Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system

Abstract

The Dicke model describing an ensemble of two-state atoms interacting with a single quantized mode of the electromagnetic field ͑with omission of the  2 term͒ exhibits a zero-temperature phase transition at a critical value of the dipole coupling strength. We propose a scheme based on multilevel atoms and cavity-mediated Raman transitions to realize an effective Dicke model operating in the phase transition regime. Optical light from the cavity carries signatures of the critical behavior, which is analyzed for the thermodynamic limit where the number of atoms is very large.

Quantum entanglement and disentanglement of multi-atom systems

“…The competition between these one and two-photon processes is the source of the phenomenon of entanglement sudden death. Figure 22 illustrates the atom-atom concurrence as a function of time and the detuning ∆, calculated from an initial condition of the atoms prepared in the non-maximally entangled state (43). We can see that in the case of ∆ = 0, the initial entanglement is lost in a discontinuous fashion and can revive periodically during the evolution.…”

“…It was originally introduced by Dicke in his famous article published in 1954, and currently a very large literature exists on a wide variety of problems involving the model, in particular on the concepts of super-radiance and the directional propagation of light in atomic ensembles [79][80][81]. Recently, the model has been employed in the studies of entanglement, in particular for creation of entanglement in atomic ensembles composed of a large number of trapped and cooled atoms [41][42][43]45]. The two-atom Dicke model is a simplified form of the twoatom system considered in the preceding section.…”

“…For example, the absence of fluorescence can be a signature for maximally entangled atom pairs which, in principle, can be used to create cluster states for one-way quantum computing [40]. An another scheme based on interactions in CQED has been proposed that uses a combination of the cavity field with atomic Raman transitions between a pair of long-lived atomic ground states [41][42][43][44][45]. The Raman transitions are mediated by two laser fields that are highly detuned from the transitions between the atomic ground and the excited states.…”

“…The schemes are based on a suitable driving of four-level atoms with two external laser fields and coupling to a damped cavity mode that prepares the atoms in a pure entangled state. Similar schemes have been proposed to realize an effective Dicke model operating in the phase transition regime [43], to create a stationary subradiant state in an ultracold atomic gas [57], and to prepare trapped and cooled ions in pure entangled vibrational states [58]. Simple procedures have been proposed to prepare ensembles of cold atoms in pure multi-mode entangled states and ensembles of hot atoms in pure entangled cluster states [45].…”

“…(180), arise naturally for the position dependent atomic transition operators and appear in a cavity with two mutually counterpropagating modes. In the case of a single-mode cavity, the Hamiltonian involves only the J (n) 0k operator [42,43,57]. The operators σ (n) j , σ (n) † j and σ (n) zj are the standard Pauli spin−1/2 operators, which satisfy the well known commuta-…”