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

Physical Review A

Identical particle scattering from a weakly coupled Bose-Einstein condensed gas

A. Wynveen, A. K. Setty, A. Howard, J. W. Halleý, C. E. Campbell

Published Jul 5, 2000• 11 citations
Publisher

Abstract

We calculate the scattering states and cross sections for a Bose-Einstein condensed dilute gas trapped in a spherical square well of finite depth. The interactions are treated in the scattering length approximation. We solve the Gross-Pitaevskii equation and the Bogoliubov equations for bound and scattering states. The results show that there are transparency effects reminiscent of those conjectured to occur for strongly coupled systems. When incident particle wavelengths $\ensuremath{\lambda}$ are comparable to the well size a, exchange induced transparency enhancement is dramatic only for particular combinations of well depth, interaction strength, and particle number. For particles with large momenta $(a/\ensuremath{\lambda}\ensuremath{\gg}1),$ however, exchange with the condensate results in enhanced transmission for all coupling strengths. We calculated the rate of decay of the scattering states to leading order in anharmonic corrections to the Bogoliubov approximation and found the corresponding inelastic cross sections to be extremely small.

DOI
10.1103/physreva.62.023602

Related papers

Signatures of Bose-Einstein condensation in very low energy atomic scattering from trapped gases

A. Wynveen, J. W. Halleý

We report wave packet analysis of scattering of identical particles from for a Bose condensed dilute gas trapped in a spherical square well of finite depth, using solutions to the Bogoliubov equations which we previously reported. Simulations show clearly that exchange effects lead to significant amplitudes for passage of the particle through the condensate, a transparency effect, accounting for the extremely small cross sections previously calculated. The interactions are treated in the scattering length approximation. The states exhibiting enhanced transparency appear to arise from a kind of self stabilizing Ramsauer-Townsend effect. We also observe anomalously large scattering of the identical particles from the condensate for a few other combinations of coupling strength and k vector. We show that these scattering states associated with large cross section are resonance states in which there is a large enhancement of the amplitude of the scattering state in the region of the condensate, corresponding to a state which is nearly bound. We also exhibit simulations of the scattering density at large k, where we previously consistently observed that exchange reduced the cross section. The simulations show enhanced transparency.

Laser Physics•Jan 1, 2002•0 citations

Weakly interacting Bose gas with two-body losses

Chang Liu, Zhe-Yu Shi, Ce Wang

We study the many-body dynamics of weakly interacting Bose gases with two-particle losses. We show that both the two-body interactions and losses in atomic gases may be tuned by controlling the inelastic scattering process between atoms by an optical Feshbach resonance. Interestingly, the low-energy behavior of the scattering amplitude is governed by a single parameter, i.e. the complex s s -wave scattering length a_c a c . The many-body dynamics are thus described by a Lindblad master equation with complex scattering length. We solve this equation by applying the Bogoliubov approximation in analogy to the closed systems. Various peculiar dynamical properties are discovered, some of them may be regarded as the dissipative counterparts of the celebrated results in closed Bose gases. For example, we show that the next-order correction to the mean-field particle decay rate is to the order of |n a_c^{3}|^{1/2} | n a c 3 | 1 / 2 , which is an analogy of the Lee-Huang-Yang correction of Bose gases. It is also found that there exists a dynamical symmetry of symplectic group Sp (4,\mathbb{C}) ( 4 , ℂ ) in the quadratic Bogoliubov master equation, which is an analogy of the SU(1,1) dynamical symmetry of the corresponding closed system. We further confirmed the validity of the Bogoliubov approximation by comparing its results with a full numerical calculation in a double-well toy model. Generalizations of other alternative approaches such as the dissipative version of the Gross-Pitaevskii equation and hydrodynamic theory are also discussed in the last.

arXiv:2209.10427•SciPost Physics•May 1, 2024•5 citations

Behavior of trapped ultracold dilute Bose gases at large scattering length near a Feshbach resonance

