Quantum Phase Transition in the Finite Jaynes-Cummings Lattice Systems

TL;DR

This paper demonstrates that finite Jaynes-Cummings lattice systems can exhibit quantum phase transitions, including symmetry-breaking and Mott-insulator to superfluid transitions, challenging the notion that such transitions only occur in large systems.

Contribution

It provides an exact analysis showing finite JC-lattices can undergo quantum phase transitions, revealing new phenomena in small quantum systems.

Findings

Finite JC-model exhibits a continuous symmetry-breaking QPT with a photonic condensate.

Two-site JC-lattice undergoes a Mott-insulator to superfluid QPT.

Finite size QPTs arise from increasing atomic energy and interaction strength.

Abstract

Phase transitions are commonly held to occur only in the thermodynamical limit of large number of system components. Here we exemplify at the hand of the exactly solvable Jaynes-Cummings (JC) model and its generalization to finite JC-lattices that finite component systems of coupled spins and bosons may exhibit quantum phase transitions (QPT). For the JC-model we find a continuous symmetry-breaking QPT, a photonic condensate with a macroscopic occupation as the ground state and a Goldstone mode as a low-energy excitation. For the two site JC-lattice we show analytically that it undergoes a Mott-insulator to superfluid QPT. We identify as the underlying principle of the emergence of finite size QPT the combination of increasing atomic energy and increasing interaction strength between the atom and the bosonic mode which allows for the exploration of an increasingly large portion of the infinite dimensional Hilbert space of the bosonic mode. This suggests that finite system phase transitions will be present in a broad range of physical systems.