The pinning quantum phase transition in a Tonks Girardeau gas: diagnostics by ground state fidelity and the Loschmidt echo

Abstract

We study the pinning quantum phase transition in a Tonks-Girardeau gas, both in equilibrium and out-of-equilibrium, using the ground state fidelity and the Loschmidt echo as diagnostic tools. The ground state fidelity (GSF) will have a dramatic decrease when the atomic density approaches the commensurate density of one particle per lattice well. This decrease is a signature of the pinning transition from the Tonks to the Mott insulating phase. We study the applicability of the fidelity for diagnosing the pinning transition in experimentally realistic scenarios. Our results are in excellent agreement with recent experimental work. In addition, we explore the out of equilibrium dynamics of the gas following a sudden quench with a lattice potential. We find all properties of the ground state fidelity are reflected in the Loschmidt echo dynamics i.e., in the non equilibrium dynamics of the Tonks-Girardeau gas initiated by a sudden quench of the lattice potential.

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Dynamics of Loschmidt echoes and fidelity decay
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Orthogonality catastrophe as a consequence of qubit embedding in an ultra-cold Fermi gas
• Decoherence Dynamics in Low-Dimensional Cold Atom Interferometers
• Long-time behavior of many-particle quantum decay
• Intrinsic dephasing in one dimensional ultracold atom interferometers
• Weakly interacting Bose gas in the one-dimensional limit
• Dephasing in coherently-split quasicondensates
• Loschmidt echo in one-dimensional interacting Bose gases
• Strongly interacting one-dimensional bosons in arbitrary-strength optical lattices: from Bose-Hubbard to sine-Gordon and beyond

Cited by in corpus (11)

• Orthogonality catastrophe and decoherence in a trapped-Fermion environment
• A many-body heat engine at criticality
• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
• Exploring chaos in Dicke Model using ground state fidelity and Loschmidt echo
• Probing the out-of-equilibrium dynamics of two interacting atoms
• Universal off-diagonal long-range order behaviour for a trapped Tonks-Girardeau gas
• Dynamical depinning of a Tonks Girardeau gas
• Self-Pinning Transition of a Tonks-Girardeau Gas in a Bose-Einstein Condensate
• Static and dynamic phases of a Tonks-Girardeau gas in an optical lattice
• Nonequilibrium quantum thermodynamics of determinantal many-body systems: Application to the Tonks-Girardeau and ideal Fermi gases
• Work statistics and Entanglement across the fermionic superfluid-insulator transition