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:cond-mat/0405225 · Physical Review Letters

Beyond the Tonks-Girardeau Gas: Strongly Correlated Regime in Quasi-One-Dimensional Bose Gases

G. E. Astrakharchik, Jordi Boronat, J. Casulleras, S. Giorgini

Published Nov 4, 2005• 210 citations
arXivHTMLPDF

Abstract

We consider a homogeneous 1D Bose gas with contact interactions and a large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using the diffusion Monte Carlo method we show that, for small densities, the gaslike state is well described by a gas of hard rods. The critical density for cluster formation is estimated using the variational Monte Carlo method. The behavior of the correlation functions and of the frequency of the lowest breathing mode for harmonically trapped systems shows that the gas is more strongly correlated than in the Tonks-Girardeau regime.

DOI
10.1103/physrevlett.95.190407

Related papers

Quantum Monte Carlo study of quasi-one-dimensional Bose gases

G. E. Astrakharchik, D. Blume, B. Granger +1 more

We study the behaviour of quasi-one-dimensional (quasi-1D) Bose gases by Monte Carlo techniques, i.e. by the variational Monte Carlo, the diffusion Monte Carlo and the fixed-node diffusion Monte Carlo techniques. Our calculations confirm and extend our results of an earlier study (Astrakharchik et al 2003 Preprint cond-mat/0308585). We find that a quasi-1D Bose gas (i) is well described by a 1D model Hamiltonian with contact interactions and renormalized coupling constant; (ii) reaches the Tonks–Girardeau regime for a critical value of the 3D scattering length a3D; (iii) enters a unitary regime for |a3D| → ∞, where the properties of the gas are independent of a3D and are similar to those of a 1D gas of hard-rods and (iv) becomes unstable against cluster formation for a critical value of the 1D gas parameter. The accuracy and implications of our results are discussed in detail.

•Jan 1, 2004•10 citations

Quantum Monte Carlo study of quasi-one-dimensional Bose gases

G. E. Astrakharchik, D Blume, S Giorgini +1 more

We study the behaviour of quasi-one-dimensional (quasi-1D) Bose gases by Monte Carlo techniques, i.e. by the variational Monte Carlo, the diffusion Monte Carlo and the fixed-node diffusion Monte Carlo techniques. Our calculations confirm and extend our results of an earlier study (Astrakharchik et al 2003 Preprint cond-mat/0308585). We find that a quasi-1D Bose gas (i) is well described by a 1D model Hamiltonian with contact interactions and renormalized coupling constant; (ii) reaches the Tonks–Girardeau regime for a critical value of the 3D scattering length a 3D ; (iii) enters a unitary regime for | a 3D | → ∞ , where the properties of the gas are independent of a 3D and are similar to those of a 1D gas of hard-rods and (iv) becomes unstable against cluster formation for a critical value of the 1D gas parameter. The accuracy and implications of our results are discussed in detail.

arXiv:cond-mat/0310749•Journal of Physics B Atomic Molecular and Optical Physics•Mar 24, 2004•23 citations

Quasi-One-Dimensional Bose Gases with a Large Scattering Length

G. E. Astrakharchik, D. Blume, S. Giorgini +1 more

Bose gases confined in highly elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1D model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1D Bose gas become independent of the actual value of the 3D scattering length a(3D). In this unitary regime, the energy of the system is well described by a hard-rod equation of state. We investigate the stability of quasi-1D Bose gases with positive and negative a(3D).

arXiv:cond-mat/0308585•Physical Review Letters•Jan 22, 2004•81 citations

Super-Tonks-Girardeau Gas of Spin- 1/2 Interacting Fermions

Liming Guan, Shu Chen

Fermi gases confined in tight one-dimensional waveguides form two-particle bound states of atoms in the presence of a strongly attractive interaction. Based on the exact solution of the one-dimensional spin-1/2 interacting Fermi gas, we demonstrate that a stable excited state with no pairing between attractive fermionic atoms can be realized by a sudden switch of interaction from the strongly repulsive regime to strongly attractive regime. Such a state is an exact fermionic analog of the experimentally observed super-Tonks-Girardeau state of bosonic Cesium atoms [Science 325, 1224 (2009)] and should be possible to be observed by the experiment. The frequency of the lowest breathing mode of the fermionic super-Tonks-Girardeau gas is calculated as a function of the interaction strength, which could be used as a detectable signature for the experimental observation.

arXiv:1005.0461•Physical Review Letters•Oct 19, 2010•49 citations

Interacting Fermions in Highly Elongated Harmonic Traps

G. E. Astrakharchik, D. Blume, S. Giorgini +1 more

Quasi-one-dimensional two-component Fermi gases with effectively attractive and repulsive interactions are characterized for arbitrary interaction strength. The ground-state properties of the gas confined in highly elongated harmonic traps are determined within the local density approximation. For strong attractive effective interactions the existence of a molecular Tonks-Girardeau gas is predicted. The frequency of the lowest breathing mode is calculated as a function of the coupling strength for both attractive and repulsive interactions.

arXiv:cond-mat/0312538•Physical Review Letters•Jul 29, 2004•86 citations

Luttinger hydrodynamics of confined one-dimensional Bose gases with dipolar interactions

R. Citro, S. De Palo, E. Orignac +2 more

Ultracold bosonic and fermionic quantum gases confined to quasi-one-dimensional (1D) geometry are promising candidates for probing fundamental concepts of Luttinger liquid (LL) physics. They can also be exploited for devising applications in quantum information processing and precision measurements. Here, we focus on 1D dipolar Bose gases, where evidence of super-strong coupling behavior has been demonstrated by analyzing the low-energy static and dynamical structures of the fluid at zero temperature by a combined reptation quantum Monte Carlo (RQMC) and bosonization approach. Fingerprints of LL behavior emerge in the whole crossover from the already strongly interacting Tonks–Girardeau at low density to a dipolar density wave regime at high density. We have also shown that a LL framework can be effectively set up and utilized to describe this strongly correlated crossover physics in the case of confined 1D geometries after using the results for the homogeneous system in LL hydrodynamic equations within a local density approximation. This leads to the prediction of observable quantities such as the frequencies of the collective modes of the trapped dipolar gas under the more realistic conditions that could be found in ongoing experiments. The present paper provides a description of the theoretical framework in which the above results have been worked out, making available all the detailed derivations of the hydrodynamic Luttinger equations for the inhomogeneous trapped gas and of the correlation functions for the homogeneous system.

