Stimulated emission of two-level atoms in a high-Q cavity is considered under conditions when pumping produces correlated many-atomic states. Based on the many-body problem, a kinetic equation is obtained for the Glauber–Sudarshan probability, which describes the field in the Fokker–Planck approximation. The statistics of light in this approximation are determined by the atomic correlation functions of the order of no higher than the second. The noise of light is found in the regime of micromaser operation for two types of pumping producing the initial separable states with a classical correlation and entangled states. It is shown that the presence of the initial diatomic correlation enhances the intensity noise. The entangled state of atoms is found from which nonclassical light is generated with a steady-state phase and noise, which can be almost completely suppressed in the low-frequency spectral region.
We consider a system of two masers that are pumped by the same beam of excited atoms. The atoms pass first through one maser and then through the other. As a result, the first maser modifies the pump going into the second and an effective coupling results. We examine this system in the amplifier configuration, i.e., we do not consider saturation effects. The fields in the two masers are mutually coherent and can, under the proper circumstances, be free of noise in their relative phase. Therefore this system exhibits behavior similar to that of a correlated-emission laser. We also find that the photon number in the second maser grows faster than that in the first. These effects should be observable even if the pump beam has a finite velocity spread.
Abstract In the photon number distribution p(θ,k) of the micromaser, distinct structures are formed by the ridges connecting the peaks in the θ-k space. We refer to these structures as phases. By a simple condition we can distinguish between "semiclassical" and "quantum" regimes of operation near and far above threshold, respectively. In the semiclassical regime, the equations of state of the phases θ= θ(k) are monotonous and coincide with the steady state solutions of the semiclassical theory. They reflect typical features of the micromaser dynamics. The transition jumps, e. g., between the phases decrease with increasing pumping parameter θ, signifying the onset of the Jaynes-Cummings collapse. On increasing 9 further, the phases first disintegrate and then restructure into new kinds of phases in the quantum regime. The equations of state are no longer monotonous. Large single peaks, the quantum island states (QIS), develop in the neighborhoods of minima. The system undergoes oscillations between two kinds of quantum island states, QIS- and QIS+ , as a function of θ. The disintegration and transformation of phases recur periodically as θ is varied, and the phases in the semiclassical region are followed by consecutive phase structures in the quantum regime. The subsequent collapses and revivals of phases are directly connected to the Jaynes-Cummings collapse and revival. The observation of these phase structures and the accompanying QIS is experimentally feasible.
We have studied the effect of pump phase fluctuations on steady-state squeezing in a one-photon micromaser for the case of both high- and low (finite)- Q cavities. Our system involves the preparation of a gain medium (atoms) in a partial coherent superposition of states, due to the finite linewidth of the pump field, before injecting them into the microwave cavity. We have found that even in the presence of a finite value of pump phase fluctuations we obtain 40% squeezing for high Q , which reduces to 25% for finite Q . In the absence of pump phase fluctuations we obtain 55% squeezing, in agreement with the previous work.
A single beam of excited two-level atoms couples two micromasers in a series. It is shown that in the absence of dissipation the possible steady states of their fields are superpositions, of two-field trapping number states. Which one is realized depends upon the initial state of the fields and the interaction parameters, g'\ensuremath{\tau}' and g''\ensuremath{\tau}'', of the two cavities. A large number of these trapping states are pure quantum states, some of them showing entanglement of the two nonlocal micromaser fields of the form \ensuremath{\Vert}N,N+M〉\ifmmode\pm\else\textpm\fi{}\ensuremath{\Vert}N+M,N〉. Here, N and N+M are arbitrary trapping numbers that belong to disconnected blocks of the photon number space and M specifies the order of correlation between the fields. The time evolution of the system toward steady states is investigated numerically, mainly concentrating on the production of pure entangled trapping states of the form discussed earlier. We describe a special procedure to amplify a number state, \ensuremath{\Vert}N,N〉, into such states that is based on conditions regarding the interaction parameters. In principle, N and M can be made arbitrarily large resulting in a steady-state nonlocal quantum superposition of distinct macroscopical fields (nonlocal ``Schr\"odinger cat''). We also present a solution of the standard master equation of a damped harmonic oscillator at finite temperature and apply it to study the effect of dissipation on the production of entangled trapping states at regular and Poissonian pump statistics.It is found that although the entanglement does not survive at a steady state it can build up in the short-time transient regime when cavity losses and the number of thermal photons are not too large. In this small-loss (large
Nex) regime the quantum correlation between the micromaser fields decays into a steady-state classical superposition at a rate that depends on the cavity lifetime and the difference (or order of correlation), M, between the superposed photon numbers. In the large-loss (small
Nex) regime, however, no transient correlation can be produced and the photon statistics spreads out towards a vacuum for increasing losses. The system undergoes a transition from an uncorrelated to a correlated behavior when the pumping parametrized by
Nex exceeds the threshold between the large- and small-loss regimes. Thermal photons enhance the decay of the correlation and by coupling the disconnected blocks of the photon number space they populate the trapping number states of adjacent blocks. However, it is shown that the production of transient entanglement is not significantly affected by either thermal radiation or pumping fluctuations. The experimental realization of the entanglement of nonlocal micromaser fields employing these two-field trapping states of small photon numbers is shown to be feasible in the short-time transient regime using the presently available high-Q cavities and low temperatures, and could be possible on the macroscopic scale in the near future.
We present a theory of the micromaser including the effect of the arrival-time statistics of the active atoms in the theoretical treatments. Our starting point is an approach that explicitly incorporates the effect of pump statistics into the dynamical description of lasers and masers. We show that the application of standard laser theory to the micromaser is tantamount to the tacit assumption of Poissonian arrival-time statistics. Hence standard laser theory and the theory of the micromaser are, in general, not equivalent, but the latter contains the former, as a limiting case, for completely random arrival times. We show, as an application, that the steady-state value of the average photon number (first moment) is essentially unaffected by the pump statistics since it depends only on the flux of active atoms (average number of atoms entering the cavity per unit time) provided the flux is constant. The intensity fluctuations (second moment), however, exhibit a stronger dependence on the pump statistics. In particular, for sub-Poissonian pump statistics the sub-Poissonian character of the field is enhanced.