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:1008.4383 · Physical Review A

Local correlations in the super-Tonks-Girardeau gas

Márton Kormos, Giuseppe Mussardo, Andrea Trombettoni

Published Jan 24, 2011• 50 citations
arXivHTMLPDF

Abstract

We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi-one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature, our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground state of the repulsive Lieb-Liniger gas, to the super-Tonks-Girardeau state. At finite temperature, we obtain that the three-body correlator has a weak dependence on temperature up to the degeneracy temperature ${T}_{\mathrm{D}}$. We also find that, for temperatures larger than ${T}_{\mathrm{D}}$, the values of the three-body correlator for the super-Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar, even for relatively small couplings.

DOI
10.1103/physreva.83.013617

Related papers

Local correlations in a strongly interacting one-dimensional Bose gas

Dimitri M. Gangardt, Gora V. Shlyapnikov

We develop an analytical method for calculating local correlations in strongly interacting 1D Bose gases, based on the exactly solvable Lieb-Liniger model. The results are obtained at zero and finite temperatures. They describe the interaction-induced reduction of local many-body correlation functions and can be used for achieving and identifying the strong-coupling Tonks-Girardeau regime in experiments with cold Bose gases in the 1D regime.

arXiv:cond-mat/0304159•New Journal of Physics•Jun 18, 2003•86 citations

Wave functions of the super-Tonks-Girardeau gas and the trapped one-dimensional hard-sphere Bose gas

Marvin D. Girardeau, G. E. Astrakharchik

Recent theoretical and experimental results demonstrate a close connection between the super-Tonks-Girardeau (STG) gas and a one-dimensional (1D) hard-sphere Bose (HSB) gas with hard-sphere diameter nearly equal to the 1D scattering length ${a}_{1\mathrm{D}}$ of the STG gas, a highly excited gaslike state with nodes only at interparticle separations $|{x}_{j\ensuremath{\ell}}|={x}_{\mathrm{node}}\ensuremath{\approx}{a}_{1\mathrm{D}}$. It is shown herein that when the coupling constant ${g}_{B}$ in the Lieb-Liniger interaction ${g}_{B}\ensuremath{\delta}({x}_{j\ensuremath{\ell}})$ is negative and $|{x}_{12}|\ensuremath{\geqslant}{x}_{\mathrm{node}}$, the STG and HSB wave functions for $N=2$ particles are not merely similar, but identical; the only difference between the STG and HSB wave functions is that the STG wave function allows a small penetration into the region $|{x}_{12}|<{x}_{\mathrm{node}}$, whereas for a HSB gas with hard-sphere diameter ${a}_{\mathrm{hs}}={x}_{\mathrm{node}}$, the HSB wave function vanishes when $|{x}_{12}|<{a}_{\mathrm{hs}}$. Arguments are given suggesting that the same theorem holds also for $N>2$. The STG and HSB wave functions for $N=2$ are given exactly in terms of a parabolic cylinder function, and for $N\ensuremath{\geqslant}2$, ${x}_{\mathrm{node}}$ is given accurately by a simple parabola. The metastability of the STG phase generated by a sudden change of the coupling constant from large positive to large negative values is explained in terms of the very small overlap between the ground state of the Tonks-Girardeau gas and collapsed cluster states.

arXiv:0912.1633•Physical Review A•Jun 21, 2010•35 citations

Exploring the growth of correlations in a quasi one-dimensional trapped Bose gas

M Eckart, R Walser, W P Schleich

Phase correlations, density fluctuations and three-body loss rates are relevant for many experiments in quasi one-dimensional geometries. Extended mean-field theory is used to evaluate correlation functions up to third order for a quasi one-dimensional trapped Bose gas at zero and finite temperature. At zero temperature and in the homogeneous limit, we also study the transition from the weakly correlated Gross–Pitaevskii regime to the strongly correlated Tonks–Girardeau regime analytically. We compare our results with the exact Lieb–Liniger solution for the homogeneous case and find good agreement up to the cross-over regime.

arXiv:0712.0311•New Journal of Physics•Apr 30, 2008•9 citations

Exploring the growth of correlations in a quasi one-dimensional trapped Bose gas

M. Eckart, R. Walser, W. P. Schleich

Phase correlations, density fluctuations and three-body loss rates are relevant for many experiments in quasi one-dimensional geometries. Extended mean-field theory is used to evaluate correlation functions up to third order for a quasi one-dimensional trapped Bose gas at zero and finite temperature. At zero temperature and in the homogeneous limit, we also study the transition from the weakly correlated Gross–Pitaevskii regime to the strongly correlated Tonks–Girardeau regime analytically. We compare our results with the exact Lieb–Liniger solution for the homogeneous case and find good agreement up to the cross-over regime.

•Apr 30, 2008•6 citations

Two-spinon effects on the thermal Tonks-Girardeau gas

Felipe Taha Sant’Ana, Hui Liu

Abstract We study the effects of the two-spinon excitations on the field-field correlator of the Tonks-Girardeau gas. While these excitations have been previously examined in the ground state of the system, their role at finite temperatures remains unexplored. Here, we extend the analysis to the one-dimensional interacting Bose gas at thermal equilibrium, focusing on the one-body correlation function of the infinitely repulsive Lieb-Liniger model. We demonstrate that two-spinon excitations, characterized by two holes within the rapidity distribution, constitute the dominant contribution to the field-field correlator at low temperatures. Furthermore, we analytically show that incorporating additional particle-hole excitations diminishes their contribution, highlighting the efficacy of the two-spinon framework in capturing the essential physics of the system. Numerical evaluations of both the Fredholm determinant and the spectral sum stemming from the two-spinon program, with the addition of particle-hole excitations, reveal convergence at low temperatures.

