Semiclassical treatment of macroscopic quantum relaxation.

Michael Joseph Duggan

Brian P. Cowan

V. L. Jacobs

Reduced density matrix descriptions are developed for linear and non-linear electromagnetic interactions of moving atomic systems, taking into account applied magnetic fields as well as atomic collisions together with other environmental decoherence and relaxation processes. Applications of interest include electromagnetically induced transparency and related pump-probe optical phenomena in warm atomic vapors. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified manner. The standard Born (lowestorder perturbation-theory) and Markov (short-memory-time) approximations are systematically introduced within the framework of the general non-perturbative and non-Markovian formulations. A preliminary semiclassical treatment of the electromagnetic interaction is adopted. However, the need for a fully quantum mechanical approach is emphasized. Compact Liouville-space operator expressions are derived for the linear and the general (n'th order) non-linear macroscopic electromagnetic-response tensors occurring in a perturbation-theory treatment of the semiclassical electromagnetic interaction. These expressions can be evaluated for coherent initial atomic excitations and for the full tetradic-matrix form of the Liouville-space self-energy operator representing the environmental interactions in the Markov approximation. Collisional interactions between atoms can be treated in various approximations for the selfenergy operator, and the influence of Zeeman coherences on the macroscopic electromagnetic response can be investigated.

Lisa Qian, Michael L. Wall, Shaoliang Zhang +2 more

We study the properties of Bose-Einstein condensates in a one-dimensional ring with periodically modulated interaction strength. We demonstrate that within the semiclassical mean-field theory, a condensate can undergo a quantum phase transition between a solitonlike state and a spatially periodic condensate that matches the scattering length modulation. However, we show via exact diagonalization of the full many-body Hamiltonian that the solitonic ground states do not exist in the true quantum treatment. Instead, the system is driven into an entangled macroscopic-quantum-superposition-like state and the semiclassical soliton state may be regarded as a decohered macroscopic quantum superposition state. We investigate how the properties of the quantum ground state scales with the total number of atoms. Our work elucidates how semiclassical properties emerge from quantum behavior.

Peter Herbert Mengert