Tan's Contact for Trapped Lieb-Liniger Bosons at Finite Temperature

Abstract

The universal Tan relations connect a variety of microscopic features of many-body quantum systems with two-body contact interactions to a single quantity, called the contact. The latter has become pivotal in the description of quantum gases.We provide a complete characterization of the Tan contact of the harmonically trapped Lieb-Liniger gas for arbitrary interactions and temperature.Combining thermal Bethe ansatz, local-density approximation, and exact quantum Monte Carlo calculations,we show that the contact is a universal function of only two scaling parameters, and determine the scaling function.We find that the temperature dependence of the contact, or equivalently the interaction dependence of the entropy, displays a maximum. The presence of this maximum provides an unequivocal signature of the crossover to the fermionized regime and it is accessible in current experiments.

References in corpus (37)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• The ALPS project release 1.3: open source software for strongly correlated systems
• Regimes of quantum degeneracy in trapped 1D gases
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations
• Pair correlations in a finite-temperature 1D Bose gas
• Verification of universal relations in a strongly interacting Fermi gas
• Contact Measurements on Atomic BEC
• Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases
• Sub-Poissonian fluctuations in a 1D Bose gas: from the quantum quasi-condensate to the strongly interacting regime
• Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling
• Tan relations in one dimension
• Measurement of the Homogeneous Contact of a Unitary Fermi gas
• Two and Three-body Contacts in the Unitary Bose Gas
• Precise determination of the structure factor and contact in a unitary Fermi gas
• High-momentum tail in the Tonks gas under harmonic confinement
• Evidence for universal relations describing a gas with $p$-wave interactions
• Expectation Values in the Lieb-Liniger Bose Gas
• Observation of Quantum Criticality and Luttinger Liquid in One-dimensional Bose Gases
• Exact three-body local correlations for excited states of the 1D Bose gas
• One-dimensional optical lattices and impenetrable bosons
• Universal contact for a Tonks-Girardeau gas at finite temperature
• Momentum-resolved observation of thermal and quantum depletion in an interacting Bose gas
• Mott Transition for Strongly-Interacting 1D Bosons in a Shallow Periodic Potential
• Universal scaling of density and momentum distributions in Lieb-Liniger gases
• High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps
• Long-lived non-thermal states realized by atom losses in one-dimensional quasi-condensates
• Exact density profiles and symmetry classification for strongly interacting multi-component Fermi gases in tight waveguides
• Connecting few-body inelastic decay to many-body correlations: a weakly coupled impurity in a resonant Fermi gas
• Universal Superfluid Transition and Transport Properties of Two-Dimensional Dirty Bosons
• Universal Tan relations for quantum gases in one dimension
• Critical behaviours of contact near phase transitions
• Universality and quantum criticality of the one-dimensional spinor Bose gas

Cited by in corpus (27)

• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Extension of the Generalized Hydrodynamics to the Dimensional Crossover Regime
• Lieb-Liniger Bosons in a Shallow Quasiperiodic Potential: Bose Glass Phase and Fractal Mott Lobes
• Breakdown of Tan's relation in lossy one-dimensional Bose gases
• Thermal instability, evaporation and thermodynamics of one-dimensional liquids in weakly-interacting Bose-Bose mixtures
• Relaxation of Bosons in One Dimension and the Onset of Dimensional Crossover
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Strongly correlated quantum droplets in quasi-1D dipolar Bose gas
• Beyond-Luttinger-Liquid thermodynamics of a one-dimensional contact repulsive Bose gas
• Strongly-interacting bosons at 2D-1D Dimensional Crossover
• Analytic thermodynamic properties of the Lieb-Liniger gas
• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Scaling properties of the Tan's contact: embedding pairs and correlation effect in the Tonks limit
• Momentum correlations of a few ultra-cold bosons escaping from an open well
• Full Counting Statistics of the momentum occupation numbers of the Tonks-Girardeau gas
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• Finite temperature contact for SU(2) fermions trapped in a 1D harmonic confinement
• Tailoring Dynamical Fermionization: Delta kick cooling of a Tonks-Girardeau gas
• Thermal fading of the $1/k^4$-tail of the momentum distribution induced by the hole anomaly
• Quantum corrections to the classical field approximation for one-dimensional quantum many-body systems in equilibrium
• Critical behavior of Tan's contact for bosonic systems with a fixed chemical potential
• Unconventional pairing in few-fermion systems at finite temperature
• Symmetries and Correlations in Strongly Interacting One-dimensional Quantum Gases
• Nucleon Short-Range Correlations and High-Momentum Dynamics: Implications on the Equation of State of Dense Matter
• Statistical properties of the momentum occupation numbers of the Tonks-Girardeau gas in a harmonic trap
• How to measure the free energy and partition function from atom-atom correlations
• Thermodynamics and Tomonaga-Luttinger liquid behavior of the quantum 1D hard rod model