Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1808.05478 · New Journal of Physics

Static and dynamic phases of a Tonks–Girardeau gas in an optical lattice

Mathias Mikkelsen, Thomás Fogarty, Thomas Busch

Published Oct 19, 2018• 12 citations
arXivHTMLPDF

Abstract

We investigate the properties of a Tonks–Girardeau gas in the presence of a one-dimensional lattice potential. Such a system is known to exhibit a pinning transition when the lattice is commensurate with the particle density, leading to the formation of an insulating state even at infinitesimally small lattice depths. Here we examine the properties of the gas at all lattices depths and, in addition to the static properties, also consider the non-adiabatic dynamics induced by the sudden motion of the lattice potential with a constant speed. Our work provides a continuum counterpart to the work done in discrete lattice models.

DOI
10.1088/1367-2630/aae98e

Related papers

Pinning quantum phase transition in a Tonks-Girardeau gas: Diagnostics by ground-state fidelity and the Loschmidt echo

Karlo Lelas, T. Ševa, Hrvoje Buljan +1 more

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 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. We find that fidelity can predict the particle number(s) at which the pinning occurs. In addition, we explore the out-of-equilibrium dynamics of the gas following a sudden quench with a lattice potential. We find that all properties of the ground-state fidelity are reflected in the Loschmidt echo dynamics, i.e., in the nonequilibrium dynamics of the Tonks-Girardeau gas initiated by a sudden quench of the lattice potential.

arXiv:1205.3151•Physical Review A•Sep 18, 2012•17 citations

Nonequilibrium dynamics of Tonks-Girardeau gases on optical lattices

Marcos Rigol, A. Muramatsu

We summarize in the present work exact results obtained for Tonks-Girardeau gases on one-dimensional optical lattices both for the ground state and nonequilibrium dynamics. On the theoretical side, impenetrable bosons offer the opportunity to study strongly interacting systems in one-dimensional lattices exactly, by means of the Jordan-Wigner transformation, and hence contribute to the topic of strong correlations at the center of interest in both condensed matter physics and quantum gases. This motivation is further enhanced by recent experimental realizations of such systems with ultracold atoms. After having shown their universal properties in equilibrium, we concentrate on their nonequilibrium dynamics. It will be shown that, starting from a pure Fock state, quasi-long-range correlations develop dynamically and lead to the formation of quasicondensates with a momentum determined by the underlying lattice. We expect this effect to be relevant for atom lasers with full control of the wavelength. Then, we will show that the free evolution of an initially confined Tonks-Girardeau gas leads to a momentum distribution that approaches at long times that of the equivalent fermionic system, giving rise to a bosonic gas with a Fermi edge, and hence a fermionization that can only be obtained out of equilibrium. Remarkably, although the momentum distribution function of the Tonks-Girardeau gas becomes equal to the one of the fermions, no loss in coherence is observed in the system, as reflected by a large occupation of eigenstates of the one-particle density matrix.

Laser Physics•Feb 1, 2006•4 citations

Self-Pinning Transition of a Tonks-Girardeau Gas in a Bose-Einstein Condensate

Tim Keller, Thomás Fogarty, Thomas Busch

We show that a Tonks-Girardeau (TG) gas that is immersed in a Bose-Einstein condensate can undergo a transition to a crystal-like Mott state with regular spacing between the atoms without any externally imposed lattice potential. We characterize this phase transition as a function of the interspecies interaction and temperature of the TG gas, and show how it can be measured via accessible observables in cold atom experiments. We also develop an effective model that accurately describes the system in the pinned insulator state and which allows us to derive the critical temperature of the transition.

arXiv:2109.01500•Physical Review Letters•Jan 31, 2022•14 citations

Ultracold Atoms in One-Dimensional Optical Lattices Approaching the Tonks-Girardeau Regime

Lode Pollet, S. Rombouts, P. J. H. Denteneer

Recent experiments on ultracold atomic alkali gases in a one-dimensional optical lattice have demonstrated the transition from a gas of soft-core bosons to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons behave like fermions in many respects. We have studied the underlying many-body physics through numerical simulations which accommodate both the soft-core and hard-core limits in one single framework. We find that the Tonks-Girardeau gas is reached only at the strongest optical lattice potentials. Results for slightly higher densities, where the gas develops a Mott-like phase already at weaker optical lattice potentials, show that these Mott-like short-range correlations do not enhance the convergence to the hard-core limit.

arXiv:cond-mat/0408596•Physical Review Letters•Nov 15, 2004•38 citations

Tonks-Girardeau gas in an optical lattice: Effects of a local potential

Hao Fu, Alberto G. Rojo

The physics of a Tonks-Girardeau gas confined in an optical lattice in the presence of a local potential is studied. In order to evaluate the single-particle density matrix (SPDM) of the many-body ground state, the Wigner-Jordan transformation is used. The eigenvector with the largest eigenvalue of the SPDM corresponds to the ``Bose-Einstein condensate''(BEC) state. We find that the BEC-state density at the position of the local potential decreases, as expected, in the case of a repulsive potential. For an attractive potential, it decreases or increases depending on the strength of the potential. The superfluidity of this system is investigated both numerically and perturbatively. An experimental method for detecting the effect of an impurity in a Tonks-Girardeau gas is discussed.