M. L. Lekala, Barnali Chakrabarti, Gaotsiwe Joel Rampho +3 more

We calculate the ground-state energy and the collective excitation frequency of trapped bosons at large scattering length interacting via the realistic two-body van der Waals potential. Our many-body method keeps two-body correlations produced by all interacting pairs. When the scattering length is small compared to the trap size and the number of bosons in the trap is of the order of a few thousands, the mean-field results are in good agreement with the many-body results. However for large particle numbers, even when the condensate is sufficiently dilute, the interatomic correlation comes into the picture. When the scattering length is quite large near the Feshbach resonance, the Bose gas becomes highly correlated. The many-body results are close to the Gross-Pitaevskii results for a small number of bosons, however, large deviations are noted in the large particle limit. We also calculate the lowest collective excitation and the interaction energy for large scattering lengths. The monopole excitation frequency exhibits a pronounced dependence on the scattering length. We also observe a universal behavior for the interaction energy at the limit of large scattering length.

Physical Review A•Feb 18, 2014•10 citations

Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature

Andreas Deuchert, Robert Seiringer, Jakob Yngvason

We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Gross–Pitaevskii (GP) limit where the trap frequency $${\omega}$$ , the temperature T, and the particle number N are related by $${N \sim (T / \omega)^{3} \to\infty}$$ while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose–Einstein condensation in the following sense: The one-particle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer.

arXiv:1803.05180•Communications in Mathematical Physics•Aug 30, 2018•26 citations

Scattering theory and equation of state of a spherical two-dimensional Bose gas

Andrea Tononi

We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies and for a radius much larger than the healing length, we express the contact interaction strength in terms of the $s$-wave scattering length. Adopting this relation, we are then able to regularize the zero-point energy of the spherical Bose gas and to obtain its equation of state, which includes the corrections due to the finite radius of the sphere and coincides with the flat-case result in the infinite-radius limit. We also provide a microscopic derivation of the superfluid density of the system, reproducing a result postulated in a previous work. Our results are relevant for modeling the ongoing microgravity experiments with two-dimensional bubble-trapped Bose-Einstein condensates.

arXiv:2201.06572•Physical Review A•Feb 24, 2022•19 citations

DILUTE BOSE-EINSTEIN CONDENSATE IN A TRAP: CHARACTERISTIC LENGTHS AND CRITICAL VELOCITIES

Alexander L. Fetter

The Bogoliubov approximation and the Gross-Pitaevskii equation characterize the effect of repulsive interactions on a dilute ideal Bose-Einstein gas in a spherical harmonic trap. For large N, the interactions expand the condensate relative to an ideal Bose gas; both the speed of sound and critical angular velocity Ωc1 for creation of a quantized vortex depend crucially on the interparticle repulsion through the coherence length ξ.

