Approximate Master Equations for Atom Optics

Christian Bordé

D. J. Atkins, Howard M. Wiseman, Prahlad Warszawski

In the field of atom optics, the basis of many experiments is a two-level atom coupled to a light field. The evolution of this system is governed by a master equation. The irreversible components of this master equation describe the spontaneous emission of photons from the atom. For many applications, it is necessary to minimize the effect of this irreversible evolution. This can be achieved by having a far detuned light field. The drawback of this regime is that making the detuning very large makes the time step required to solve the master equation very small, much smaller than the time scale of any significant evolution. This makes the problem very numerically intensive. For this reason, approximations are used to simulate the master equation, which are more numerically tractable to solve. This paper analyzes four approximations: The standard adiabatic approximation, a more sophisticated adiabatic approximation (not used before), a secular approximation, and a fully quantum dressed-state approximation. The advantages and disadvantages of each are investigated with respect to accuracy, complexity, and the resources required to simulate. In a parameter regime of particular experimental interest, only the sophisticated adiabatic and dressed-state approximations agree well with the exact evolution.

Georg Lenz, Pierre Meystre

H. J. Carmichael, Daniel F. Walls

A quantum theory of the laser is presented in which the coupling between atoms and field is retained in the treatment of the irreversible behavior of the atoms. A master equation for the optical field is obtained and compared with that resulting from the laser theory of Scully and Lamb, where atom-field correlations are neglected in describing the relaxation of the atoms. It is confirmed that for laser powers currently available the approximation employed by Scully and Lamb is valid.

A. Kowalewska-Kudłaszyk, R. Tanaś

The master equation for a two-level atom driven by a strong classical field and damped into a tailored reservoir with nonflat density of modes is derived under the Born-Markov approximation. To derive the master equation, the dressing transformation on the atomic operators is performed first, and, next, the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The effects of a strong field and/or structured reservoir are seen as nonstandard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The master equation leads to the generalized optical Bloch equations that can easily be solved for the steady state and, together with the quantum regression theorem, allow for analytical expressions for the fluorescence, as well as absorption spectra.

G. S. Agarwal