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

International Journal of Modern Physics B

QUANTIZED HYDRODYNAMIC THEORY OF BOSONS IN QUASI-ONE-DIMENSIONAL HARMONIC TRAP

Tarun Kanti Ghosh

Published Dec 27, 2006• 13 citations
Publisher

Abstract

We analytically study effects of density and phase fluctuations of quasi-one-dimensional degenerate atomic Bose gases in the mean-field as well as in the hard-core bosons regimes. We obtain the analytic expressions for dynamic structure factors in both the regimes. We also calculate single-particle density matrix and momentum distribution by taking care of the phase fluctuations upto fourth-order term, the density fluctuations as well as the non-condensate density in both the regimes. In the mean-field regime, there is a long-tail in the momentum distributions at large temperature, which can be used to identify the quasi-condensate from a pure condensate. The single-particle correlation functions of hard-core bosons is almost zero even at zero temperature due to the fermionization of the bosonic systems. Two-particle correlation function in the hard-core bosons regime shows many deep valleys at various relative separations. These valleys at various relative separations imply shell structure due to the Pauli blocking in real space.

DOI
10.1142/s0217979206035783

Related papers

Quantized Hydrodynamic Theory of One-Dimensional Hard Core Bosons

Tarun Kanti Ghosh

We present a quantized hydrodynamic theory and its applications of one-dimensional hard-core bosons in a harmonic trap. Quantizing the Hamiltonian of a trapped hard-core bosons and diagonalize it in terms of the phase and density fluctuations associated with the Bose field operator. As an applications, we calculate discrete energy spectrum, dynamic structure factor, momentum transferred by a two-photon Bragg pulse, single-particle density matrix, momentum distribution, and two-particle correlation function. The dynamic structure factor has multiple peaks due to the discrete nature of the energy spectrum which can be observed by a two-photon Bragg pulse with long duration. The coherence length at zero temperature is very small due to the "fermionization" of the system. We also compute the momentum distributions which has oscillatory behavior at large momentum. The pair distribution function shows that there are many deep valleys at various relative separations which implies shell structure due to the Pauli blocking in real space.

arXiv:cond-mat/0402080•Feb 3, 2004•1 citation

Quasi-one dimensional degenerate Bose gases

Tarun Kanti Ghosh, Abdus Salam

Motivated by the MIT experiment [Gorlitz {\em et al.}, Phys. Rev. Lett. {\bf 87}, 130402 (2001)], we analytically study the effect of density and phase fluctuations on various observables in a quasi one-dimensional degenerate Bose gases. Quantizing the Gross-Pitaevskii Hamiltonian and diagonalize it in terms of the normal modes associated with the density and phase fluctuations of a quasi-one dimensional Bose gas. We calculate dynamic structure factor $S(q,\omega)$ from low-energy condensate density fluctuations and find that there are multiple peaks in $S(q,\omega)$ for a given momentum $q$ due to the discrete energy spectrum. These multiple peaks can be resolved by a two-photon Bragg pulse with a long duration which transfer the momentum to the system. We calculate the momentum transferred $ P_z(t)$ by using the phase-density representation of the Bose order parameter. We also calculate the single-particle density matrix, phase coherence length, and momentum distribution by taking care of the phase fluctuations upto fourth-order term as well as the density fluctuations. Our studies on coherence properties shows that 1D Bose gases of MIT experiment do not form a true condensate, but it can be obtained by a moderate changes of the current experimental parameters.

•Jan 1, 2008•0 citations

Quasi-one dimensional degenerate Bose gas

Tarun Kanti Ghosh

Motivated by the MIT experiment [Gorlitz {\em et al.}, Phys. Rev. Lett. {\bf 87}, 130402 (2001)], we analytically study the effect of density and phase fluctuations on various observables in a quasi one-dimensional degenerate Bose gases. Quantizing the Gross-Pitaevskii Hamiltonian and diagonalize it in terms of the normal modes associated with the density and phase fluctuations of a quasi-one dimensional Bose gas. We calculate dynamic structure factor $S(q,ω)$ from low-energy condensate density fluctuations and find that there are multiple peaks in $S(q,ω)$ for a given momentum $q$ due to the discrete energy spectrum. These multiple peaks can be resolved by a two-photon Bragg pulse with a long duration which transfer the momentum to the system. We calculate the momentum transferred $ P_z(t)$ by using the phase-density representation of the Bose order parameter. We also calculate the single-particle density matrix, phase coherence length, and momentum distribution by taking care of the phase fluctuations upto fourth-order term as well as the density fluctuations. Our studies on coherence properties shows that 1D Bose gases of MIT experiment do not form a true condensate, but it can be obtained by a moderate changes of the current experimental parameters.

