Excitation spectrum of three dressed Bose-Einstein condensates

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. Typeset using REVTEX 1 ] Recently, multicomponent Bose-Einstein condensates (MBEC’s) [1,2] have attracted much attention due to the recent experimental realizations of two and three component Bose-Einstein condensates (BEC’s) [3,4]. MBEC’s offer new degrees of freedom, which give rise to a rich set of new phenomena that do not exist in a single condensate. Especially, the interaction of BEC’s with light leads to fascinating effects including the extreme slowing down of the speed of light [5] and matter-wave four-wave mixing [6]. Goldstein, Wright and Meystre (GWM) [7] proposed an approach to produce MBEC’s, called dressed BEC’s, inside a high-Q multimode cavity, and investigated the quasiparticle excitation spectrum for the case of two dressed BEC’s which dress one-photon. The purpose of this letter is to study the quasiparticle excitation spectrum for a system of three dressed BEC’s which dress two photons. We will investigate quantum dynamics of the three dressed BEC’s, and calculate numerically their elementary excitations. Consider the GWM model of dressed BEC’s [7], which consists of a condensate which interacts with two counter-propagating modes by a high-Q ring cavity with n1 photons being in the mode 1 and n2 photons being in the mode 2. We consider a state composing n = n1 + n2 photons and N atoms which comprises the condensate confined by an external trapping potential U(r). The state of the system can be written |ΨN,n〉 =