Effective damping in the Raman cooling of trapped ions

Abstract

We present a method of treating the interaction of a single three-level ion with two laser beams. The idea is to apply a unitary transformation such that the exact transformed Hamiltonian has one of the three levels decoupled for all values of the detunings. When one takes into account damping, the evolution of the system is governed by a master equation usually obtained via adiabatic approximation under the assumption of far-detuned lasers. To go around the drawbacks of this technique, we use the same unitary transformation to get an effective master equation.

Steady-state spin synchronization through the collective motion of trapped ions

“…In writing Eq. ( 10), we have omitted certain 'cross-terms' [27] which eventually contribute at order Γ 2 1,2 /∆ 2 ( 1) lesser than the interactions of interest. To avoid digressing, we outline the reasoning behind this omission in Appendix B.…”

Long-lived entangled qudits in a trapped three-level ion beyond the Lamb–Dicke limit

“…A further rotating wave approximation (RWA) yields the well-known two-level quantum optical Hamiltonians to govern vibrational phonon dynamics. Alternatively, one can avoid adiabatic elimination, and the problems associated with it [35] by using some unitary transformations in order to get the desired quantum optical models for vibrational phonon dynamics [36][37][38]. By considering full three-level system, one can examine higher dimensional entanglement.…”

Time-dependent perturbation treatment of independent Raman schemes

“…The analysis of a trapped ion single Raman scheme dynamics has been carried out by means of the method called 'adiabatic elimination' [13][14][15], widely used in different physical situations [16][17][18][19][20] and, in some sense, overcome by techniques based on unitary transformations which decouple the auxiliary level [21,22]. Recently, a more systematic and transparent approach relying on a time-independent perturbative method [23][24][25] has been used.…”