Collective Rabi Oscillations and Cold Collisions

We examine cold atomic collisions within a resonant optical cavity. The quantized cavity mode can be used to manipulate the collisions between the cold atoms, such that periodic exchange of excitations between the atoms and the electromagnetic field strongly alters the collision dynamics. A colliding pair of atoms can thereby oscillate between its ground and excited states during the collision time. Using a semiclassical model, it can be predicted that such Rabi-like oscillations are revealed in the atomic trap-loss probabilities, which show maxima and minima as a function of the detuning between the frequencies of the mode and the atomic transition. Exchange of excitations between the energy levels of atoms or molecules and the quantum eletromagnetic field [1] is one basic interaction process between matter and light. In this context, the Jaynes-Cummings model [2], describing a single two-level system and a monochromatic lossless field, reveals several characteristics of this interaction. In the quantum Rabi oscillation [3,4], in particular, a single energy quantum is periodically exchanged between system and field. On the other hand, when several atoms or molecules interact with the same field, quantum coherence can build among them leading to well known collective behaviors, such as superradiance [5–9], for which multiparticle entanglement plays a major role. It should be noticed, however, that the systems with which the field interacts need not be solely composed of stable atoms or molecules. The above characteristics of the matter-field interaction can be present as well when two cold atoms collide in presence of a quantum field. An additional effect is that the very dynamics of the cold atomic collision [10,11] can be strongly modified by this field. Indeed, pairs of colliding atoms so far apart from each other that their direct mutual interaction is neglegible, can be entangled by the field and, thereby, influence one another in a nonlocal way. In the following we study cold atomic collisions within a gas of cold atoms trapped in the center of a high-Q cavity. It is possible to show that an analogous collective Rabi oscillation can show up in the trap-loss probabilities as a function of the detuning between the cavity mode frequency and the atomic resonance. The internuclear potential energy of two colliding atoms depends on the electronic states. In particular, the inverse-cube law dipole-dipole potential ±1/R3 between alkali neutral atoms, separated by a distance R, predominates when the asymptotic atomic states involved are nS1/2 and nP1/2 (Fig. 1). When the collision is slow [10,11], the atoms can undergo changes in their electronic states during the collision, either as spontaneous decay or induced transitions. In a previous work [12], it was examined how cold collisions can be manipulated as spontaneous decay is driven by the colored vacuum of a cavity. The highly increased emission rate of multiply entangled pairs being able to emit coherently to the same cavity mode was then predicted to pratically interrupt the collision process. In the present case, we neglect the cavity loss (high-Q) and allow reabsortions of the field energy. We study how these induced transitions affect cold collisions. Cavity Quantum Electrodynamics (CQED) effects on atomic motion in high-Q cavities have been investigated recently. Modifications of mechanical forces of light acting on atoms [13,14], or appearance of new quasi-bound molecular states of two colliding atoms [15] illustrate the interplay between CQED and cold atoms.