Quantum Dynamics of Collective Spin States in a Thermal Gas

Abstract

Ensembles of alkali or noble-gas atoms at room temperature and above are widely applied in quantum optics and metrology owing to their long-lived spins. Their collective spin states maintain nonclassical nonlocal correlations, despite the atomic thermal motion in the bulk and at the boundaries. Here we present a stochastic, fully-quantum description of the effect of atomic diffusion in these systems. We employ the Bloch-Heisenberg-Langevin formalism to account for the quantum noise originating from diffusion and from various boundary conditions corresponding to typical wall coatings, thus modeling the dynamics of nonclassical spin states with spatial inter-atomic correlations. As examples, we apply the model to calculate spin noise spectroscopy, temporal relaxation of squeezed spin states, and the coherent coupling between two spin species in a hybrid system.

Optimal control of an optical quantum memory based on noble-gas spins

“…The overall dynamics can be described using the Heisenberg-Bloch-Langevin formalism of open quantum systems [17,61,63]. The atomic dynamics, in terms of the continuous quantum operators σµν (r, t) in the Heisenberg picture, is given by the stochastic differential equations…”

“…The uniform mode of the alkali spins has a large overlap with the long-lived uniform mode of the noble-gas spins, which is unaffected by diffusion [63] and therefore chosen as the quantum memory. The dynamics of the uniform mode K of the noble-gas spin is given by…”

“…5, the control field is turned off (Ω = 0), and the excitation is coherently transferred from the alkali to the noble-gas spins Ŝ(T ) → K(T ) via the spin-exchange interaction. In general, the dynamics of spin-exchange in the presence of diffusion is multi-mode [57,63], and we present the complete multi-mode calculation in Appendix H. Here we present the approximated dynamics for the uniform modes. This solution is accurate for anti-relaxation coated cells [63].…”

“…In general, the dynamics of spin-exchange in the presence of diffusion is multi-mode [57,63], and we present the complete multi-mode calculation in Appendix H. Here we present the approximated dynamics for the uniform modes. This solution is accurate for anti-relaxation coated cells [63].…”

“…The natural choice of mode functions for the collective noble-gas spin is the set of eigenmodes of the diffusionrelaxation operator [63] represents the relaxation rate of the n th mode. Using these mode functions, the equations of motion of the noble-gas spin can be written as…”