Collisional decoherence of internal-state superpositions in a trapped ultracold gas

Abstract

We analyze collisional decoherence of atoms or molecules prepared in a coherent superposition of nondegenerate internal states at ultralow temperatures and placed in an ultracold buffer gas. Our analysis is applicable for an arbitrary bath-particle to tracer-particle mass ratio. Both elastic and inelastic collisions contribute to decoherence. We obtain an expression relating the observable decoherence rate to pairwise scattering properties, specifically the scattering lengths and low-temperature scattering amplitudes. We consider the dependence on the bath-particle to tracer-particle mass ratio for the case of light bath and heavy tracer particles. The expressions obtained may be useful in low-temperature applications where accurate estimates of decoherence rates are needed. The results suggest a method for determining the scattering lengths of atoms and molecules in different internal states by measuring decoherence-induced damping of coherent oscillations.

Collisional decoherence of superposition states in an ultracold gas near a Feshbach resonance

“…To do this, it is necessary to measure the time evolution of both |ρ el a,b (t)| and η a,b (t). At low temperatures, the time evolution of |ρ el a,b (t)| is given by [17] …”

“…Reference [17] presents the expressions for the coefficients ξ in terms of the expansion coefficients a i and b i of the scattering amplitude. It is more convenient for the present study to express the coefficients ξ in terms of the real and imaginary parts of the scattering length for molecules in states a and b.…”

Stochastic simulation algorithm for the quantum linear Boltzmann equation

“…and a realization of the random waiting time τ is obtained by solving Eq. ( 29) for τ with the effective Hamiltonian (34). The jump at time t + τ is effected by…”

“…By using the definition of H eff (34), the fact that the two summands in H eff commute, and the jump rate (48), this yields…”

Collisional decoherence of polar molecules

“…In order to formulate the theory of collisional decoherence for nonspherical particles, one must take the molecule's center of mass as well as its orientational degrees of freedom into account. In general, this implies solving the full inelastic scattering problem to obtain the scattering amplitudes required for the master equation [12,23,24]. Yet, if the molecule is sufficiently massive and approximately static during a single collision, the scattering event is effectively elastic [25].…”