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arXiv:1005.3884 · Journal of the Optical Society of America B

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

B. M. Rodríguez-Lara, Ray‐Kuang Lee

Published Oct 29, 2010• 18 citations
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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 co-existence of squeezed fields and squeezed atomic ensembles.

DOI
10.1364/josab.27.002443

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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 co-existence of squeezed fields and squeezed atomic ensembles.
In this paper we investigate a ground state quantum phase transition of nonlinear light in a generalized finite size Dicke model, which includes a Kerr-type nonlinear field term along with the counter-rotating interaction. The numerical solution is presented. We show that, in the ground state, the intracavity photons exhibit a third-order QPT from the bunching to the antibunching quantum phase. This phase transition stems from the competition between the atom-induced coupling and the effective photon–photon interaction. We also demonstrate that the general properties of the phase transition do not qualitatively alter by the size of the atomic ensemble and by the detuning between atoms and light, as well.
We investigate quantum phase transitions, quantum criticality, and Berry phase for the ground state of an ensemble of non-interacting two-level atoms embedded in a non-linear optical medium, coupled to a single-mode quantized electromagnetic field. The optical medium is pumped externally through a classical electric field, so that there is a degenerate parametric amplification effect, which strongly modifies the field dynamics without affecting the atomic sector. Through a semiclassical description the different phases of this extended Dicke model are described. The quantum phase transition is characterized with the expectation values of some observables of the system as well as the Berry phase and its first derivative, where such quantities serve as order parameters. It is remarkable that the model allows the control of the quantum criticality through a suitable choice of the parameters of the non-linear optical medium, which could make possible the use of a low intensity laser to access the superradiant region experimentally.
We introduce a group-theoretical extension of the Dicke model, which describes an ensemble of two-level atoms interacting with a finite radiation field. The latter is described by a spin model whose main feature is that it possesses a maximum number of excitations. The approach adopted here leads to a nonlinear extension of the Dicke model that takes into account both the intensity dependent coupling between the atoms and the radiation field and an additional nonlinear Kerr-like or Pösch–Teller-like oscillator term, depending on the degree of nonlinearity. We use the energy surface minimization method to demonstrate that the extended Dicke model exhibits a quantum phase transition, and we analyze its dependence upon the maximum number of excitations of the model. Our analysis is carried out via three methods: through mean-field analysis (i.e., by using the tensor product of coherent states), by using parity-preserving symmetry-adapted states (using the critical values obtained in the mean-field analysis and numerically minimizing the energy surface), and by means of the exact quantum solution (i.e., by numerically diagonalizing the Hamiltonian). Possible connections with the qp-deformed algebras are also discussed.
In this study, the energy spectrum and thermal equilibrium states of the finite-size Dicke-Stark model were numerically obtained within the extended coherent state space by solving the dressed master equation for strongly coupled light-atom systems. The critical point of the superradiant phase transition in the infinite-size Dicke-Stark model was analytically derived using the mean-field approach and confirmed with numerical calculation. Under thermal equilibrium conditions, analyses of the negativity, zero-time-delay two-photon correlation function, and atom-spin squeezing parameters in the finite-size Dicke-Stark model reveal that as the coupling strength increases, the light field undergoes a transition from photon bunching to anti-bunching and then back to bunching. The Stark field can modulate both the maximum and minimum values of the two-photon correlation function and their corresponding coupling strengths. At low temperatures, the system exhibits entanglement and spin squeezing. As temperature rises, entanglement gradually diminishes, while strong coupling facilitates the preservation of entanglement in the system state. Atom-spin squeezing spin squeezing is highly sensitive to temperature and vanishes rapidly with increasing temperature. This work contributes to the fundamental understanding of quantum phenomena in Dicke-Stark systems.
Information about quantum phase transitions in conventional condensed matter systems, must be sought by probing the matter system itself. By contrast, we show that mixed matter-light systems offer a distinct advantage in that the photon field carries clear signatures of the associated quantum critical phenomena. Having derived an accurate, size-consistent Hamiltonian for the photonic field in the well-known Dicke model, we predict striking behavior of the optical squeezing and photon statistics near the phase transition. The corresponding dynamics resemble those of a degenerate parametric amplifier. Possible realizations include atom-cavity, nanostructure-cavity, and nanostructure-photonic-band-gap systems.
Two interacting atomic ensembles display a Dicke-like quantum phase transition above a critical coupling strength. We show that an ensemble-ensemble entanglement accompanies the quantum phase transition. We derive entanglement criteria which can witness the entanglement of the two interacting ensembles. We observe that all criteria are successful in the thermodynamic limit, while only the newly introduced ones (number-squeezing-like criteria) can witness the ensemble-ensemble entanglement for a finite number of particles. We also mention the implementations of these criteria to two-component condensate systems and nanoscale quantum plasmonics.