Quantum statistics of the collective excitations of an atomic ensemble inside a cavity

TL;DR

This paper investigates the quantum statistical behavior of collective atomic excitations in a cavity, revealing long-range interactions, atomic blockade, and quantum phase transitions influenced by photon number, with implications for various quantum systems.

Contribution

It introduces a model demonstrating photon-number-dependent quantum phase transitions and atomic blockade in an atomic ensemble inside a cavity, extending understanding of collective quantum phenomena.

Findings

Virtual photon exchange induces long-range atomic interactions.

Atomic blockade suppresses double excitations at specific photon numbers.

Quantum phase transitions occur at critical photon numbers.

Abstract

We study the quantum statistical properties of the collective excitations of an atomic ensemble inside a high-finesse cavity. In the large-detuning regime, it is found that the virtual photon exchange can induce a long-range interaction between atoms, which results in correlated excitations. In particular, the atomic blockade phenomenon occurs when the induced long-range interaction effectively suppresses the double atomic excitation, when the average photon number takes certain values, which makes the two nearest energy levels degenerate. We also show that quantum phase transitions occur in the indirectly-interacting atomic ensemble when the average photon number reaches several critical points. In this sense, the quantum statistical properties of the collective excitations are very sensitive to the change of the average photon number. Our model exhibits quantum phase transitions similar to the ones in the Lipkin-Meshkov-Glick model. Our proposal could be implemented in a variety of systems including cavity quantum electrodynamics (QED), Bose-Einstein condensates, and circuit QED.