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European Quantum Electronics Conference (EQEC)

Inelastic collisions between Bogoliubov excitations due to three-wave mixing

Roee Ozeri, Nadav Y. Katz, J. Steihhauer, Eitan E. Rowen, Erez Gershnabel, Nir Davidson

Published Nov 15, 2004• 0 citations
Publisher

Abstract

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.

DOI
10.1109/eqec.2003.1314080

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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.
A dressed-state approach to mixing of bosonic matter waves is presented. Two cases are studied using this formalism. In the first, two macroscopically populated modes of atoms (two-wave mixing) are coupled through the presence of light. In the second case, three modes of Bogoliubov quasiparticles (three-wave mixing) are coupled through sss-wave interaction. In both cases, wave mixing induces oscillations in the population of the different modes that decay due to interactions. Analytic expressions for the dressed basis spectrum and the evolution of the mode populations in time are derived both for resonant mixing and nonresonant mixing. Oscillations in the population of a given mode are shown to lead to a splitting in the decay spectrum of that mode, in analogy with the optical Autler-Townes splitting in the decay spectrum of a strongly driven atom. These effects cannot be described by a mean-field approximation.
Abstract We present new features of low energy Bogoliubov quasiparticle excitations of a two-component Bose–Einstein condensate (TBEC) in quasi-2D geometry at zero temperature using Hartree–Fock–Bogoliubov formalism. We, in particular, consider the TBECs of 133 Cs– 87 Rb and 85 Rb– 87 Rb, and show specific features in the low energy excitation spectrum as a function of the interaction strength. For 85 Rb– 87 Rb TBEC, the appearance of a new zero energy mode is observed. Whereas for 133 Cs– 87 Rb TBEC we report a bifurcation of the slosh mode at the point of transition from miscible to immiscible domain. The lower energy mode, after the bifurcation, goes soft and becomes a new Nambu–Goldstone mode of the system.
We investigate the zero-temperature properties of an impurity particle interacting with a Bose-Einstein condensate (BEC), using a variational wave function that includes up to two Bogoliubov excitations of the BEC. This allows one to capture three-body Efimov physics, as well as to recover the first nontrivial terms in the weak-coupling expansion. We show that the energy and quasiparticle residue of the dressed impurity (polaron) are significantly lowered by three-body correlations, even for weak interactions where there is no Efimov trimer state in a vacuum. For increasing attraction between the impurity and the BEC, we observe a smooth crossover from atom to Efimov trimer, with a superposition of states near the Efimov resonance. We furthermore demonstrate that three-body loss does not prohibit the experimental observation of these effects. Our results thus suggest a route to realizing Efimov physics in a stable quantum many-body system for the first time.
We make a systematic study of the resonant mode coupling of the collective excitations at zero temperature in a Bose-Einstein condensate (BEC). (i) Based on the Gross-Pitaevskii equation we derive a set of nonlinearly coupled envelope equations for a three-mode resonant interaction (TMRI) by means of a method of multiple scales. (ii) We calculate the coupling matrix elements for the TMRI and show that the divergence appearing in previous studies can be eliminated completely by using a Fetter-like variational approximation for the ground-state wave function of the condensate. (iii) We provide the selection rules in mode-mode interaction processes [including TMRI and second-harmonic generation (SHG)] according to the symmetry of the excitations. (iv) By solving the nonlinearly coupled envelope equations we obtain divergence-free nonlinear amplitudes for the TMRI and SHG processes and show that our theoretical results on the shape oscillations of the condensate agree well with the experimental ones. We suggest also an experiment to check the theoretical prediction of the present study on the TMRI of collective excitations in a BEC.
The Bogoliubov treatment of a weakly interacting Bose gas is extended by allowing macroscopic occupation of many single-particle quantum states. This generalization of having more than a single condensed mode gives rise to a nonuniform condensate and is being considered as a possible mechanism for the description of a dense strongly interacting Bose gas at low temperatures. The model with a repulsive $\ensuremath{\delta}$-function interparticle potential gives an energy spectrum of elementary excitations or quasiparticles with both phonon and roton features. The values obtained for the roton minimum energy $\ensuremath{\Delta}$ and the speed of (first) sound agree reasonably well with inelastic-neutron-scattering data.