Nonadiabatic energy fluctuations of scale-invariant quantum systems in a time-dependent trap

Abstract

We consider the nonadiabatic energy fluctuations of a many-body system in a time-dependent harmonic trap. In the presence of scale-invariance, the dynamics becomes self-similar and the nondiabatic energy fluctuations can be found in terms of the initial expectation values of the second moments of the Hamiltonian, square position, and squeezing operators. Nonadiabatic features are expressed in terms of the scaling factor governing the size of the atomic cloud, which can be extracted from time-of-flight images. We apply this exact relation to a number of examples: the single-particle harmonic oscillator, the one-dimensional Calogero-Sutherland model, describing bosons with inverse-square interactions that includes the non-interacting Bose gas and the Tonks-Girdardeau gas as limiting cases, and the unitary Fermi gas. We illustrate these results for various expansion protocols involving sudden quenches of the trap frequency, linear ramps and shortcuts to adiabaticity. Our results pave the way to the experimental study of nonadiabatic energy fluctuations in driven quantum fluids.

13 pages, 3 figures, minor changes

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Cited by in corpus (8)

• Probing Quantum Speed Limits with Ultracold Gases
• Shortcuts to Adiabaticity in Krylov Space
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Exact Delta Kick Cooling, Time-Optimal Control of Scale-Invariant Dynamics, and Shortcuts to Adiabaticity Assisted by Kicks
• Nonequilibrium quantum thermodynamics of determinantal many-body systems: Application to the Tonks-Girardeau and ideal Fermi gases
• Easy access to energy fluctuations in non-equilibrium quantum many-body systems
• Exact Dynamics and Shortcuts to Adiabaticity in the Tomonaga-Luttinger Liquid
• The time-dependent quantum harmonic oscillator: a pedagogical approach via the Lewis-Riesenfeld dynamical invariant method