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:1503.08884 · Physical Review A

Damping of confined excitation modes of one-dimensional condensates in an optical lattice

C. Trallero‐Giner, Darío G. Santiago-Pérez, Ming-Chiang Chung, G. E. Marques, R. Cipolatti

Published Oct 5, 2015• 3 citations
arXivHTMLPDF

Abstract

We study the damping of the collective excitations of Bose-Einstein condensates in a harmonic trap potential loaded in an optical lattice. In the presence of a confining potential the system is inhomogeneous and the collective excitations are characterized by a set of discrete confined phononlike excitations. We derive a general convenient analytical description for the damping rate, which takes into account the trapping potential and the optical lattice for the Landau and Beliaev processes at any temperature $T$. At high temperature or weak spatial confinement, we show that both mechanisms display a linear dependence on $T$. In the quantum limit, we find that the Landau damping is exponentially suppressed at low temperatures and the total damping is independent of $T$. Our theoretical predictions for the damping rate under the thermal regime is in complete correspondence with the experimental values reported for the one-dimensional (1D) condensate of sodium atoms. We show that the laser intensity can tune the collision process, allowing a resonant effect for the condensate lifetime. Also, we study the influence of the attractive or repulsive nonlinear terms on the decay rate of the collective excitations. A general expression for the renormalized Goldstone frequency is obtained as a function of the 1D nonlinear self-interaction parameter, laser intensity, and temperature.

DOI
10.1103/physreva.92.042502

Related papers

Collective modes of trapped spinor Bose–Einstein condensates

C Trallero-Giner, Darío G. Santiago-Pérez, Vı́ctor Romero-Rochı́n +1 more

Abstract We study the structure of quasi-one-dimensional Bogoliubov–de Genes collective excitations of inhomogeneous F = 1 spinor Bose–Einstein condensates confined by a harmonic trap potential and loaded into an optical lattice. Employing a perturbative method, we report general analytical expressions for the polar and ferromagnetic confined collective oscillations. In both cases, the excited eigenfrequencies are given as functions of the effective 1D coupling constants, the trap frequency and the optical lattice parameters. While the presence of the trap yields quantized longitudinal collective modes, whose spectra depends on the collision scattering lengths, the optical lattice shifts their frequencies and, more importantly, yields tunable oscillations of the spin populations, for the even modes, as experimentally observed.

arXiv:1608.01020•Journal of Physics B Atomic Molecular and Optical Physics•Oct 23, 2017•0 citations

Excitations of Bose-Einstein condensates at finite temperatures

Martin Rusch, Rusch, Martin

Recent experimental observations of collective excitations of Bose condensed atomic vapours have stimulated interest in the microscopic description of the dynamics of a Bose-Einstein condensate confined in an external potential. We present a finite temperature field theory for collective excitations of trapped Bose-Einstein condensates and use a finite-temperature linear response formalism, which goes beyond the simple mean-field approximation of the Gross-Pitaevskii equation. The effect of the non-condensed thermal atoms we include using perturbation theory in a quasiparticle basis. This presents a simple scheme to understand the interaction between condensate and non-condensed atoms and enables us to include the effect the condensate has on collision dynamics. At first we limit our treatment to the case of a spatially homogeneous Bose gas. We include the effect of pair and triplet anomalous averages and thus obtain a gapless theory for the excitations of a weakly interacting system, which we can link to well known results for Landau and Beliaev damping rates. A gapless theory for trapped systems with a static thermal component follows straightforwardly. We then investigate finite temperature excitations of a condensate in a spherically symmetric harmonic trap. We avoid approximations to the density of states and thus emphasise finite size aspects of the problem. We show that excitations couple strongly to a restricted number of modes, giving rise to resonance structure in their frequency spectra. Where possible we derive energy shifts and lifetimes of excitations. For one particular mode, the breathing mode, the effects of the discreteness of the system are sufficiently pronounced that the simple picture of an energy shift and width fails. Experiments in spherical traps have recently become feasible and should be able to test our detailed quantitative predictions.

