Collective atomic recoil lasing in cold atoms and related topic
The experimental realization of Bose-Einstein condensates (BECs) with alkali trapped atoms has opened the possibility of investigating several fundamental aspects of quantum mechanics in macroscopic, i.e. many particle, systems . The possibility to create coherent superpositions of different macroscopic states lies at the heart of exciting development such as teleportation and quantum computing. In the past years, quantum coherence has belonged almost exclusively to the radiation generated by lasers and only recently it has been shared with the new branch of physics named `atom optics', where the observation of coherent matter waves interference has been realized using BECs. The interaction between coherent radiation and coherent matter waves realizes a natural synthesis of the two worlds. In this contest, the pioneering work of Ketterle et al. [1] on superradiant Rayleigh scattering from an elongated Bose-Einstein condensate has shown how the coherent nature of the condensate leads to strong correlations between successive scattering events. The effect observed by Ketterle is an example of a spontaneous formation of a regular density grating in an initially disordered atomic system, arising from a collective instability as described in the CARL model (Collective Atomic Recoil Laser ) [2]. In the CARL model, a cold two level atoms gas is exposed to an intense far-off-resonant pump laser. The correlation between atoms are produced by the backscattering of the laser photons, so that the atoms spontaneously organize in a lattice and then emit a coherent radiation field. Before the experimental realisation of BEC the CARL effect was observed in an optical cavity containing a sodium vapours cell [3]. In the absence of thermal broadening (as it happens in a BEC), the CARL appears as a promising source of macroscopic entangled or squeezed systems. In particular the CARL allows to crete quantum correlations between atoms with different momentum and between atoms and radiation. From an experimental point of view up to now the CARL with Bose Einstein condensate was only observed in superradiant regime and without the optical cavity. Some experiment are under progress at LENS labs [4], Tokio University [5] and MIT [1]. At the beginning the CARL process was studied in a semi-classical regime where the atom centre of mass motion and the radiation were classically described. The results showed how the collective atomic recoil could produce deep modification to the radiation and atoms interaction in phenomena such that the super fluorescence [6] absorptive [7] and dispersive [8] optical bistability and the bi-directional laser inside a ring cavity [9]. The recent experiments performed on BECs showed the necessity of a quantum mechanical description of the atomic motion in CARL. Recently, the quantum model of CARL was used to describe the evolution of the macroscopic wave function of the atoms in the state of Bose Einstein condensation [10,11,12]. The model was able to quantitatively describe the collective Rayleigh scattering experiments performed at MIT in 1999 [1], interpreted ad due to the CARL process in superradiant regime. In particular, a full quantum description of the interaction between a Bose-Einstein condensate and a single-mode quantized radiation field in the presence of a strong far off-resonant pump laser was developed (quantum CARL) [13]. This allowed to demonstrate that the system can be atom-atom or atom-field thermally entangled. Moreover, the Florence unit, performing some superradiant Rayleigh scattering experiments, has demonstrated that the decoherence can be controlled varying the condensate initial velocity [4]. The condensate temporal evolution observed in the experiment is well fitted by a simple model where the condensate is described by a density operator for the momentum states where the off-diagonal elements decay proportionally to the squared energy difference between the states. However, in a real BEC several effects due, for instance, to spontaneous emission, inhomogeneous broadening and collisions may seriously inhibit the CARL process and destroy the coherence in the matter wave field [14]. The elimination of decoherence in the photon-BEC interaction would be a significant step in the road to the achievement of macroscopic entanglement of coherent matter waves.
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