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

Quantum Monte Carlo study of the three- to one-dimensional crossover for a trapped Bose gas

G. E. Astrakharchik, S. Giorgini

Published Jun 18, 2007• 0 citations
Publisher

Abstract

Abstract These two papers, published back to back, provide superb examples of the use of a quantum Monte Carlo method to obtain exact solutions for a problem difficult to treat by other methods. The problem is that of a bosonic atomic gas confined in a cigarshaped trap. As the cigar is narrowed the atoms are less able to pass each other, their behavior approaches that of fermions, and they are said to exhibit “fermionization.” Using diffusion QMC the authors were able to determine the ground-state energies, examine structural properties, confirm that fermionization can occur, and predict conditions under which it might be observed. The calculations by Blume were carried out for 2-20 atoms confined in axially symmetric traps of varied aspect ratios. The confining potential for each atom was given by Vk = CpPl + Czzl (radial and axial positions squared). The atom-atom interactions were simple hard-sphere potentials. The (nodeless) guided diffusion calculations used a trial wave function of the Jastrow type, a product of atom-trap terms and atom-atom terms. The calculations by Astrakharchik and Giorgini were carried out similarly but included both hard and soft spheres with numbers in the range of 5 to 100 atoms. Comparisons were made with predictions of the Lieb Liniger equation of state.

DOI
10.1093/oso/9780195310108.003.00140

Related papers

Fermionization of a bosonic gas under highly elongated confinement: A diffusion quantum Monte Carlo study

D. Blume

Abstract These two papers, published back to back, provide superb examples of the use of a quantum Monte Carlo method to obtain exact solutions for a problem difficult to treat by other methods. The problem is that of a bosonic atomic gas confined in a cigarshaped trap. As the cigar is narrowed the atoms are less able to pass each other, their behavior approaches that of fermions, and they are said to exhibit “fermionization.” Using diffusion QMC the authors were able to determine the ground-state energies, examine structural properties, confirm that fermionization can occur, and predict conditions under which it might be observed. The calculations by Blume were carried out for 2-20 atoms confined in axially symmetric traps of varied aspect ratios. The confining potential for each atom was given by Vk = CpPl + Czzl (radial and axial positions squared). The atom-atom interactions were simple hard-sphere potentials. The (nodeless) guided diffusion calculations used a trial wavefunction of the Jastrow type, a product of atom-trap terms and atom-atom terms. The calculations by Astrakharchik and Giorgini were carried out similarly but included both hard and soft spheres with numbers in the range of 5 to 100 atoms. Comparisons were made with predictions of the LiebLiniger equation of state.

•Jun 18, 2007•0 citations

Fermionization of a bosonic gas under highly elongated confinement: A diffusion quantum Monte Carlo study

D. Blume

The diffusion quantum Monte Carlo technique is used to solve the many-body Schr\"odinger equation fully quantum mechanically and nonperturbatively for bosonic atomic gases in cigar-shaped confining potentials. By varying the aspect ratio of the confining potential from 1 (spherical trap) to 10 000 (highly elongated trap), we characterize the transition from the three-dimensional regime to the (quasi-)one-dimensional regime. Our results confirm that the bosonic gas undergoes ``fermionization'' for large aspect ratios. Importantly, many-body correlations are included explicitly in our approach.

arXiv:cond-mat/0206244•Physical Review A•Nov 15, 2002•36 citations

Quantum Monte Carlo study of the three- to one-dimensional crossover for a trapped Bose gas

G. E. Astrakharchik, S. Giorgini

We investigate the crossover from three to one dimension in a Bose gas confined in highly anisotropic traps. By using quantum Monte Carlo techniques, we solve the many-body Schr\"odinger equation for the ground state and obtain exact results for the energy per particle and the mean square radii of the cloud in the transverse and longitudinal direction. Results are compared with the predictions of mean-field theory obtained from the Gross-Pitaevskii equation and with the one-dimensional Lieb-Liniger equation of state. We explicitly prove the occurrence of important beyond mean-field effects, including the appearance of Fermi-like properties as the system enters the Tonks gas regime.

arXiv:cond-mat/0207613•Physical Review A•Nov 15, 2002•39 citations

Quantum Monte Carlo Method For Boson Ground States: Application To Trapped Bosons With Attractive And Repulsive Interactions