New Journal of Physics•Apr 30, 2008•51 citations
We consider a homogeneous 1D Bose gas with contact interactions and a large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using the diffusion Monte Carlo method we show that, for small densities, the gaslike state is well described by a gas of hard rods. The critical density for cluster formation is estimated using the variational Monte Carlo method. The behavior of the correlation functions and of the frequency of the lowest breathing mode for harmonically trapped systems shows that the gas is more strongly correlated than in the Tonks-Girardeau regime.
We study the behaviour of quasi-one-dimensional (quasi-1D) Bose gases by Monte Carlo techniques, i.e. by the variational Monte Carlo, the diffusion Monte Carlo and the fixed-node diffusion Monte Carlo techniques. Our calculations confirm and extend our results of an earlier study (Astrakharchik et al 2003 Preprint cond-mat/0308585). We find that a quasi-1D Bose gas (i) is well described by a 1D model Hamiltonian with contact interactions and renormalized coupling constant; (ii) reaches the Tonks–Girardeau regime for a critical value of the 3D scattering length a3D; (iii) enters a unitary regime for |a3D| → ∞, where the properties of the gas are independent of a3D and are similar to those of a 1D gas of hard-rods and (iv) becomes unstable against cluster formation for a critical value of the 1D gas parameter. The accuracy and implications of our results are discussed in detail.
We study the behaviour of quasi-one-dimensional (quasi-1D) Bose gases by Monte Carlo techniques, i.e. by the variational Monte Carlo, the diffusion Monte Carlo and the fixed-node diffusion Monte Carlo techniques. Our calculations confirm and extend our results of an earlier study (Astrakharchik et al 2003 Preprint cond-mat/0308585). We find that a quasi-1D Bose gas (i) is well described by a 1D model Hamiltonian with contact interactions and renormalized coupling constant; (ii) reaches the Tonks–Girardeau regime for a critical value of the 3D scattering length a 3D ; (iii) enters a unitary regime for | a 3D | → ∞ , where the properties of the gas are independent of a 3D and are similar to those of a 1D gas of hard-rods and (iv) becomes unstable against cluster formation for a critical value of the 1D gas parameter. The accuracy and implications of our results are discussed in detail.
Bose gases confined in highly elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1D model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1D Bose gas become independent of the actual value of the 3D scattering length a(3D). In this unitary regime, the energy of the system is well described by a hard-rod equation of state. We investigate the stability of quasi-1D Bose gases with positive and negative a(3D).
Fermi gases confined in tight one-dimensional waveguides form two-particle bound states of atoms in the presence of a strongly attractive interaction. Based on the exact solution of the one-dimensional spin-1/2 interacting Fermi gas, we demonstrate that a stable excited state with no pairing between attractive fermionic atoms can be realized by a sudden switch of interaction from the strongly repulsive regime to strongly attractive regime. Such a state is an exact fermionic analog of the experimentally observed super-Tonks-Girardeau state of bosonic Cesium atoms [Science 325, 1224 (2009)] and should be possible to be observed by the experiment. The frequency of the lowest breathing mode of the fermionic super-Tonks-Girardeau gas is calculated as a function of the interaction strength, which could be used as a detectable signature for the experimental observation.
Quasi-one-dimensional two-component Fermi gases with effectively attractive and repulsive interactions are characterized for arbitrary interaction strength. The ground-state properties of the gas confined in highly elongated harmonic traps are determined within the local density approximation. For strong attractive effective interactions the existence of a molecular Tonks-Girardeau gas is predicted. The frequency of the lowest breathing mode is calculated as a function of the coupling strength for both attractive and repulsive interactions.
Ultracold bosonic and fermionic quantum gases confined to quasi-one-dimensional (1D) geometry are promising candidates for probing fundamental concepts of Luttinger liquid (LL) physics. They can also be exploited for devising applications in quantum information processing and precision measurements. Here, we focus on 1D dipolar Bose gases, where evidence of super-strong coupling behavior has been demonstrated by analyzing the low-energy static and dynamical structures of the fluid at zero temperature by a combined reptation quantum Monte Carlo (RQMC) and bosonization approach. Fingerprints of LL behavior emerge in the whole crossover from the already strongly interacting Tonks–Girardeau at low density to a dipolar density wave regime at high density. We have also shown that a LL framework can be effectively set up and utilized to describe this strongly correlated crossover physics in the case of confined 1D geometries after using the results for the homogeneous system in LL hydrodynamic equations within a local density approximation. This leads to the prediction of observable quantities such as the frequencies of the collective modes of the trapped dipolar gas under the more realistic conditions that could be found in ongoing experiments. The present paper provides a description of the theoretical framework in which the above results have been worked out, making available all the detailed derivations of the hydrodynamic Luttinger equations for the inhomogeneous trapped gas and of the correlation functions for the homogeneous system.