Mean-field dynamics of a Bose Josephson junction in an optical cavity

Abstract

We study the mean-field dynamics of a Bose Josephson junction which is dispersively coupled to a single mode of a high-finesse optical cavity. An effective classical Hamiltonian for the Bose Josephson junction is derived, and its dynamics is studied from the perspective of a phase portrait. It is shown that the strong condensate-field interplay does alter the dynamics of the Bose Josephson junction drastically. The possibility of coherent manipulating and in situ observation of the dynamics of the Bose Josephson junction is discussed. Cavity quantum electrodynamics cavity QED has now grown into a paradigm in the study of the matter-field interaction. To tailor the atom-field coupling effectively, a high degree of control over the center-of-mass motion of the atoms is essential. Although previous works have focused on the few-atom level 1, recently, a great step was made as two groups succeeded independently in coupling a BoseEinstein condensate to a single-cavity mode 2,3. That is, a single-cavity mode dressed condensate has been achieved. This opens up a new regime in both the fields of cavity QED and ultracold atom physics. In the condensate, all the atoms occupy the same motional mode and couple identically to the cavity mode, thus realizing the Dicke model 4 in a broad sense. As shown by these experiments, the condensate is quite robust; it would not be destroyed by its interaction with the cavity mode in the time scale of the experiments. In this paper, we investigate the mean-field dynamics of a Bose Josephson junction BJJ5, which is coupled to a driven cavity mode. This extends our previous work to the many-atom case 6. The system may be constructed by splitting a Bose-Einstein condensate, which is already coupled to a single-cavity mode, into two weakly linked condensates, as can be done in a variety of ways 7‐11. We restrict ourselves to the large-detuning and low-excitation limit, so that atomic spontaneous emission can be neglected. In this limit, the effect of the strong coupling between the atoms and the field, seen by the field, is to shift the cavity resonance frequency and hence modify the field intensity. Unlike the single-condensate case, we now have two, which may couple with different strengths to the cavity mode because of the position dependence of the atom-field coupling. Consequently, the field dynamics couples to the tunneling dynamics of the BJJ and vice versa. It is the very interplay between the two sides that we are interested in. The interplay is made possible by the greatly enhanced atom-field coupling in a microcavity, which is unique in the context of cavity QED. In the usual optical traps and optical lattices, the interaction between the atoms and the light field is one way in the sense that the light field affects the motion of the atoms effectively, while the atoms have little back-action on the light field—the laser intensity is almost the same with or without the presence of the atoms. We would like to stress that, although there had already been some experimental investigations on this subject and phenomena such as dispersive optical bistability were observed 12,13, all of them dealt with thermally cold atoms. However, here, the long-range coherence of the condensates will surely make a difference. The Hamiltonian of the system consists of three parts: H = Ha + Hf + Hint. 1 Ha is the canonical Bose-Josephson-junction Hamiltonian in the two-mode approximation =1 throughout,