arXiv:cond-mat/0602163•Physical Review A•Jul 21, 2006•6 citations

Ground-state properties of a Tonks-Girardeau gas in a periodic potential

Bo-Bo Wei, Shi-Jian Gu, Hai-Qing Lin

In this paper, we investigate the ground-state properties of a bosonic Tonks-Girardeau (TG) gas confined in a one-dimensional periodic potential. The single-particle reduced density matrix is computed numerically for systems up to $N=265$ bosons. Scaling analysis of the occupation number of the lowest orbital shows that there are no Bose-Einstein condensation (BEC) for the periodically trapped TG gas in both commensurate and incommensurate cases. We find that, in the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, $\ensuremath{-}0.5$ and 1, respectively, while in the incommensurate case, they are 0.5, $\ensuremath{-}0.5$, and 1.5, respectively. These exponents are related to each other in a universal relation.

arXiv:0812.1277•Physical Review A•Jun 24, 2009•5 citations
We investigate the properties of a Tonks–Girardeau gas in the presence of a one-dimensional lattice potential. Such a system is known to exhibit a pinning transition when the lattice is commensurate with the particle density, leading to the formation of an insulating state even at infinitesimally small lattice depths. Here we examine the properties of the gas at all lattices depths and, in addition to the static properties, also consider the non-adiabatic dynamics induced by the sudden motion of the lattice potential with a constant speed. Our work provides a continuum counterpart to the work done in discrete lattice models.
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 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. We find that fidelity can predict the particle number(s) at which the pinning occurs. In addition, we explore the out-of-equilibrium dynamics of the gas following a sudden quench with a lattice potential. We find that all properties of the ground-state fidelity are reflected in the Loschmidt echo dynamics, i.e., in the nonequilibrium dynamics of the Tonks-Girardeau gas initiated by a sudden quench of the lattice potential.
We summarize in the present work exact results obtained for Tonks-Girardeau gases on one-dimensional optical lattices both for the ground state and nonequilibrium dynamics. On the theoretical side, impenetrable bosons offer the opportunity to study strongly interacting systems in one-dimensional lattices exactly, by means of the Jordan-Wigner transformation, and hence contribute to the topic of strong correlations at the center of interest in both condensed matter physics and quantum gases. This motivation is further enhanced by recent experimental realizations of such systems with ultracold atoms. After having shown their universal properties in equilibrium, we concentrate on their nonequilibrium dynamics. It will be shown that, starting from a pure Fock state, quasi-long-range correlations develop dynamically and lead to the formation of quasicondensates with a momentum determined by the underlying lattice. We expect this effect to be relevant for atom lasers with full control of the wavelength. Then, we will show that the free evolution of an initially confined Tonks-Girardeau gas leads to a momentum distribution that approaches at long times that of the equivalent fermionic system, giving rise to a bosonic gas with a Fermi edge, and hence a fermionization that can only be obtained out of equilibrium. Remarkably, although the momentum distribution function of the Tonks-Girardeau gas becomes equal to the one of the fermions, no loss in coherence is observed in the system, as reflected by a large occupation of eigenstates of the one-particle density matrix.
We show that a Tonks-Girardeau (TG) gas that is immersed in a Bose-Einstein condensate can undergo a transition to a crystal-like Mott state with regular spacing between the atoms without any externally imposed lattice potential. We characterize this phase transition as a function of the interspecies interaction and temperature of the TG gas, and show how it can be measured via accessible observables in cold atom experiments. We also develop an effective model that accurately describes the system in the pinned insulator state and which allows us to derive the critical temperature of the transition.
Recent experiments on ultracold atomic alkali gases in a one-dimensional optical lattice have demonstrated the transition from a gas of soft-core bosons to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons behave like fermions in many respects. We have studied the underlying many-body physics through numerical simulations which accommodate both the soft-core and hard-core limits in one single framework. We find that the Tonks-Girardeau gas is reached only at the strongest optical lattice potentials. Results for slightly higher densities, where the gas develops a Mott-like phase already at weaker optical lattice potentials, show that these Mott-like short-range correlations do not enhance the convergence to the hard-core limit.
The physics of a Tonks-Girardeau gas confined in an optical lattice in the presence of a local potential is studied. In order to evaluate the single-particle density matrix (SPDM) of the many-body ground state, the Wigner-Jordan transformation is used. The eigenvector with the largest eigenvalue of the SPDM corresponds to the ``Bose-Einstein condensate''(BEC) state. We find that the BEC-state density at the position of the local potential decreases, as expected, in the case of a repulsive potential. For an attractive potential, it decreases or increases depending on the strength of the potential. The superfluidity of this system is investigated both numerically and perturbatively. An experimental method for detecting the effect of an impurity in a Tonks-Girardeau gas is discussed.
In this paper, we investigate the ground-state properties of a bosonic Tonks-Girardeau (TG) gas confined in a one-dimensional periodic potential. The single-particle reduced density matrix is computed numerically for systems up to N=265N=265N=265 bosons. Scaling analysis of the occupation number of the lowest orbital shows that there are no Bose-Einstein condensation (BEC) for the periodically trapped TG gas in both commensurate and incommensurate cases. We find that, in the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, $\ensuremath{-}0.5$ and 1, respectively, while in the incommensurate case, they are 0.5, $\ensuremath{-}0.5$, and 1.5, respectively. These exponents are related to each other in a universal relation.