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:0807.3366 · Physical Review A

Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons

Marvin D. Girardeau, Anna Minguzzi

Published Mar 12, 2009• 23 citations
arXivHTMLPDF

Abstract

The low-lying energy eigenstates of a one-dimensional (1D) system of many impenetrable point bosons and one moving impurity particle with repulsive zero-range impurity-boson interaction are found for all values of the impurity-boson mass ratio and coupling constant. The moving entity is a polaronlike composite object consisting of the impurity clothed by a comoving gray soliton. The special case with impurity-boson interaction of point hard-core form and impurity-boson mass ratio ${m}_{i}/m$ unity is first solved exactly as a special case of a previous Fermi-Bose (FB) mapping treatment of soluble 1D Bose-Fermi mixture problems. Then a more general treatment is given using second quantization for the bosons and the second-quantized form of the FB mapping, eliminating the impurity degrees of freedom by a Lee-Low-Pines canonical transformation. This yields the exact ground state (total linear momentum $q=0$) and exact boson-impurity distribution function in the thermodynamic limit for arbitrary ${m}_{i}/m$ and arbitrary impurity-boson interaction strength. These results are then extended to states with $q>0$.

DOI
10.1103/physreva.79.033610

Related papers

Reply to “Comment on ‘Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons’ ”

Marvin D. Girardeau, Anna Minguzzi

In their Comment Giraud and Combescot (GC) [Phys. Rev. A 82, 037603 (2010)] point out that the contribution to the impurity-boson distribution function ${\ensuremath{\rho}}_{\mathit{bi}}(x\ensuremath{-}y)$ of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but our results for ${\ensuremath{\rho}}_{\mathit{bi}}$ are highly accurate for large impurity-boson mass ratio ${m}_{i}/m$, for all values of $x\ensuremath{-}y$ and boson-impurity coupling constant.

Physical Review A•Sep 7, 2010•2 citations

Motion of an Impurity Particle in a Boson Superfluid

Marvin D. Girardeau

The problem of the low-lying spectrum of a system of many bosons and one impurity particle interacting by repulsive, central, two-body forces is treated by first eliminating the dynamical variables of the impurity in terms of an added effective boson-boson interaction, and then treating the boson system by an extension of Bogolubov's method. In this way various physical properties of the clothed impurity particle, including its dispersion relation and effective mass, are obtained; singularities associated with the onset of acoustical wave drag as the impurity speed reaches the speed of sound in the boson medium are predicted. The parameters measuring the smallness of the corrections to the above results are shown to be the dimensionless boson-boson interaction, the dimensionless boson-impurity interaction, and the boson-impurity mass ratio. The treatment is then adapted to the case of hard spheres at low density by employing the Huang-Yang-Lee pseudopotential method; the results are valid if the dimensionless boson density and the boson-impurity mass ratio are small. A few remarks are made concerning the connection of the models treated with experimentally accessible results.

The Physics of Fluids•Mar 1, 1961•32 citations

Comment on “Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons”

S. Giraud, R. Combescot

Very recently Girardeau and Minguzzi [Phys. Rev. A 79, 033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core bosons. In particular they dealt with the general case where the mass of the impurity is different from the mass of the bosons and the impurity-boson interaction is not necessarily infinitely repulsive. We show that one of their initial steps is unjustified, contradicting known exact results. Their results in the general case apply only actually when the mass of the impurity is infinite.

arXiv:1002.4366•Physical Review A•Sep 7, 2010•2 citations

Reply to arXiv:1002.4366, "Comment on `Motion of an impurity in an ultracold quasi-one-dimensional gas of hard-core bosons`", by S. Giraud and R. Combescot

Marvin D. Girardeau, Anna Minguzzi

In their Comment [1] Giraud and Combescot point out that the contribution to the impurity-boson distribution function $ρ_{bi}(x-y)$ of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but nevertheless our results for $ρ_{bi}$ are highly accurate for large impurity-boson mass ratio $m_i/m$ and remain qualitatively correct for all values of $m_i/m$ and all values of the boson-impurity coupling constant.

arXiv:1003.0652•Mar 2, 2010•1 citation

Quantum Monte Carlo study of the Bose-polaron problem in a one-dimensional gas with contact interactions

L. Parisi, S. Giorgini

We present a theoretical study based upon quantum Monte Carlo methods of the Bose polaron in one-dimensional systems with contact interactions. In this instance of the problem of a single impurity immersed in a quantum bath, the medium is a Lieb-Liniger gas of bosons ranging from the weakly interacting to the Tonks-Girardeau regime, whereas the impurity is coupled to the bath via a different contact potential, producing both repulsive and attractive interactions. Both the case of a mobile impurity, having the same mass as the particles in the medium, and the case of a static impurity with infinite mass are considered. We make use of numerical techniques that allow us to calculate the ground-state energy of the impurity, its effective mass, and the contact parameter between the impurity and the bath. These quantities are investigated as a function of the strength of interactions between the impurity and the bath and within the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. This heavy impurity hardly moves within the medium, thereby realizing the ``self-localization'' regime of the Landau-Pekar polaron. Furthermore, we compare our results with predictions of perturbation theory valid for weak interactions and with exact solutions available when the bosons in the medium behave as impenetrable particles.