arXiv:cond-mat/0402079•Feb 3, 2004•0 citations

Ground-state properties of hard-core bosons in one-dimensional harmonic traps

T. Papenbrock

The one-particle density matrices for hard-core bosons in a one-dimensional harmonic trap are computed numerically for systems with up to 160 bosons. Diagonalization of the density matrix shows that the many-body ground state is not Bose-Einstein condensed. The ground-state occupation, the amplitude of the lowest natural orbital, and the zero momentum peak height scale as powers of the particle number, and the corresponding exponents are related to each other. Close to its diagonal, the density matrix for hard-core bosons is similar to that of noninteracting fermions.

arXiv:cond-mat/0209300•Physical Review A•Apr 10, 2003•72 citations

Fermionization of a strongly interacting Bose-Fermi mixture in a one-dimensional harmonic trap

Bess Fang, Patrizia Vignolo, Christian Miniatura +1 more

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient $C$ is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.

arXiv:0809.4419•Physical Review A•Feb 26, 2009•20 citations

The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical

K. Bencheikh, Luis Miguel Nieto, L. U. Ancarani

Abstract For a harmonically trapped system consisting of two bosons in one spatial dimension with infinite contact repulsion (hard core bosons), we derive an expression for the one-body density matrix $$\rho _\mathrm{B}$$ ρ B in terms of center of mass and relative coordinates of the particles. The deviation from $$\rho _\mathrm{F}$$ ρ F , the density matrix for the two fermions case, can be clearly identified. Moreover, the obtained $$\rho _\mathrm{B}$$ ρ B allows us to derive a closed form expression of the corresponding momentum distribution $$n_\mathrm{B}(p)$$ n B ( p ) . We show how the result deviates from the noninteracting fermionic case, the deviation being associated with the short-range character of the interaction. Mathematically, our analytical momentum distribution is expressed in terms of one and two variables confluent hypergeometric functions. Our formula satisfies the correct normalization and possesses the expected behavior at zero momentum. It also exhibits the high momentum $$1/p^4 $$ 1 / p 4 tail with the appropriate Tan’s coefficient. Numerical results support our findings.

