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/0308585 · Physical Review Letters

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

G. E. Astrakharchik, D. Blume, S. Giorgini, Brian Granger

Published Jan 22, 2004• 81 citations
arXivHTMLPDF

Abstract

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).

DOI
10.1103/physrevlett.92.030402

Related papers

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

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

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

G. E. Astrakharchik, Jordi Boronat, J. Casulleras +1 more

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.

arXiv:cond-mat/0405225•Physical Review Letters•Nov 4, 2005•210 citations

Excitation spectrum and effective interactions of a highly elongated Fermi gas

D. Blume, Debraj Rakshit

Full three-dimensional (3D) calculations of small two-component Fermi gases under highly elongated confinement, in which unlike fermions interact through short-range potentials with variable atom-atom $s$-wave scattering length, are performed using the correlated Gaussian approach. In addition, microscopic one-dimensional (1D) calculations are performed for effective ``atomic'' and ``molecular'' 1D model Hamiltonian. Comparisons of the 3D and 1D energies and excitation frequencies establish the validity regimes of the effective 1D Hamiltonian. Our numerical results for three- and four-particle systems suggest that the effective 1D atom-dimer and dimer-dimer interactions are to a good approximation determined by simple analytical expressions. Implications for the description of quasi-1D Fermi gases within strict 1D frameworks are discussed.

arXiv:0901.3862•Physical Review A•Jul 1, 2009•8 citations

Dilute Fermi Gas in Quasi-One-Dimensional Traps: From Weakly Interacting Fermions via Hard Core Bosons to a Weakly Interacting Bose Gas

I. V. Tokatly

We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size ${l}_{\ensuremath{\perp}}$. In the dilute limit ($n{l}_{\ensuremath{\perp}}\ensuremath{\ll}1$, where $n$ is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length ${a}_{F}$. When ${l}_{\ensuremath{\perp}}/{a}_{F}$ goes from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$, the system successively passes three regimes: weakly interacting Fermi gas, hard core Bose gas, and weakly coupled Bose gas. The regimes are separated by two crossovers at ${a}_{F}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}n{l}_{\ensuremath{\perp}}^{2}$. In conclusion, we discuss experimental implications of these results.

arXiv:cond-mat/0402276•Physical Review Letters•Aug 25, 2004•104 citations

Confinement and finite-range effects in a quasi-two-dimensional gas of fermionic dimers

Giovanni Midei, Jordi Boronat, G. E. Astrakharchik

We investigate the ground-state properties of ultracold two-component Fermi gases in the presence of a transverse harmonic potential, focusing on the strongly interacting regime in which pairs of fermions form tightly bound molecules. Using the fixed-node diffusion Monte Carlo method, we calculate the equation of state and density profiles for the full fermionic system, which allows us to address the importance of finite-range corrections arising from the internal fermionic structure of the dimers. We interpret the results in terms of a molecular Bose gas in quasi-two-dimensional confinement and compare them with theoretical predictions for a weakly interacting two-dimensional Bose gas, identifying the range of validity of mean-field and beyond-mean-field descriptions. We also develop an analytical theory for the transverse density profile, capturing its broadening with increasing interaction strength. This work provides a benchmark for an effective bosonic description of strongly bound fermionic dimers and offers insights into confinement-induced dimensional effects.

arXiv:2512.09753•Physical Review Research•May 20, 2026•0 citations
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).
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.
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 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.
Full three-dimensional (3D) calculations of small two-component Fermi gases under highly elongated confinement, in which unlike fermions interact through short-range potentials with variable atom-atom sss-wave scattering length, are performed using the correlated Gaussian approach. In addition, microscopic one-dimensional (1D) calculations are performed for effective ``atomic'' and ``molecular'' 1D model Hamiltonian. Comparisons of the 3D and 1D energies and excitation frequencies establish the validity regimes of the effective 1D Hamiltonian. Our numerical results for three- and four-particle systems suggest that the effective 1D atom-dimer and dimer-dimer interactions are to a good approximation determined by simple analytical expressions. Implications for the description of quasi-1D Fermi gases within strict 1D frameworks are discussed.
We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size ${l}_{\ensuremath{\perp}}$. In the dilute limit ($n{l}_{\ensuremath{\perp}}\ensuremath{\ll}1$, where nnn is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length aF{a}_{F}aF​. When ${l}_{\ensuremath{\perp}}/{a}_{F}$ goes from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$, the system successively passes three regimes: weakly interacting Fermi gas, hard core Bose gas, and weakly coupled Bose gas. The regimes are separated by two crossovers at ${a}_{F}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}n{l}_{\ensuremath{\perp}}^{2}$. In conclusion, we discuss experimental implications of these results.
We investigate the ground-state properties of ultracold two-component Fermi gases in the presence of a transverse harmonic potential, focusing on the strongly interacting regime in which pairs of fermions form tightly bound molecules. Using the fixed-node diffusion Monte Carlo method, we calculate the equation of state and density profiles for the full fermionic system, which allows us to address the importance of finite-range corrections arising from the internal fermionic structure of the dimers. We interpret the results in terms of a molecular Bose gas in quasi-two-dimensional confinement and compare them with theoretical predictions for a weakly interacting two-dimensional Bose gas, identifying the range of validity of mean-field and beyond-mean-field descriptions. We also develop an analytical theory for the transverse density profile, capturing its broadening with increasing interaction strength. This work provides a benchmark for an effective bosonic description of strongly bound fermionic dimers and offers insights into confinement-induced dimensional effects.