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Bulletin of the Russian Academy of Sciences Physics

Phase transition for coupled atom-light states in the presence of optical collisions

Igor Yu. Chestnov, A. P. Alodjants, Sergei M Arakelyan

Published Oct 1, 2012• 0 citations
Publisher

Abstract

The problem of photon phase transition in a system of two-level atoms interacting with a quantized single-mode electromagnetic field in the presence of optical collisions is discussed. The photon field is shown to undergo a high-temperature second order phase transition into the coherent (superradiant) state at large negative values of atom-field detuning and under the condition of thermalization of coupled atom-light states.

DOI
10.3103/s1062873812060123

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The problem of photon phase transition in a system of two-level atoms interacting with a quantized single-mode electromagnetic field in the presence of optical collisions is discussed. The photon field is shown to undergo a high-temperature second order phase transition into the coherent (superradiant) state at large negative values of atom-field detuning and under the condition of thermalization of coupled atom-light states.
The problem of photonic phase transition for the system of a two-level atomic ensemble interacting with a quantized single-mode electromagnetic field in the presence of optical collisions (OCs) is considered. We have shown that for large and negative atom-field detuning a photonic field exhibits high-temperature second-order phase transition to superradiant state under thermalization condition for coupled atom-light states. Such a transition can be connected with superfluid (coherent) properties of photonlike low branch (LB) polaritons. We discuss the application of metallic cylindrical waveguide for observing predicted effects.
The interaction of a two-level atomic ensemble with a quantized single-mode electromagnetic field in the presence of optical collisions is investigated both theoretically and experimentally. The main focus is on achieving thermal equilibrium for coupled atom-light states (in particular dressed states). We propose a model of atomic dressed-state thermalization that accounts for the evolution of the pseudo-spin Bloch vector components and characterize the essential role of the spontaneous emission rate in the thermalization process. Our model shows that the time of thermalization of the coupled atom-light states depends strictly on the ratio of the detuning to the resonant Rabi frequency. The predicted time of thermalization is in the nanosecond domain at full optical power and about 10 times shorter than the natural lifetime in our experiment. Experimentally we investigate the interaction of the optical field with rubidium atoms in an ultrahigh-pressure buffer gas cell under the conditions of large atom-field detuning comparable to the thermal energy in frequency units. In particular, an observed asymmetry of the saturated lineshape is interpreted as evidence of thermal equilibrium of coupled atom-light states.
The problem of phase transitions in the system of high-density gas of two-level atoms non-resonantly interacting with a pump field in the presence of optical collisions (OCs) and placed in the cavity is studied. The OCs are considered in the framework of thermalization of atomic dressed state (DS) population. For the case of a strong atom-field coupling condition we analyze the problem of thermodynamic equilibrium superradiant phase transition for the order parameter representing real amplitude of cavity mode and taking place as a result of the atomic DS thermalization process. At the same time such a transition can be connected with condensed (coherent) properties of low branch DS-polaritons occurring in the cavity. Various aspects of non-equilibrium phase transition to laser field generation by using atomic DS levels are studied in detail. It is important that for positive atom-light detuning DS lasing can be obtained in the presence of quasi-equilibrium DS population that corresponds to a true two-level atomic system with inversion in perturbative limit.
We consider the fundamental problem of high-temperature phase transitions in the system of high-density two-level atoms off-resonantly interacting with a pump field in the presence of optical collisions (OCs) and placed in the cavity. OCs are considered in the framework of thermalization of atomic dressed-state (DS) population. For the case of a strong atom-field coupling condition, we analyze the problem of a thermodynamically equilibrium superradiant phase transition for the order parameter representing a real amplitude of cavity mode and taking place as a result of the atomic DSs thermalization process. Such a transition is also connected with condensed (coherent) properties of low branch DS polaritons occurring in the cavity. For describing nonequilibrium phase transitions we derive Maxwell-Bloch--like equations which account for cavity decay rate, collisional decay rate, and spontaneous emission. Various aspects of transitions to laser field formation by using atomic DS levels for both positive and negative detuning of a pump field from atomic transition frequency are studied in detail. It is revealed that for positive atom-light detuning DS lasing can be obtained in the presence of quasiequilibrium DS population that corresponds to a true two-level atomic system with the inversion in a nonresonant limit.
The atom - electromagnetic field interaction is studied in the Dicke model, wherein a single field mode is interacting with a collection of two level atoms at thermal equilibrium. It is found that in the superradiant phase of the system, wherein the Bose-Einstein condensation of photons takes place, the notion of photon as an elementary electromagnetic excitation ceases to exist. The phase and intensity excitations of the condensate are found to be the true excitations of electromagnetic field. It is found that in this phase, the atom interacts with these excitations in a distinct coherent transition process, apart from the known stimulated emission/absorption and spontaneous emission processes. In the coherent transition it is found that while the atomic state changes in course of the transition process, the state of electromagnetic field remains unaffected. It is found that the transition probability of such coherent transition process is macroscopically large compared to other stimulated emission/absorption and spontaneous emission processes.
Entanglement and quantum correlations between atoms are not usually considered key ingredients of the superradiant phase transition. Here we consider the Tavis-Cummings model, a solvable system of two-levels atoms, coupled with a single-mode quantized electromagnetic field. This system undergoes a superradiant phase transition, even in a finite-size framework, accompanied by a spontaneous symmetry breaking, and an infinite sequence of energy level crossings. We find approximated expressions for the ground state, its energy, and the position of the level crossings, valid in the limit of a very large number of photons with respect to that of the atoms. In that same limit, we find that the number of photons scales quadratically with the coupling strength, and linearly with the system size, providing a new insight into the superradiance phenomenon. Resorting to novel multipartite measures, we then demonstrate that this quantum phase transition is accompanied by a crossover in the quantum correlations and entanglement between the atoms (qubits). The latters therefore represent suited order parameters for this transition. Finally, we show that these properties of the quantum phase transition persist in the thermodynamic limit.