arXiv:2104.06693•The European Physical Journal Plus•Jul 1, 2021•0 citations
We analytically study effects of density and phase fluctuations of quasi-one-dimensional degenerate atomic Bose gases in the mean-field as well as in the hard-core bosons regimes. We obtain the analytic expressions for dynamic structure factors in both the regimes. We also calculate single-particle density matrix and momentum distribution by taking care of the phase fluctuations upto fourth-order term, the density fluctuations as well as the non-condensate density in both the regimes. In the mean-field regime, there is a long-tail in the momentum distributions at large temperature, which can be used to identify the quasi-condensate from a pure condensate. The single-particle correlation functions of hard-core bosons is almost zero even at zero temperature due to the fermionization of the bosonic systems. Two-particle correlation function in the hard-core bosons regime shows many deep valleys at various relative separations. These valleys at various relative separations imply shell structure due to the Pauli blocking in real space.
We present a quantized hydrodynamic theory and its applications of one-dimensional hard-core bosons in a harmonic trap. Quantizing the Hamiltonian of a trapped hard-core bosons and diagonalize it in terms of the phase and density fluctuations associated with the Bose field operator. As an applications, we calculate discrete energy spectrum, dynamic structure factor, momentum transferred by a two-photon Bragg pulse, single-particle density matrix, momentum distribution, and two-particle correlation function. The dynamic structure factor has multiple peaks due to the discrete nature of the energy spectrum which can be observed by a two-photon Bragg pulse with long duration. The coherence length at zero temperature is very small due to the "fermionization" of the system. We also compute the momentum distributions which has oscillatory behavior at large momentum. The pair distribution function shows that there are many deep valleys at various relative separations which implies shell structure due to the Pauli blocking in real space.
Motivated by the MIT experiment [Gorlitz {\em et al.}, Phys. Rev. Lett. {\bf 87}, 130402 (2001)], we analytically study the effect of density and phase fluctuations on various observables in a quasi one-dimensional degenerate Bose gases. Quantizing the Gross-Pitaevskii Hamiltonian and diagonalize it in terms of the normal modes associated with the density and phase fluctuations of a quasi-one dimensional Bose gas. We calculate dynamic structure factor S(q,ω)S(q,\omega)S(q,ω) from low-energy condensate density fluctuations and find that there are multiple peaks in S(q,ω)S(q,\omega)S(q,ω) for a given momentum qqq due to the discrete energy spectrum. These multiple peaks can be resolved by a two-photon Bragg pulse with a long duration which transfer the momentum to the system. We calculate the momentum transferred $ P_z(t)$ by using the phase-density representation of the Bose order parameter. We also calculate the single-particle density matrix, phase coherence length, and momentum distribution by taking care of the phase fluctuations upto fourth-order term as well as the density fluctuations. Our studies on coherence properties shows that 1D Bose gases of MIT experiment do not form a true condensate, but it can be obtained by a moderate changes of the current experimental parameters.
Motivated by the MIT experiment [Gorlitz {\em et al.}, Phys. Rev. Lett. {\bf 87}, 130402 (2001)], we analytically study the effect of density and phase fluctuations on various observables in a quasi one-dimensional degenerate Bose gases. Quantizing the Gross-Pitaevskii Hamiltonian and diagonalize it in terms of the normal modes associated with the density and phase fluctuations of a quasi-one dimensional Bose gas. We calculate dynamic structure factor S(q,ω)S(q,ω)S(q,ω) from low-energy condensate density fluctuations and find that there are multiple peaks in S(q,ω)S(q,ω)S(q,ω) for a given momentum qqq due to the discrete energy spectrum. These multiple peaks can be resolved by a two-photon Bragg pulse with a long duration which transfer the momentum to the system. We calculate the momentum transferred $ P_z(t)$ by using the phase-density representation of the Bose order parameter. We also calculate the single-particle density matrix, phase coherence length, and momentum distribution by taking care of the phase fluctuations upto fourth-order term as well as the density fluctuations. Our studies on coherence properties shows that 1D Bose gases of MIT experiment do not form a true condensate, but it can be obtained by a moderate changes of the current experimental parameters.
The one-particle density matrices for hard-core bosons in a one-dimensional harmonic trap are computed numerically for systems with up to 160 bosons. Diagonalization of the density matrix shows that the many-body ground state is not Bose-Einstein condensed. The ground-state occupation, the amplitude of the lowest natural orbital, and the zero momentum peak height scale as powers of the particle number, and the corresponding exponents are related to each other. Close to its diagonal, the density matrix for hard-core bosons is similar to that of noninteracting fermions.
We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient CCC is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.
Abstract For a harmonically trapped system consisting of two bosons in one spatial dimension with infinite contact repulsion (hard core bosons), we derive an expression for the one-body density matrix ρB\rho _\mathrm{B}ρB​ ρ B in terms of center of mass and relative coordinates of the particles. The deviation from ρF\rho _\mathrm{F}ρF​ ρ F , the density matrix for the two fermions case, can be clearly identified. Moreover, the obtained ρB\rho _\mathrm{B}ρB​ ρ B allows us to derive a closed form expression of the corresponding momentum distribution nB(p)n_\mathrm{B}(p)nB​(p) n B ( p ) . We show how the result deviates from the noninteracting fermionic case, the deviation being associated with the short-range character of the interaction. Mathematically, our analytical momentum distribution is expressed in terms of one and two variables confluent hypergeometric functions. Our formula satisfies the correct normalization and possesses the expected behavior at zero momentum. It also exhibits the high momentum 1/p41/p^4 1/p4 1 / p 4 tail with the appropriate Tan’s coefficient. Numerical results support our findings.