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(Color online) Normalized wave function width w versus time t. The parameters are the following: ν = 1, R0 ≈ 0.3 µm and α 1/ν = 0.0005 µm −1 . An initial condition is w (τ = 0) = 0.75 for solid (blue) curve, w (τ = 0) = 0.8 for dashed (red) curve, and w (τ = 0) = 0.9 for dotted (green) curve. In all cases ˙ w (τ = 0) = 0. The horizontal line w = 1 corresponds to the stationary solution of Eq.(42).
Source publication
We study the problem of high temperature Bose-Einstein condensation (BEC) of
atom-light polaritons in a waveguide cavity appearing due to interaction of
two-level atoms with (non-resonant) quantized optical radiation, in the strong
coupling regime, in the presence of optical collisions (OCs) with buffer gas
particles. Specifically, we propose a spe...
Contexts in source publication
Context 1
... the presence of polariton trapping the analytical solution of Eq.(42) is much more complicated. Figure 6 demon- strates the temporal dynamics of the normalized polari- ton condensate wave function width w, using the Ru- bidium parameters described in section III (cf. [24][25][26]), which shows oscillations around the equilibrium solution. ...
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Citations
... Such a feature of the Dicke-Ising model that we offer in this work, may be useful for the problem of obtaining high-temperature BEC, which is now a hot topic of research in statistical physics and material science, cf. [43,44]. ...
... Second, the grand canonical approach presumes a non-zero chemical potential when photons and spins (or two-level systems) can form coupled states (dressed states, polaritons), which possess the SR phase transition [34,36]. In other words, at non-zero chemical potential we can speak about BEC of low branch polaritons that occurs in the system in the presence of appropriate trapping potential [43][44][45]. In this work we restrict ourselves by canonical ensemble approach to the network spin-1/2 system, which interacts with classical and quantized fields. ...
In this work we consider a superradiant phase transition problem for the Dicke-Ising model, which generalizes the Dicke and Ising models for annealed complex networks presuming spin-spin interaction. The model accounts the interaction between a spin (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the delta-function, random (Poisson), and power-law exponent degree distributions, respectively. To describe paramagnetic (PM) - ferromagnetic (FM) and superradiant (SR) phase transitions we introduce two order parameters: the total weighted spin z-component and the normalized transverse field amplitude, which correspond to the spontaneous magnetization in z and x directions, respectively. Due to the interplay between the spin interaction and the finite size effects in the networks we first elucidate novel features of the SR state in the presence of the PM-FM phase transition. We reveal that the critical temperature of the SR phase transition grows monotonically from some certain value that corresponds to the critical number of nodes. For the scale-free networks we find that this critical temperature rises with the degree exponent increase accompanied both by establishing spontaneous magnetization in a quantum transverse field and vanishing of the collective spin component in z direction. In addition, we establish the conditions for the network parameters to obtain a quantum phase transition in the spin system when the critical temperature approaches zero. The fundamental features, which involve critical values of the classical and quantum field parameters, are discussed for the occurrence of the superradiance phase in this limit.
... Most recently, the investigation of two-dimensional photons has evoked strong interest in the BEC of one-dimensional photons [18,19]. In our previous paper [20], we proposed a rigorous analytical solution to the problem of BEC in harmonically trapped, one-dimensional and ideal photons. ...
Our experimental scheme is based on a barrel optical microcavity filled with a dye solution.
It is found that the number of non-condensed photons is characterized by an analytical
function, which involves a q-digamma function in mathematics.We employ the q-digamma
function to calculate the spatial and momentum distributions of ideal photons in a onedimensional
barrel cavity. The first main finding in this paper is that the spatial and
momentum distributions possess a similar profile. The second main finding is that when
photons are in the normal state, the density profile exhibits Friedel oscillations. The third
main finding is that when photons are in the BEC state, the density profile exhibits a sharp
peak with extremely narrow width. The fourth main finding is that the central peak of the
density distribution is a monotonically increasing function of the photon number N but is a monotonically decreasing function of the temperature T .
... The one-dimensional character makes the problem simple enough that some exact analytical solutions can be obtained using specific methods, and these solutions can lead to incredibly rich physics. Originally, the BEC of atomic polaritons in a biconical waveguide cavity was investigated under the quasiclassical approximation [29]. The biconical waveguide cavity provides a linear confining potential for an atom polariton. ...
... where L(q) is given by Eq. (23). At room temperature (T = 300 K), the calculation of Eq. (29) gives N c = 1691. It is interesting to note that the critical number N c of a one-dimensional photon gas is smaller than that of a twodimensional photon gas by two orders of magnitude. ...
... When calculating I , we must combine Eq. (19) with Eq. (36). According to Eq. (36), the variation of the spectral radiance I with the wavelength λ is given in Fig. 9 for various N at T = 300 K. From Eq. (29), one finds that at T = 300 K, N c = 1691. Figure 9 shows that for a fixed T and N , the spectral radiance I is a monotonically increasing function of the wavelength λ. ...