arXiv:cond-mat/9709207•International Journal of Modern Physics B•Mar 10, 1999•3 citations
We calculate the scattering states and cross sections for a Bose-Einstein condensed dilute gas trapped in a spherical square well of finite depth. The interactions are treated in the scattering length approximation. We solve the Gross-Pitaevskii equation and the Bogoliubov equations for bound and scattering states. The results show that there are transparency effects reminiscent of those conjectured to occur for strongly coupled systems. When incident particle wavelengths \ensuremathλ\ensuremath{\lambda}\ensuremathλ are comparable to the well size a, exchange induced transparency enhancement is dramatic only for particular combinations of well depth, interaction strength, and particle number. For particles with large momenta (a/\ensuremathλ\ensuremath≫1),(a/\ensuremath{\lambda}\ensuremath{\gg}1),(a/\ensuremathλ\ensuremath≫1), however, exchange with the condensate results in enhanced transmission for all coupling strengths. We calculated the rate of decay of the scattering states to leading order in anharmonic corrections to the Bogoliubov approximation and found the corresponding inelastic cross sections to be extremely small.
We report wave packet analysis of scattering of identical particles from for a Bose condensed dilute gas trapped in a spherical square well of finite depth, using solutions to the Bogoliubov equations which we previously reported. Simulations show clearly that exchange effects lead to significant amplitudes for passage of the particle through the condensate, a transparency effect, accounting for the extremely small cross sections previously calculated. The interactions are treated in the scattering length approximation. The states exhibiting enhanced transparency appear to arise from a kind of self stabilizing Ramsauer-Townsend effect. We also observe anomalously large scattering of the identical particles from the condensate for a few other combinations of coupling strength and k vector. We show that these scattering states associated with large cross section are resonance states in which there is a large enhancement of the amplitude of the scattering state in the region of the condensate, corresponding to a state which is nearly bound. We also exhibit simulations of the scattering density at large k, where we previously consistently observed that exchange reduced the cross section. The simulations show enhanced transparency.
We study the many-body dynamics of weakly interacting Bose gases with two-particle losses. We show that both the two-body interactions and losses in atomic gases may be tuned by controlling the inelastic scattering process between atoms by an optical Feshbach resonance. Interestingly, the low-energy behavior of the scattering amplitude is governed by a single parameter, i.e. the complex s s -wave scattering length a_c a c . The many-body dynamics are thus described by a Lindblad master equation with complex scattering length. We solve this equation by applying the Bogoliubov approximation in analogy to the closed systems. Various peculiar dynamical properties are discovered, some of them may be regarded as the dissipative counterparts of the celebrated results in closed Bose gases. For example, we show that the next-order correction to the mean-field particle decay rate is to the order of |n a_c^{3}|^{1/2} | n a c 3 | 1 / 2 , which is an analogy of the Lee-Huang-Yang correction of Bose gases. It is also found that there exists a dynamical symmetry of symplectic group Sp (4,\mathbb{C}) ( 4 , ℂ ) in the quadratic Bogoliubov master equation, which is an analogy of the SU(1,1) dynamical symmetry of the corresponding closed system. We further confirmed the validity of the Bogoliubov approximation by comparing its results with a full numerical calculation in a double-well toy model. Generalizations of other alternative approaches such as the dissipative version of the Gross-Pitaevskii equation and hydrodynamic theory are also discussed in the last.
We calculate the ground-state energy and the collective excitation frequency of trapped bosons at large scattering length interacting via the realistic two-body van der Waals potential. Our many-body method keeps two-body correlations produced by all interacting pairs. When the scattering length is small compared to the trap size and the number of bosons in the trap is of the order of a few thousands, the mean-field results are in good agreement with the many-body results. However for large particle numbers, even when the condensate is sufficiently dilute, the interatomic correlation comes into the picture. When the scattering length is quite large near the Feshbach resonance, the Bose gas becomes highly correlated. The many-body results are close to the Gross-Pitaevskii results for a small number of bosons, however, large deviations are noted in the large particle limit. We also calculate the lowest collective excitation and the interaction energy for large scattering lengths. The monopole excitation frequency exhibits a pronounced dependence on the scattering length. We also observe a universal behavior for the interaction energy at the limit of large scattering length.
We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Gross–Pitaevskii (GP) limit where the trap frequency ω{\omega}ω , the temperature T, and the particle number N are related by N∼(T/ω)3→∞{N \sim (T / \omega)^{3} \to\infty}N∼(T/ω)3→∞ while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose–Einstein condensation in the following sense: The one-particle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer.
We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies and for a radius much larger than the healing length, we express the contact interaction strength in terms of the sss-wave scattering length. Adopting this relation, we are then able to regularize the zero-point energy of the spherical Bose gas and to obtain its equation of state, which includes the corrections due to the finite radius of the sphere and coincides with the flat-case result in the infinite-radius limit. We also provide a microscopic derivation of the superfluid density of the system, reproducing a result postulated in a previous work. Our results are relevant for modeling the ongoing microgravity experiments with two-dimensional bubble-trapped Bose-Einstein condensates.