arXiv:1612.01322•Physical Review A•Feb 21, 2017•68 citations

Ultracold bosons in lattices with binary disorder

Konstantin V. Krutitsky, Michael Thorwart, Reinhold Egger +1 more

Quantum phases of ultracold bosons with repulsive interactions in lattices in the presence of quenched disorder are investigated. The disorder is assumed to be caused by the interaction of the bosons with impurity atoms having a large effective mass. The system is described by the Bose-Hubbard Hamiltonian with random on-site energies which have a discrete binary probability distribution. The phase diagram at zero temperature is calculated using several methods like a strong-coupling expansion, an exact numerical diagonalization, and a Bose-Fermi mapping valid in the hard-core limit. It is shown that the Mott-insulator phase exists for any strength of disorder in contrast to the case of continuous probability distribution. We find that the compressibility of the Bose glass phase varies in a wide range and can be extremely low. Furthermore, we evaluate experimentally accessible quantities like the momentum distribution, the static and dynamic structure factors, and the density of excited states. The influence of finite temperature is discussed as well.

arXiv:0801.2343•Physical Review A•May 16, 2008•29 citations
The low-lying energy eigenstates of a one-dimensional (1D) system of many impenetrable point bosons and one moving impurity particle with repulsive zero-range impurity-boson interaction are found for all values of the impurity-boson mass ratio and coupling constant. The moving entity is a polaronlike composite object consisting of the impurity clothed by a comoving gray soliton. The special case with impurity-boson interaction of point hard-core form and impurity-boson mass ratio mi/m{m}_{i}/mmi​/m unity is first solved exactly as a special case of a previous Fermi-Bose (FB) mapping treatment of soluble 1D Bose-Fermi mixture problems. Then a more general treatment is given using second quantization for the bosons and the second-quantized form of the FB mapping, eliminating the impurity degrees of freedom by a Lee-Low-Pines canonical transformation. This yields the exact ground state (total linear momentum q=0q=0q=0) and exact boson-impurity distribution function in the thermodynamic limit for arbitrary mi/m{m}_{i}/mmi​/m and arbitrary impurity-boson interaction strength. These results are then extended to states with q>0q>0q>0.
In their Comment Giraud and Combescot (GC) [Phys. Rev. A 82, 037603 (2010)] point out that the contribution to the impurity-boson distribution function ${\ensuremath{\rho}}_{\mathit{bi}}(x\ensuremath{-}y)$ of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but our results for ${\ensuremath{\rho}}_{\mathit{bi}}$ are highly accurate for large impurity-boson mass ratio mi/m{m}_{i}/mmi​/m, for all values of $x\ensuremath{-}y$ and boson-impurity coupling constant.
The problem of the low-lying spectrum of a system of many bosons and one impurity particle interacting by repulsive, central, two-body forces is treated by first eliminating the dynamical variables of the impurity in terms of an added effective boson-boson interaction, and then treating the boson system by an extension of Bogolubov's method. In this way various physical properties of the clothed impurity particle, including its dispersion relation and effective mass, are obtained; singularities associated with the onset of acoustical wave drag as the impurity speed reaches the speed of sound in the boson medium are predicted. The parameters measuring the smallness of the corrections to the above results are shown to be the dimensionless boson-boson interaction, the dimensionless boson-impurity interaction, and the boson-impurity mass ratio. The treatment is then adapted to the case of hard spheres at low density by employing the Huang-Yang-Lee pseudopotential method; the results are valid if the dimensionless boson density and the boson-impurity mass ratio are small. A few remarks are made concerning the connection of the models treated with experimentally accessible results.
Very recently Girardeau and Minguzzi [Phys. Rev. A 79, 033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core bosons. In particular they dealt with the general case where the mass of the impurity is different from the mass of the bosons and the impurity-boson interaction is not necessarily infinitely repulsive. We show that one of their initial steps is unjustified, contradicting known exact results. Their results in the general case apply only actually when the mass of the impurity is infinite.
In their Comment [1] Giraud and Combescot point out that the contribution to the impurity-boson distribution function ρbi(x−y)ρ_{bi}(x-y)ρbi​(x−y) of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but nevertheless our results for ρbiρ_{bi}ρbi​ are highly accurate for large impurity-boson mass ratio mi/mm_i/mmi​/m and remain qualitatively correct for all values of mi/mm_i/mmi​/m and all values of the boson-impurity coupling constant.
We present a theoretical study based upon quantum Monte Carlo methods of the Bose polaron in one-dimensional systems with contact interactions. In this instance of the problem of a single impurity immersed in a quantum bath, the medium is a Lieb-Liniger gas of bosons ranging from the weakly interacting to the Tonks-Girardeau regime, whereas the impurity is coupled to the bath via a different contact potential, producing both repulsive and attractive interactions. Both the case of a mobile impurity, having the same mass as the particles in the medium, and the case of a static impurity with infinite mass are considered. We make use of numerical techniques that allow us to calculate the ground-state energy of the impurity, its effective mass, and the contact parameter between the impurity and the bath. These quantities are investigated as a function of the strength of interactions between the impurity and the bath and within the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. This heavy impurity hardly moves within the medium, thereby realizing the ``self-localization'' regime of the Landau-Pekar polaron. Furthermore, we compare our results with predictions of perturbation theory valid for weak interactions and with exact solutions available when the bosons in the medium behave as impenetrable particles.
Quantum phases of ultracold bosons with repulsive interactions in lattices in the presence of quenched disorder are investigated. The disorder is assumed to be caused by the interaction of the bosons with impurity atoms having a large effective mass. The system is described by the Bose-Hubbard Hamiltonian with random on-site energies which have a discrete binary probability distribution. The phase diagram at zero temperature is calculated using several methods like a strong-coupling expansion, an exact numerical diagonalization, and a Bose-Fermi mapping valid in the hard-core limit. It is shown that the Mott-insulator phase exists for any strength of disorder in contrast to the case of continuous probability distribution. We find that the compressibility of the Bose glass phase varies in a wide range and can be extremely low. Furthermore, we evaluate experimentally accessible quantities like the momentum distribution, the static and dynamic structure factors, and the density of excited states. The influence of finite temperature is discussed as well.