Ultracold atoms in optical lattices generated by quantized light fields

TL;DR

This paper investigates ultracold atoms in optical lattices created by quantized light fields within a high-Q cavity, revealing modified phase transitions, new phases, and quantum superpositions due to quantum light-matter interactions.

Contribution

It derives multiparticle Bose-Hubbard Hamiltonians from cavity QED models incorporating quantum light effects, and analyzes phase transitions and dynamics including dissipation.

Findings

Quantum uncertainties modify phase transition characteristics.

Identification of new quantum phases and superpositions.

Microscopic insight into transition from Mott insulator to superradiant state.

Abstract

We study an ultracold gas of neutral atoms subject to the periodic optical potential generated by a high-$Q$ cavity mode. In the limit of very low temperatures, cavity field and atomic dynamics require a quantum description. Starting from a cavity QED single atom Hamiltonian we use different routes to derive approximative multiparticle Hamiltonians in Bose-Hubbard form with rescaled or even dynamical parameters. In the limit of large enough cavity damping the different models agree. Compared to free space optical lattices, quantum uncertainties of the potential and the possibility of atom-field entanglement lead to modified phase transition characteristics, the appearance of new phases or even quantum superpositions of different phases. Using a corresponding effective master equation, which can be numerically solved for few particles, we can study time evolution including dissipation. As an example we exhibit the microscopic processes behind the transition dynamics from a Mott insulator like state to a self-ordered superradiant state of the atoms, which appears as steady state for transverse atomic pumping.