined 1+1-Dimensional Systems