•Jan 1, 2000•0 citations

Damping of condensate oscillations of a trapped Bose gas in a one-dimensional optical lattice at finite temperatures

Emiko Arahata, Tetsuro Nikuni

We study damping of the dipole oscillation in a Bose-condensed gas in a combined cigar-shaped harmonic trap and one-dimensional (1D) optical lattice potential at finite temperatures. In order to include the effect of thermal excitations in the radial direction, we derive a quasi-1D model of the Gross-Pitaevskii equation and the Bogoliubov equations. We use the Popov approximation to calculate the temperature dependence of the condensate fraction with varying lattice depth. We then calculate the Landau damping rate of the dipole oscillation as a function of the lattice depth and temperature. The damping rate increases with increasing lattice depth, which is consistent with experimental observations. The magnitude of the damping rate is in reasonable agreement with experimental data. We also find that the damping rate has a strong temperature dependence, showing a sharp increase with increasing temperature. Finally, we emphasize the importance of the radial thermal excitations in both equilibrium properties and the Landau damping.

arXiv:0710.4610•Physical Review A•Mar 13, 2008•12 citations

Macroscopic Dynamics of a Trapped Bose-Einstein Condensate in the Presence of 1D and 2D Optical Lattices

Meret Krämer, Лев П. Питаевский, S. Stringari

The hydrodynamic equations of superfluids for a weakly interacting Bose gas are generalized to include the effects of periodic optical potentials produced by stationary laser beams. The new equations are characterized by a renormalized interaction coupling constant and by an effective mass accounting for the inertia of the system along the laser direction. For large laser intensities the effective mass is directly related to the tunneling rate between two consecutive wells. The predictions for the frequencies of the collective modes of a condensate confined by a magnetic harmonic trap are discussed for both 1D and 2D optical lattices and compared with recent experimental data.

arXiv:cond-mat/0201398•Physical Review Letters•Apr 22, 2002•133 citations

Landau Damping of Collective Mode in a Quasi-One-Dimensional Repulsive Bose—Einstein Condensate

Zhan-Jin Yang, Zhao-Liang Chai, Chenxu Li +1 more

We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose—Einstein condensate by using the self-consistent time-dependent Hartree—Fock—Bogoliubov approximation. We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature, on transverse trapping frequency, on atom number in the condensate, and on length of the system. Different from the usual calculation method for the three dimension system, our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation. With little approximation, our theoretical calculation results agree with the experimental ones. Comparing with the usual calculation method, our theory is helpful to deduce the inter-particle interactions in damping phenomenon.

Communications in Theoretical Physics•May 1, 2012•6 citations

Analytical calculations on Landau damping of collective modes in anisotropic Bose-Einstein condensates

Xiaodong Ma, Yong-li Ma, Guoxiang Huang

We develop an analytical approach for calculating the Landau damping of collective modes in the Bose-Einstein condensate trapped by an anisotropic harmonic potential. Based on a variational ground-state wave function obtained by solving the time-independent Gross-Pitaevskii equation beyond Thomas-Fermi approximation, we solve the Bogoliubov--de Gennes equations describing thermal excited quasiparticles and provide divergence-free analytical solutions for the Bogoliubov amplitudes and coupling matrix elements that characterize the interaction between the collective modes and the quasiparticles. With these analytical results we evaluate the Landau damping rates of several collective modes for various anisotropic parameters of the trapping potential in terms of the formulas derived from a time-dependent mean-field theory. In addition, we discuss the dependence of the damping rates on temperature, particle number, trapping frequency, and anisotropic parameter of the system, and compare our theoretical results with experimental and numerical data reported in literature.