Wirawan Purwanto

We formulate a quantum Monte Carlo (QMC) method for calculating the ground state of many-boson systems. The method is based on a field-theoretical approach, and is closely related to existing fermion auxiliary-field QMC methods which are applied in several fields of physics. The ground-state projection is implemented as a branching random walk in the space of permanents consisting of identical single-particle orbitals. Any single-particle basis can be used, and the method is in principle exact. We apply this method to an atomic Bose gas, where the atoms interact via an attractive or repulsive contact two-body potential parametrized by the s-wave scattering length. We choose as the single-particle basis a real-space grid. We compare with exact results in small systems, and arbitrarily-sized systems of untrapped bosons with attractive interactions in one dimension, where analytical solutions exist. Our method provides a way to systematically improve upon the mean-field Gross-Pitaevskii (GP) method while using the same framework, capturing interaction and correlation effects with a stochastic, coherent ensemble of non-interacting solutions. to study the role of many-body correlations in the ground state, we examine the properties of the gas, such as the energetics, condensate fraction, and the density and momentum distributions as a function of the number of particles and the scattering length, both in the homogenous and trapped gases. Results are presented for systems with up to 1000 bosons. Comparing our results to the mean-field GP results, we find significant departure from mean field at large positive scattering lengths. The many-body correlations tend to increase the kinetic energy and reduce the interaction energy compared to GP. In the trapped gases, this results in a qualitatively different behavior as a function of the scattering length. Possible experimental observation is discussed.

•Jan 1, 2005•0 citations

Bose-Einstein condensation in trapped bosons: A variational Monte Carlo analysis

Jonathan L. DuBois, H. R. Glyde

Several properties of trapped hard-sphere bosons are evaluated using variational Monte Carlo techniques. A trial wave function composed of a renormalized single-particle Gaussian and a hard-sphere Jastrow function for pair correlations is used to study the sensitivity of condensate and noncondensate properties to the hard-sphere radius and the number of particles. Special attention is given to diagonalizing the one-body density matrix and obtaining the corresponding single-particle natural orbitals and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single-particle orbital with the highest occupation. The effect of interaction on other quantities such as the ground-state energy, the mean radial displacement, and the momentum distribution is calculated as well. Results are compared with mean-field theory in the dilute limit.

arXiv:cond-mat/0008368•Physical Review A•Jan 5, 2001•83 citations

One-dimensional multicomponent Fermi gas in a trap: quantum Monte Carlo study

N Matveeva, G E Astrakharchik

A one-dimensional world is very unusual as there is an interplay between quantum statistics and geometry, and a strong short-range repulsion between atoms mimics Fermi exclusion principle, fermionizing the system. Instead, a system with a large number of components with a single atom in each, on the opposite acquires many bosonic properties. We study the ground-state properties of a multicomponent repulsive Fermi gas trapped in a harmonic trap by a fixed-node diffusion Monte Carlo method. The interaction between all components is considered to be the same. We investigate how the energetic properties (energy, contact) and correlation functions (density profile and momentum distribution) evolve as the number of components is changed. It is shown that the system fermionizes in the limit of strong interactions. Analytical expressions are derived in the limit of weak interactions within the local density approximation for an arbitrary number of components and for one plus one particle using an exact solution.