Our experimental scheme is based on a barrel optical microresonator filled with a dye solution. The barrel mirror provides a confining potential, a chemical potential, and an effective mass for a photon, making the system formally equivalent to a one-dimensional gas of harmonically trapped, number-conserving, and massive bosons. Within the framework of quantum statistical mechanics, we propose an exact analytical solution to the problem of Bose-Einstein condensation in harmonically trapped, one-dimensional, and ideal photons. It is found that the photon number of vapor is characterized by an analytical function, which involves a q-digamma function in mathematics. The numerical calculation of the analytical solution gives many interesting results. In the thermodynamic limit, the analytical expressions of the critical temperature and the condensate fraction are derived. We find that the spectral radiance of a one-dimensional barrel cavity has a sharp peak at the frequency of the cavity cutoff when the photon number exceeds the critical value determined by a temperature.
We present a theoretical study of a Berezinskii-Kosterlitz-Thouless-like phase transition in lattices of nonequilibrium photon condensates. Starting from linearized fluctuation theory and the properties of vortices, we propose an analytical formula for the critical point containing four fitting parameters, that captures well all our numerical simulations. We find that the ordered phase becomes more stable when driving and dissipation are increased.
In this work we consider a superradiant phase transition problem for the Dicke-Ising model, which generalizes the Dicke and Ising models for annealed complex networks presuming spin-spin interaction. The model accounts for the interaction between a spin-1/2 (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the δ function, random (Poisson), and power-law exponent [p(k)∝k−γ] degree distributions, respectively. To describe paramagnetic (PM)-ferromagrenic (FM) and superradiant (SR) phase transitions we introduce two order parameters: the total weighted spin z component and the normalized transverse field amplitude, which correspond to the spontaneous magnetization in z and x directions, respectively. For the regular networks and vanishing external field we demonstrate that these phase transitions generally represent prerequisites for the crossover from a disordered spin state to the ordered one inherent to the FM and/or SR phase. Due to the interplay between the spin interaction and the finite-size effects in networks we elucidate novel features of the SR state in the presence of the PM-FM phase transition. In particular, we show that the critical temperature may be high enough and essentially depends on parameters which characterize statistical properties of the network structure. For the scale-free networks we demonstrate that the network architecture, characterized by the particular value of γ, plays a key role in the SR phase transition problem. Within the anomalous regime scale-free networks possess a strong effective spin-spin interaction supporting fully ordered FM state, which is practically nonsensitive to variations of the quantum transverse field or moderate classical magnetic field. In a scale-free regime the networks exhibit vanishing of the collective spin component in z direction with increasing γ accompanied by establishing spontaneous magnetization in the transverse field. The SR phase transition occurs in the presence of some FM state. We establish the conditions for the network parameters, classical and quantum field features to obtain a quantum phase transition in the spin system when the critical temperature approaches zero.
This paper introduces a quasiequilibrium one-dimensional Bose-Einstein
condensation of photons trapped in a microtube. Light modes with a cut-off
frequency (a photon's "mass") interact through different processes of
absorption, emission, and scattering on molecules and atoms. In this paper, we
study the conditions for the one-dimensional condensation of light and the role
of photon-photon interactions in the system. The technique in use is the
Matsubara's Green's functions formalism modified for the quasiequilibrium
system under study.
We propose a method for obtaining a Bose-Einstein condensate of an ideal one-dimensional gas of atom-light polaritons of the lower branch in a trap at high temperatures (on the order of room temperature or higher). The system under consideration is an atomic ensemble that interacts with a single-mode quantum electromagnetic field in the presence of optical collisions with a high-pressure buffer gas. The possibility of using biconical waveguides for revealing the predicted phenomenon is discussed. The dynamics of the polariton condensate in the trap is investigated on the basis of the variational approach.
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 propose a novel physical mechanism for creation of long lived macroscopic
exciton-photon qubits in semiconductor microcavities with embedded quantum
wells in the strong couping regime. We argue that the coherence time of Rabi
oscillations can be dramatically enhanced due to their stimulated pumping from
a permanent thermal reservoir of polaritons. The polariton qubit is a
superposition of lower branch (LP) and upper branch (UP) exciton-polariton
states. We discuss applications of such qubits for quantum information
processing, cloning and storage purposes.
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 thermodynamically equilibrium superradiant phase
transition for the order parameter representing a real amplitude of cavity mode
and taking place as a result of atomic DSs thermalization process. Such
transition is also connected with condensed (coherent) properties of low branch
(LB) DS-polaritons occurring in the cavity. For describing non-equilibrium
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 quasi-equilibrium DS
population that corresponds to a true two-level atomic system with the
inversion in nonresonant limit.
