Quantum fluctuations in cavity BEC systems

Abstract

This thesis investigates the role of quantum fluctuations in a cavity Bose-Einstein condensate (BEC) system, where a condensate of atoms is placed in an optical resonator. The atoms are quantum two-level systems and their transitions are pumped off-resonance by a retroreflected laser. Due to the Purcell effect, the atoms and the cavity light strongly couple by enhanced Rayleigh scattering and form strongly coupled polaritons. Weak atom-atom interactions in the BEC are modeled by s-wave scattering, resulting in quantum fluctuations in both the atomic and light fields. The system exhibits a rich phase diagram with quantum fluctuations playing a key role. Light leaving the cavity can be detected to analyze the quantum many-body system non-destructively. This setup is well suited for the study of quantum fluctuation phenomena, and we investigate decoherence effects and novel aggregate states of matter.

In the first part, we explore decoherence and its control. Damping effects arise from quantum fluctuations in the weakly interacting condensate and manifest as phonon-like damping in the form of Landau and Beliaev processes. This damping couples to both the atomic and photon modes, with stronger coupling to the photon mode. We derive exotic spectral properties of the dissipative bath, including competition between damping and antidamping channels, and sub-Ohmic signatures associated with non-Markovian dynamics. The bath is tunable via experimental parameters. We study the central polariton system and find that the quantum fluctuation bath renormalizes the light-matter system, shifting the critical point of the non-equilibrium quantum phase transition. Additional signatures of the quantum bath in the observables are uncovered and shown to be tunable by external parameters.

In the second part, we examine the formation of cavity-induced quantum droplets, a novel state of matter formed by the competition between attractive and repulsive interactions. A classification based on effective energy potentials that incorporates important finite-size effects is introduced. We study a generic long-range interaction with a periodic signature and exponential decay and develop a Bogoliubov theory to analyze the quantum corrections. The leading corrections are those from rotons, which depend on the system size, and as such compete with the mean-field, leading to the formation of a quantum droplet.

This formalism is applied to the cavity BEC setup, focusing on the long-range interaction induced by the cavity mode and the pump field. We show that the zero-point energy of a roton mode selected by the light field can induce droplet formation of the newly identified droplet class. Corrections to the infinite-range interaction are critical for droplet formation, and we develop a model that provides an analytical solution for droplet size. We also investigate droplet optimization using typical experimental parameters and offer a thermodynamic interpretation in terms of pressure, compressibility, and chemical potential. Furthermore, finite temperature effects are discussed and a critical temperature for droplet existence is found. Finally, we study how engineering the interaction, its envelope shape, and symmetries, affects droplet formation.