Quantum phase transition of nonlinear light in the finite size Dicke Hamiltonian

Abstract

We study the quantum phase transition of an N two-level system ensemble interacting with an optical degenerate parametric process, which can be described by the finite size Dicke Hamiltonian plus counter-rotating and quadratic field terms. Analytical closed forms of the critical coupling value and their corresponding separable ground states are derived in the weak and strong coupling regimes. The existence of bipartite entanglement between the two-level system ensemble and photon field as well as between ensemble components for moderate coupling is shown through numerical analysis. Given a finite size, our results also indicate the coexistence of squeezed fields and squeezed atomic ensembles.

The Dicke model in quantum optics: Dicke model revisited

“…In the case of dipole radiation a no-go theorem stimulated much discussion [59][60][61]. In the case of CQED, for example, the no-go theorem does not apply [5].…”

Excited-state phase transition and onset of chaos in quantum optical models

“…Both versions have recently stirred up great interest, since the implementation of a tunable matter-light coupling represents a route to study quantum critical effects [15][16][17]. The QPT to a superradiant phase within the Dicke model was studied theoretically [2,[18][19][20], and recently realized experimentally using a superfluid gas in an optical cavity [17]. This paper is organized as follows.…”

The Critical Point Entanglement and Chaos in the Dicke Model

“…We use the logarithm to the base N + 1 instead of base two to ensure that the maximal measure is normalized to one [39,40]. In addition, Koashi entangled webs [41] were used to measure entanglement in the atomic part of the ground state of finite-size models related to the extended Dicke models [42,43], which provide another good measure of average qubit-qubit entanglement to show the highest entanglement occurring at the critical point. Moreover, the Shannon information entropy of the ground state of quantum many-body systems is also a good measure of correlations among local states [44], which, in the Dicke model, is defined by:…”