Collective spin systems in dispersive optical cavity QED: Quantum phase transitions and entanglement

Morrison, Sam; Parkins, Scott

doi:10.1103/physreva.77.043810

Cited by 68 publications

(80 citation statements)

References 60 publications

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“…However, it also captures the physics of interacting bosons in a double-well-like structure 5,6 and is thus relevant to (two-mode) Bose-Einstein condensates 7 as well as Josephson junctions. It has also been recently used in optical cavity quantum electrodynamics in its dissipative version 8,9 for studying the decoherence of a single spin coupled to a spin bath 10,11 or quench dynamics 12 . Note also that, in recent years, the entanglement properties of its ground state 13,14,15,16,17,18,19,20,21,22 as well as the finite-size behavior 23,24,25,26 have focused much attention on this model.…”

Section: Introductionmentioning

confidence: 99%

Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections

2008

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The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin-coherent-state formalism. In the first step, a classical analysis allows one to distinguish between four distinct regions in the parameter space according to the nature of the singularities arising in the classical energy surface; these correspond to spectral critical points. The eigenfunctions are then analyzed more precisely in terms of the associated roots of the Majorana polynomial, leading to exact expressions for the density of states in the thermodynamic limit. Finitesize effects are also analyzed, leading in particular to logarithmic corrections near the singularities occurring in the spectrum. Finally, we also compute expectation values of the spin operators in a semiclassical analysis in order to illustrate some subtle effects occurring in one region of the parameter space.

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Section: Introductionmentioning

confidence: 99%

Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections

2008

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“…For example, using the results shown in (49), (50) and (46) of the initial step for j = 1/2 case, we can use (27)- (33) to do the k = 1 step diagonalization. In this case, according to (35), we have:…”

Section: The Pds For the Dicke Modelmentioning

confidence: 99%

“…Though noticeable change in the atomic inversion fluctuation was also observed in the large-N limit of the Dicke model calculated from the exact steady-state solution through the equivalent Fokker-Planck equation of the system [31,32], there is no sharp peak emerging in the atomic inversion fluctuation at the critical point from the calculation, while, as clearly shown in the right panel of Figure 3, a sharp peak develops in the atomic inversion fluctuation near the critical point in the finite-N cases studied in this paper. Moreover, the rescaled concurrence, which can be used as an entanglement measure and also related to the atomic inversion fluctuation, in the dispersive limit of the model with ω {ω 0 , λ} was also studied [33]. It should be noted that the Dicke Hamiltonian (1) in the dispersive limit is reduced to the Lipkin-Meshkov-Glick (LMG) model.…”

Section: The Qpt and Entanglementmentioning

confidence: 99%

The Critical Point Entanglement and Chaos in the Dicke Model

Bao

Pan

et al. 2015

Entropy

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Ground state properties and level statistics of the Dicke model for a finite number of atoms are investigated based on a progressive diagonalization scheme (PDS). Particle number statistics, the entanglement measure and the Shannon information entropy at the resonance point in cases with a finite number of atoms as functions of the coupling parameter are calculated. It is shown that the entanglement measure defined in terms of the normalized von Neumann entropy of the reduced density matrix of the atoms reaches its maximum value at the critical point of the quantum phase transition where the system is most chaotic. Noticeable change in the Shannon information entropy near or at the critical point of the quantum phase transition is also observed. In addition, the quantum phase transition may be observed not only in the ground state mean photon number and the ground state atomic inversion as shown previously, but also in fluctuations of these two quantities in the ground state, especially in the atomic inversion fluctuation.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Quantum entanglement and disentanglement of multi-atom systems

Ficek

2009

Front. Phys. China

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We present a review of recent research on quantum entanglement, with special emphasis on entanglement between single atoms, processing of an encoded entanglement and its temporary evolution. Analysis based on the density matrix formalism are described. We give a simple description of the entangling procedure and explore the role of the environment in creation of entanglement and in disentanglement of atomic systems. A particular process we will focus on is spontaneous emission, usually recognized as an irreversible loss of information and entanglement encoded in the internal states of the system. We illustrate some certain circumstances where this irreversible process can in fact induce entanglement between separated systems. We also show how spontaneous emission reveals a competition between the Bell states of a two qubit system that leads to the recently discovered "sudden" features in the temporal evolution of entanglement. An another problem illustrated in details is a deterministic preparation of atoms and atomic ensembles in long-lived stationary squeezed states and entangled cluster states. We then determine how to trigger the evolution of the stable entanglement and also address the issue of a steered evolution of entanglement between desired pairs of qubits that can be achieved simply by varying the parameters of a given system.

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Collective spin systems in dispersive optical cavity QED: Quantum phase transitions and entanglement

Cited by 68 publications

References 60 publications

Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections

Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections

The Critical Point Entanglement and Chaos in the Dicke Model

Quantum entanglement and disentanglement of multi-atom systems

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