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arXiv:1311.4187 · Physical Review A

Lasing and high-temperature phase transitions in atomic systems with dressed-state polaritons

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

Published Dec 20, 2013• 8 citations
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Abstract

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.

DOI
10.1103/physreva.88.063834

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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 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.
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 theoretically investigated. The main accent is made 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 strictly depends on the ratio of the detuning and the resonant Rabi frequency. The predicted time of thermalization is in the nanosecond domain and about ten times shorter than the natural lifetime of rubidium D-lines.
We study the operational properties of the lasing field generated from strongly driven two-level atoms in a ring cavity by including the field saturation to all orders. Lasing without inversion between bare atomic states can occur for both off-resonant-- and resonant-pump fields. In the case of an off-resonant--pump field, lasing occurs at one of the Rabi sidebands, for which there exists population inversion between the relevant dressed-atom--field states. In the case of a resonant-pump field, lasing can occur near either of two Rabi sidebands, for which there is no population inversion between the dressed states; here the gain is due to the atomic coherence between the dressed states. While the operation of the off-resonantly--pumped dressed-state laser is similar to that of an ordinary laser, the operation of the resonantly pumped dressed-state laser exhibits some interesting features, such as (1) mode pushing and (2) larger laser intensity coming from smaller linear gain as the detuning is changed. In order to show such features, the calculations have to go beyond the secular approximation.
Pattern formation of atoms in high-finesse optical resonators results from the mechanical forces of light associated with superradiant scattering into the cavity mode. It occurs when the laser intensity exceeds a threshold value such that the pumping processes counteract the losses. We consider atoms driven by a laser and coupling with a mode of a standing-wave cavity and describe their dynamics with a Fokker-Planck equation, in which the atomic motion is semiclassical but the cavity field is a full quantum variable. The asymptotic state of the atoms is a thermal state, whose temperature is solely controlled by the detuning between the laser and the cavity frequency and by the cavity loss rate. From this result we derive the free energy and show that in the thermodynamic limit self-organization is a second-order phase transition. The order parameter is the field inside the resonator to which one can associate a magnetization in analogy to ferromagnetism, the control field is the laser intensity, but the steady state is intrinsically out of equilibrium. In the symmetry-broken phase, quantum noise induces jumps of the spatial density between two ordered patterns: We characterize the statistical properties of this temporal behavior at steady state and show that the thermodynamic properties of the system can be extracted by detecting the light at the cavity output. The results of our analysis are in full agreement with previous studies; we extend them by deriving a self-consistent theory which is valid also when the cavity field is in the shot-noise limit and elucidate the nature of the self-organization transition.