Physical Review A•Jan 31, 2007•5 citations
We study the damping of the collective excitations of Bose-Einstein condensates in a harmonic trap potential loaded in an optical lattice. In the presence of a confining potential the system is inhomogeneous and the collective excitations are characterized by a set of discrete confined phononlike excitations. We derive a general convenient analytical description for the damping rate, which takes into account the trapping potential and the optical lattice for the Landau and Beliaev processes at any temperature TTT. At high temperature or weak spatial confinement, we show that both mechanisms display a linear dependence on TTT. In the quantum limit, we find that the Landau damping is exponentially suppressed at low temperatures and the total damping is independent of TTT. Our theoretical predictions for the damping rate under the thermal regime is in complete correspondence with the experimental values reported for the one-dimensional (1D) condensate of sodium atoms. We show that the laser intensity can tune the collision process, allowing a resonant effect for the condensate lifetime. Also, we study the influence of the attractive or repulsive nonlinear terms on the decay rate of the collective excitations. A general expression for the renormalized Goldstone frequency is obtained as a function of the 1D nonlinear self-interaction parameter, laser intensity, and temperature.
Abstract We study the structure of quasi-one-dimensional Bogoliubov–de Genes collective excitations of inhomogeneous F = 1 spinor Bose–Einstein condensates confined by a harmonic trap potential and loaded into an optical lattice. Employing a perturbative method, we report general analytical expressions for the polar and ferromagnetic confined collective oscillations. In both cases, the excited eigenfrequencies are given as functions of the effective 1D coupling constants, the trap frequency and the optical lattice parameters. While the presence of the trap yields quantized longitudinal collective modes, whose spectra depends on the collision scattering lengths, the optical lattice shifts their frequencies and, more importantly, yields tunable oscillations of the spin populations, for the even modes, as experimentally observed.
Recent experimental observations of collective excitations of Bose condensed atomic vapours have stimulated interest in the microscopic description of the dynamics of a Bose-Einstein condensate confined in an external potential. We present a finite temperature field theory for collective excitations of trapped Bose-Einstein condensates and use a finite-temperature linear response formalism, which goes beyond the simple mean-field approximation of the Gross-Pitaevskii equation. The effect of the non-condensed thermal atoms we include using perturbation theory in a quasiparticle basis. This presents a simple scheme to understand the interaction between condensate and non-condensed atoms and enables us to include the effect the condensate has on collision dynamics. At first we limit our treatment to the case of a spatially homogeneous Bose gas. We include the effect of pair and triplet anomalous averages and thus obtain a gapless theory for the excitations of a weakly interacting system, which we can link to well known results for Landau and Beliaev damping rates. A gapless theory for trapped systems with a static thermal component follows straightforwardly. We then investigate finite temperature excitations of a condensate in a spherically symmetric harmonic trap. We avoid approximations to the density of states and thus emphasise finite size aspects of the problem. We show that excitations couple strongly to a restricted number of modes, giving rise to resonance structure in their frequency spectra. Where possible we derive energy shifts and lifetimes of excitations. For one particular mode, the breathing mode, the effects of the discreteness of the system are sufficiently pronounced that the simple picture of an energy shift and width fails. Experiments in spherical traps have recently become feasible and should be able to test our detailed quantitative predictions.
We study damping of the dipole oscillation in a Bose-condensed gas in a combined cigar-shaped harmonic trap and one-dimensional (1D) optical lattice potential at finite temperatures. In order to include the effect of thermal excitations in the radial direction, we derive a quasi-1D model of the Gross-Pitaevskii equation and the Bogoliubov equations. We use the Popov approximation to calculate the temperature dependence of the condensate fraction with varying lattice depth. We then calculate the Landau damping rate of the dipole oscillation as a function of the lattice depth and temperature. The damping rate increases with increasing lattice depth, which is consistent with experimental observations. The magnitude of the damping rate is in reasonable agreement with experimental data. We also find that the damping rate has a strong temperature dependence, showing a sharp increase with increasing temperature. Finally, we emphasize the importance of the radial thermal excitations in both equilibrium properties and the Landau damping.
The hydrodynamic equations of superfluids for a weakly interacting Bose gas are generalized to include the effects of periodic optical potentials produced by stationary laser beams. The new equations are characterized by a renormalized interaction coupling constant and by an effective mass accounting for the inertia of the system along the laser direction. For large laser intensities the effective mass is directly related to the tunneling rate between two consecutive wells. The predictions for the frequencies of the collective modes of a condensate confined by a magnetic harmonic trap are discussed for both 1D and 2D optical lattices and compared with recent experimental data.
We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose—Einstein condensate by using the self-consistent time-dependent Hartree—Fock—Bogoliubov approximation. We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature, on transverse trapping frequency, on atom number in the condensate, and on length of the system. Different from the usual calculation method for the three dimension system, our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation. With little approximation, our theoretical calculation results agree with the experimental ones. Comparing with the usual calculation method, our theory is helpful to deduce the inter-particle interactions in damping phenomenon.
We develop an analytical approach for calculating the Landau damping of collective modes in the Bose-Einstein condensate trapped by an anisotropic harmonic potential. Based on a variational ground-state wave function obtained by solving the time-independent Gross-Pitaevskii equation beyond Thomas-Fermi approximation, we solve the Bogoliubov--de Gennes equations describing thermal excited quasiparticles and provide divergence-free analytical solutions for the Bogoliubov amplitudes and coupling matrix elements that characterize the interaction between the collective modes and the quasiparticles. With these analytical results we evaluate the Landau damping rates of several collective modes for various anisotropic parameters of the trapping potential in terms of the formulas derived from a time-dependent mean-field theory. In addition, we discuss the dependence of the damping rates on temperature, particle number, trapping frequency, and anisotropic parameter of the system, and compare our theoretical results with experimental and numerical data reported in literature.