Approximate Master Equations for Atom Optics

Abstract

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 timestep required to solve the master equation very small, much smaller than the timescale 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 analyses 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.

11 pages, 5 figures. Submitted to Phys Rev A. Returned for major corrections, v2 submitted to PRA

References in corpus (4)

• Quantum state transfer and entanglement distribution among distant nodes in a quantum network
• Quantum Trajectories and Quantum Measurement Theory
• Mesoscopic quantum coherence in an optical lattice
• Adiabatic Elimination in Compound Quantum Systems with Feedback

Cited by in corpus (7)

• Optimal control of an inhomogeneous spin ensemble coupled to a cavity
• Eternal Adiabaticity
• Effective damping in the Raman cooling of trapped ions
• Convergence and adiabatic elimination for a driven dissipative quantum harmonic oscillator
• Delocalization of ultracold atoms in a disordered potential due to light scattering
• Entanglement characteristics of subharmonic modes reflected from cavity for type II second harmonic generation
• Towards generic adiabatic elimination for bipartite open quantum systems