Classical and Quantum Dynamics of Cold Atoms in Optical Cavities

Pumped by Phase-Modulated Light

M. Hemmerling & G.R.M. Robb

Scottish Universities Physics Alliance (SUP A), University of Strathclyde, Department of Physics,

John Anderson Building, 107 Rottenrow, Glasgow G4 ONG, Scotland, u.K.

The utilisation of phase/frequency modulated optical fields can significantly influence light-matter interactions e.g. it has been demonstrated experimentally that phase/frequency modulation increases optical forces exerted on atoms (1]. Recently, there has been significant theoretical and experimental interest in light­matter interactions and instabilities which can occur when many cold atoms interact collectively or cooperatively with a common optical field, Experiments carried out by the Zimmermann group in Tubingen demonstrated

Collective Atomic Recoil Lasing, (CARL)[2], where atoms in a unidirectionally pumped ring cavity spontaneously undergo a transition from a disordered state, where the atomic positions are essentially random, to an ordered state where the atoms form a dynamic, spatially periodic density grating which backscatters the pump field[3,4]. It has been shown recently that the effect of a phase-modulated pump beam on the CARL instability

involving a classical cold gas can give rise to three different dynamical regimes depending on the frequency of modulation [5,6] and that for certain values of modulation frequency the atomic dynamics is chaotic.

A theoretical study of the interaction between a modulated pump beam and a quantum-degenerate gas (e.g. Bose-Einstein Condensate) in a ring cavity will be described and the influence of the quantum nature of the atoms on the atom-cavity interaction will be investigated. This analysis predicts that phenomena such as dynamical localisation [7] i.e. quantum suppression of classical chaos, may be observable via the evolution of the cavity field intensity. These results suggest that atomic gases in optical cavities may be useful testing

grounds for fundamental investigations of classical and quantum regimes of nonlinear mean-field interactions such as those which occur in e.g. plasma physics and condensed matter physics.

References

[I) M. Cashen, O. Rivoire, V. Romanenko, L. Yatsenko, and H. Metcalf, Phys. Rev. A 64, 063411 (2004). [2] R. Bonifacio and L. De Salvo Nucl. Inst. Meth. Phys. Res. A341, 360 (\ 994) ; R. Bonifacio, L. De Salvo, L.M. Narducci and EJ.

D'Angelo Phys. Rev. A 50,1716 (1994). [3] D. Kruse et. al. Phys. Rev. Lett. 91,183601 (2004); c. von Cube et. al Phys. Rev. Lett. 93, 083601 (2004). [4] S. Slama, S. Bux, G. Krenz, C. Zimmermann and Ph. W. CourteiIIe Phys. Rev. Lett. 98 ,053603 (2007). [5] G.R.M. Robb, R.T.L. Burgess, W.J. Firth, Phys. Rev. A 78, 041804 (2008). [6] M. Hemmerling & G.R.M. Robb, Phys. Rev. A 82, 053420 (2010) [7] see e.g. R. Graham, M. Schlautmann and D.L. Shepelyansky, Phys. Rev. Lett. 67,255 (\ 991).