Abstract
We consider an ultracold quantum degenerate gas in an optical lattice inside a cavity. This system represents a simple but
key model for “quantum optics with quantum gases,” where a quantum description of both light and atomic motion is equally
important. Due to the dynamical entanglement of atomic motion and light, the measurement of light affects the many-body atomic
state as well. The conditional atomic dynamics can be described using the Quantum Monte Carlo Wave Function Simulation method.
In this paper, we emphasize how this usually complicated numerical procedure can be reduced to an analytical solution after
some assumptions and approximations valid for macroscopic Bose-Einstein condensates (BEC) with large atom numbers. The theory
can be applied for lattices with both low filling factors (e.g. one atom per lattice site in average) and very high filling
factors (e.g., a BEC in a double-well potential). The purity of the resulting multipartite entangled atomic state is analyzed.
key model for “quantum optics with quantum gases,” where a quantum description of both light and atomic motion is equally
important. Due to the dynamical entanglement of atomic motion and light, the measurement of light affects the many-body atomic
state as well. The conditional atomic dynamics can be described using the Quantum Monte Carlo Wave Function Simulation method.
In this paper, we emphasize how this usually complicated numerical procedure can be reduced to an analytical solution after
some assumptions and approximations valid for macroscopic Bose-Einstein condensates (BEC) with large atom numbers. The theory
can be applied for lattices with both low filling factors (e.g. one atom per lattice site in average) and very high filling
factors (e.g., a BEC in a double-well potential). The purity of the resulting multipartite entangled atomic state is analyzed.