arXiv:2410.20929•Physica Scripta•Nov 26, 2025•0 citations

Dynamics of Pair Correlations in the Attractive Lieb-Liniger Gas

Dominik Muth, Michael Fleischhauer

We investigate the dynamics of a one-dimensional Bose gas after a quench from the Tonks-Girardeau regime to the regime of strong attractive interactions applying analytical techniques and numerical simulations. After the quench the system is found to be predominantly in an excited gaslike state, the so-called super-Tonks gas, however with a small coherent admixture of two-particle bound states. Despite its small amplitude, the latter leads to a pronounced oscillation of the local density correlation with a frequency corresponding to the binding energy of the pair. Contributions from bound states with larger particle numbers are found to be negligible.

arXiv:1006.5312•Physical Review Letters•Oct 6, 2010•47 citations
We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi-one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature, our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground state of the repulsive Lieb-Liniger gas, to the super-Tonks-Girardeau state. At finite temperature, we obtain that the three-body correlator has a weak dependence on temperature up to the degeneracy temperature TD{T}_{\mathrm{D}}TD​. We also find that, for temperatures larger than TD{T}_{\mathrm{D}}TD​, the values of the three-body correlator for the super-Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar, even for relatively small couplings.
Recent theoretical and experimental results demonstrate a close connection between the super-Tonks-Girardeau (STG) gas and a one-dimensional (1D) hard-sphere Bose (HSB) gas with hard-sphere diameter nearly equal to the 1D scattering length a1D{a}_{1\mathrm{D}}a1D​ of the STG gas, a highly excited gaslike state with nodes only at interparticle separations $|{x}_{j\ensuremath{\ell}}|={x}_{\mathrm{node}}\ensuremath{\approx}{a}_{1\mathrm{D}}$. It is shown herein that when the coupling constant gB{g}_{B}gB​ in the Lieb-Liniger interaction ${g}_{B}\ensuremath{\delta}({x}_{j\ensuremath{\ell}})$ is negative and $|{x}_{12}|\ensuremath{\geqslant}{x}_{\mathrm{node}}$, the STG and HSB wave functions for N=2N=2N=2 particles are not merely similar, but identical; the only difference between the STG and HSB wave functions is that the STG wave function allows a small penetration into the region ∣x12∣<xnode|{x}_{12}|<{x}_{\mathrm{node}}∣x12​∣<xnode​, whereas for a HSB gas with hard-sphere diameter ahs=xnode{a}_{\mathrm{hs}}={x}_{\mathrm{node}}ahs​=xnode​, the HSB wave function vanishes when ∣x12∣<ahs|{x}_{12}|<{a}_{\mathrm{hs}}∣x12​∣<ahs​. Arguments are given suggesting that the same theorem holds also for N>2N>2N>2. The STG and HSB wave functions for N=2N=2N=2 are given exactly in terms of a parabolic cylinder function, and for $N\ensuremath{\geqslant}2$, xnode{x}_{\mathrm{node}}xnode​ is given accurately by a simple parabola. The metastability of the STG phase generated by a sudden change of the coupling constant from large positive to large negative values is explained in terms of the very small overlap between the ground state of the Tonks-Girardeau gas and collapsed cluster states.
Phase correlations, density fluctuations and three-body loss rates are relevant for many experiments in quasi one-dimensional geometries. Extended mean-field theory is used to evaluate correlation functions up to third order for a quasi one-dimensional trapped Bose gas at zero and finite temperature. At zero temperature and in the homogeneous limit, we also study the transition from the weakly correlated Gross–Pitaevskii regime to the strongly correlated Tonks–Girardeau regime analytically. We compare our results with the exact Lieb–Liniger solution for the homogeneous case and find good agreement up to the cross-over regime.
Phase correlations, density fluctuations and three-body loss rates are relevant for many experiments in quasi one-dimensional geometries. Extended mean-field theory is used to evaluate correlation functions up to third order for a quasi one-dimensional trapped Bose gas at zero and finite temperature. At zero temperature and in the homogeneous limit, we also study the transition from the weakly correlated Gross–Pitaevskii regime to the strongly correlated Tonks–Girardeau regime analytically. We compare our results with the exact Lieb–Liniger solution for the homogeneous case and find good agreement up to the cross-over regime.
Abstract We study the effects of the two-spinon excitations on the field-field correlator of the Tonks-Girardeau gas. While these excitations have been previously examined in the ground state of the system, their role at finite temperatures remains unexplored. Here, we extend the analysis to the one-dimensional interacting Bose gas at thermal equilibrium, focusing on the one-body correlation function of the infinitely repulsive Lieb-Liniger model. We demonstrate that two-spinon excitations, characterized by two holes within the rapidity distribution, constitute the dominant contribution to the field-field correlator at low temperatures. Furthermore, we analytically show that incorporating additional particle-hole excitations diminishes their contribution, highlighting the efficacy of the two-spinon framework in capturing the essential physics of the system. Numerical evaluations of both the Fredholm determinant and the spectral sum stemming from the two-spinon program, with the addition of particle-hole excitations, reveal convergence at low temperatures.
We investigate the dynamics of a one-dimensional Bose gas after a quench from the Tonks-Girardeau regime to the regime of strong attractive interactions applying analytical techniques and numerical simulations. After the quench the system is found to be predominantly in an excited gaslike state, the so-called super-Tonks gas, however with a small coherent admixture of two-particle bound states. Despite its small amplitude, the latter leads to a pronounced oscillation of the local density correlation with a frequency corresponding to the binding energy of the pair. Contributions from bound states with larger particle numbers are found to be negligible.