arXiv:1603.08794•New Journal of Physics•Jun 22, 2016•27 citations
Abstract These two papers, published back to back, provide superb examples of the use of a quantum Monte Carlo method to obtain exact solutions for a problem difficult to treat by other methods. The problem is that of a bosonic atomic gas confined in a cigarshaped trap. As the cigar is narrowed the atoms are less able to pass each other, their behavior approaches that of fermions, and they are said to exhibit “fermionization.” Using diffusion QMC the authors were able to determine the ground-state energies, examine structural properties, confirm that fermionization can occur, and predict conditions under which it might be observed. The calculations by Blume were carried out for 2-20 atoms confined in axially symmetric traps of varied aspect ratios. The confining potential for each atom was given by Vk = CpPl + Czzl (radial and axial positions squared). The atom-atom interactions were simple hard-sphere potentials. The (nodeless) guided diffusion calculations used a trial wave function of the Jastrow type, a product of atom-trap terms and atom-atom terms. The calculations by Astrakharchik and Giorgini were carried out similarly but included both hard and soft spheres with numbers in the range of 5 to 100 atoms. Comparisons were made with predictions of the Lieb Liniger equation of state.
Abstract These two papers, published back to back, provide superb examples of the use of a quantum Monte Carlo method to obtain exact solutions for a problem difficult to treat by other methods. The problem is that of a bosonic atomic gas confined in a cigarshaped trap. As the cigar is narrowed the atoms are less able to pass each other, their behavior approaches that of fermions, and they are said to exhibit “fermionization.” Using diffusion QMC the authors were able to determine the ground-state energies, examine structural properties, confirm that fermionization can occur, and predict conditions under which it might be observed. The calculations by Blume were carried out for 2-20 atoms confined in axially symmetric traps of varied aspect ratios. The confining potential for each atom was given by Vk = CpPl + Czzl (radial and axial positions squared). The atom-atom interactions were simple hard-sphere potentials. The (nodeless) guided diffusion calculations used a trial wavefunction of the Jastrow type, a product of atom-trap terms and atom-atom terms. The calculations by Astrakharchik and Giorgini were carried out similarly but included both hard and soft spheres with numbers in the range of 5 to 100 atoms. Comparisons were made with predictions of the LiebLiniger equation of state.
The diffusion quantum Monte Carlo technique is used to solve the many-body Schr\"odinger equation fully quantum mechanically and nonperturbatively for bosonic atomic gases in cigar-shaped confining potentials. By varying the aspect ratio of the confining potential from 1 (spherical trap) to 10 000 (highly elongated trap), we characterize the transition from the three-dimensional regime to the (quasi-)one-dimensional regime. Our results confirm that the bosonic gas undergoes ``fermionization'' for large aspect ratios. Importantly, many-body correlations are included explicitly in our approach.
We investigate the crossover from three to one dimension in a Bose gas confined in highly anisotropic traps. By using quantum Monte Carlo techniques, we solve the many-body Schr\"odinger equation for the ground state and obtain exact results for the energy per particle and the mean square radii of the cloud in the transverse and longitudinal direction. Results are compared with the predictions of mean-field theory obtained from the Gross-Pitaevskii equation and with the one-dimensional Lieb-Liniger equation of state. We explicitly prove the occurrence of important beyond mean-field effects, including the appearance of Fermi-like properties as the system enters the Tonks gas regime.
We formulate a quantum Monte Carlo (QMC) method for calculating the ground state of many-boson systems. The method is based on a field-theoretical approach, and is closely related to existing fermion auxiliary-field QMC methods which are applied in several fields of physics. The ground-state projection is implemented as a branching random walk in the space of permanents consisting of identical single-particle orbitals. Any single-particle basis can be used, and the method is in principle exact. We apply this method to an atomic Bose gas, where the atoms interact via an attractive or repulsive contact two-body potential parametrized by the s-wave scattering length. We choose as the single-particle basis a real-space grid. We compare with exact results in small systems, and arbitrarily-sized systems of untrapped bosons with attractive interactions in one dimension, where analytical solutions exist. Our method provides a way to systematically improve upon the mean-field Gross-Pitaevskii (GP) method while using the same framework, capturing interaction and correlation effects with a stochastic, coherent ensemble of non-interacting solutions. to study the role of many-body correlations in the ground state, we examine the properties of the gas, such as the energetics, condensate fraction, and the density and momentum distributions as a function of the number of particles and the scattering length, both in the homogenous and trapped gases. Results are presented for systems with up to 1000 bosons. Comparing our results to the mean-field GP results, we find significant departure from mean field at large positive scattering lengths. The many-body correlations tend to increase the kinetic energy and reduce the interaction energy compared to GP. In the trapped gases, this results in a qualitatively different behavior as a function of the scattering length. Possible experimental observation is discussed.
Several properties of trapped hard-sphere bosons are evaluated using variational Monte Carlo techniques. A trial wave function composed of a renormalized single-particle Gaussian and a hard-sphere Jastrow function for pair correlations is used to study the sensitivity of condensate and noncondensate properties to the hard-sphere radius and the number of particles. Special attention is given to diagonalizing the one-body density matrix and obtaining the corresponding single-particle natural orbitals and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single-particle orbital with the highest occupation. The effect of interaction on other quantities such as the ground-state energy, the mean radial displacement, and the momentum distribution is calculated as well. Results are compared with mean-field theory in the dilute limit.
A one-dimensional world is very unusual as there is an interplay between quantum statistics and geometry, and a strong short-range repulsion between atoms mimics Fermi exclusion principle, fermionizing the system. Instead, a system with a large number of components with a single atom in each, on the opposite acquires many bosonic properties. We study the ground-state properties of a multicomponent repulsive Fermi gas trapped in a harmonic trap by a fixed-node diffusion Monte Carlo method. The interaction between all components is considered to be the same. We investigate how the energetic properties (energy, contact) and correlation functions (density profile and momentum distribution) evolve as the number of components is changed. It is shown that the system fermionizes in the limit of strong interactions. Analytical expressions are derived in the limit of weak interactions within the local density approximation for an arbitrary number of components and for one plus one particle using an exact solution.