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:cond-mat/0208283 · Physical Review Letters

Three-Wave Mixing of Bogoliubov Quasiparticles in a Bose-Einstein Condensate

Roee Ozeri, Nadav Y. Katz, Jeff Steinhauer, Eitan E. Rowen, Nir Davidson

Published Apr 28, 2003• 13 citations
arXivHTMLPDF

Abstract

A dressed basis is used to calculate the dynamics of three-wave mixing between Bogoliubov quasiparticles in a Bose condensate. Because of the observed oscillations between different momentum modes, an energy splitting, analogous to the optical Mollow triplet, appears in the Beliaev damping spectrum of the excitations from the oscillating modes.

DOI
10.1103/physrevlett.90.170401

Related papers

Inelastic collisions between Bogoliubov excitations due to three-wave mixing

Roee Ozeri, Nadav Y. Katz, J. Steihhauer +3 more

This study introduces a basis of states which are dressed by the interaction between three, largely populated, modes of Bogoliubov quasi-particles in a Bose-Einstein condensate at zero temperature. The dressed basis is obtained by diagonalizing the N/spl times/M matrix, which represents the coupling between mode k with N excitations and mode q with M excitations. The degeneracy between the excitation Fock states is removed by the interaction. The new dressed basis spans a spectrum of energies which is symmetric around E=0. The spectrum appears to be roughly linear, however, due to the non-linearity of the problem, energy differences between each pair of dressed states are slightly different.

European Quantum Electronics Conference (EQEC)•Nov 15, 2004•0 citations

Beliaev Damping of Quasiparticles in a Bose-Einstein Condensate

Nadav Y. Katz, Jeff Steinhauer, Roee Ozeri +1 more

We report a measurement of the suppression of collisions of quasiparticles with ground state atoms within a Bose-Einstein condensate at low momentum. These collisions correspond to Beliaev damping of the excitations, in the previously unexplored regime of the continuous quasiparticle energy spectrum. We use a hydrodynamic simulation of the expansion dynamics, with the Beliaev damping cross section, in order to confirm the assumptions of our analysis.

arXiv:cond-mat/0206234•Physical Review Letters•Nov 6, 2002•81 citations

Phonon decay in one-dimensional atomic Bose quasicondensates via Beliaev-Landau damping

Amaury Micheli, Scott Robertson

In a one-dimensional Bose gas, there is no nontrivial scattering channel involving three Bogoliubov quasiparticles that conserves both energy and momentum. Nevertheless, we show that such three-wave mixing processes (Beliaev and Landau damping) account for their decay via interactions with thermal fluctuations. Within an appropriate time window where the Fermi golden rule is expected to apply, the occupation number of the initially occupied mode decays exponentially and the rate takes a simple analytic form. The result is shown to compare favorably with simulations based on the truncated Wigner approximation. It is also shown that the same processes slow down the exponential growth of phonons induced by a parametric oscillation.

arXiv:2205.15826•Physical review. B./Physical review. B•Dec 29, 2022•13 citations

Damping of Bogoliubov excitations in optical lattices

Shunji Tsuchiya, Allan Griffin

Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to the coupling to a thermal cloud of such excitations. For simplicity, we consider a one-dimensional Bose-Hubbard model and restrict ourselves to the first energy band. For energy conservation to be satisfied, the excitations in the collision processes must exhibit ``anomalous dispersion,'' analogous to phonons in superfluid $^{4}\mathrm{He}$. This leads to the disappearance of all damping processes when $U{n}^{\mathrm{c}0}\ensuremath{\geqslant}6J$, where $U$ is the on-site interaction, $J$ is the hopping matrix element, and ${n}^{\mathrm{c}0}(T)$ is the number of condensate atoms at a lattice site. This phenomenon also occurs in two-dimensional and three-dimensional optical lattices. The disappearance of Beliaev damping above a threshold wave vector is noted.

arXiv:cond-mat/0311321•Physical Review A•Aug 30, 2004•30 citations

Excitation Spectrum of Three Dressed Bose-Einstein Condensates

Ou-Yang Zhong-Wen, Kuang Le-Man

We study quantum dynamics of three dressed Bose-Einstein condensates in a high- Q cavity. The quasiparticle excitation spectrum of this system is found numerically. The stability of the quasiparticle excitation is analyzed. It is shown that there exist instabilities in the excitation spectrum.

Chinese Physics Letters•Sep 1, 2000•0 citations

Excitation spectrum of three dressed Bose-Einstein condensates

Zhongwen Ouyang, Le‐Man Kuang

We study quantum dynamics of three dressed Bose-Einstein condensates in a high-Q cavity. The quasiparticle excitation spectrum of this system is found numerically. The stability of the quasiparticle excitation is analyzed. It is shown that there exist instabilities in the excitation spectrum.

arXiv:cond-mat/0004016•Apr 3, 2000•0 citations
A dressed basis is used to calculate the dynamics of three-wave mixing between Bogoliubov quasiparticles in a Bose condensate. Because of the observed oscillations between different momentum modes, an energy splitting, analogous to the optical Mollow triplet, appears in the Beliaev damping spectrum of the excitations from the oscillating modes.
This study introduces a basis of states which are dressed by the interaction between three, largely populated, modes of Bogoliubov quasi-particles in a Bose-Einstein condensate at zero temperature. The dressed basis is obtained by diagonalizing the N/spl times/M matrix, which represents the coupling between mode k with N excitations and mode q with M excitations. The degeneracy between the excitation Fock states is removed by the interaction. The new dressed basis spans a spectrum of energies which is symmetric around E=0. The spectrum appears to be roughly linear, however, due to the non-linearity of the problem, energy differences between each pair of dressed states are slightly different.
In a one-dimensional Bose gas, there is no nontrivial scattering channel involving three Bogoliubov quasiparticles that conserves both energy and momentum. Nevertheless, we show that such three-wave mixing processes (Beliaev and Landau damping) account for their decay via interactions with thermal fluctuations. Within an appropriate time window where the Fermi golden rule is expected to apply, the occupation number of the initially occupied mode decays exponentially and the rate takes a simple analytic form. The result is shown to compare favorably with simulations based on the truncated Wigner approximation. It is also shown that the same processes slow down the exponential growth of phonons induced by a parametric oscillation.
Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to the coupling to a thermal cloud of such excitations. For simplicity, we consider a one-dimensional Bose-Hubbard model and restrict ourselves to the first energy band. For energy conservation to be satisfied, the excitations in the collision processes must exhibit ``anomalous dispersion,'' analogous to phonons in superfluid 4He^{4}\mathrm{He}4He. This leads to the disappearance of all damping processes when $U{n}^{\mathrm{c}0}\ensuremath{\geqslant}6J$, where UUU is the on-site interaction, JJJ is the hopping matrix element, and nc0(T){n}^{\mathrm{c}0}(T)nc0(T) is the number of condensate atoms at a lattice site. This phenomenon also occurs in two-dimensional and three-dimensional optical lattices. The disappearance of Beliaev damping above a threshold wave vector is noted.