We examine the competition among one- and two-photon processes in an ultracold, three-level atom undergoing cascade transitions as a result of its interaction with a bimodal cavity. We show parameter domains where two-photon transitions are dominant, and we also study the effect of two-photon emission on the mazer action in the cavity. The two-photon emission leads to the loss of detailed balance and therefore we obtain the photon statistics of the cavity field by the numerical integration of the master equation. The photon distribution in each cavity mode exhibits sub- and super-Poissonian behaviors depending on the strength of atom-field coupling. The photon distribution becomes identical to a Poisson distribution when the atom-field coupling strengths of the modes are equal.
We examine the competition among one- and two-photon processes in an ultracold, three-level atom undergoing cascade transitions as a result of its interaction with a bimodal cavity. We show parameter domains where two-photon transitions are dominant, and we also study the effect of two-photon emission on the mazer action in the cavity. The two-photon emission leads to the loss of detailed balance and therefore we obtain the photon statistics of the cavity field by the numerical integration of the master equation. The photon distribution in each cavity mode exhibits sub- and super-Poissonian behaviors depending on the strength of atom-field coupling. The photon distribution becomes identical to a Poisson distribution when the atom-field coupling strengths of the modes are equal.
The work of Meyer, Scully, and Walther [Phys. Rev. A 56, 4142 (1997)] is generalized to study the operation of a two-mode mazer with particular reference to the question of mode-mode correlations. The explicit expression for the detailed balance steady-state photon distribution has been derived. It is shown that the two-mode mazer exhibits much stronger sub-Poissonian statistics for each mode. The photon-number distributions are found to be quite sensitive to the presence of blackbody photons in the cavity. The interferences among contributions from different dressed states enable one to obtain the phase of the transmission amplitude of finding the atom in the initial excited state by considering a set of two measurements involving two different initial states of the atom-field system.
The interaction between an ultracold cascade three-level atom and a two-mode cavity field has been studied. The effects of the centre-of-mass motion, the cavity length, the coupling constants, the initial field states and the initial field intensity on the atomic dynamics have been examined. We have found that the population probabilities show dependence on the interaction time in the fast-atom region while they show dependence on the interaction length in the slow-atom region. The variations of the probabilities versus the cavity length show resonant peaks, and the peaks become sharper as the atom moves more slowly. The coupling constants, the initial field states and the initial field intensity also influence the atomic dynamics significantly. The two transitions are competitive for the atomic probability in the middle state, while they are cooperative for that in the lower state.
The analytical form of the emission probability produced by the interaction of an ultracold three-level atom with an electromagnetic bimodal cavity field with multi-photon transitions of the atoms (multi-photon mazer) is analysed in the framework of the dressed-state formalism, but is distinguished from other treatments by the inclusion of the spatial variation along the cavity axis. In particular, the cavity field mode profile is considered by using the mesa-mode function and differences in the collapse–revival patterns are reported. We demonstrate that, when propagation effects are taken into consideration, the emission probability is influenced significantly. We provide the necessary arguments to justify the validity of our conclusions for emission probability and the micromaser, whose dynamics are governed by the wavefunction. Our main conclusion is that, in the present system, the inclusion of the spatial dependence is necessary and important. The numerical illustrations provide evidence that, in cases of physical interest, the emission probability can be significant and can be reliably estimated for a broad range of field parameters using the present formalism.
Abstract We investigate the steady-state photon statistics and quantum properties of a cascade three-level atom coupled to a two-mode squeezed-vacuum reservoir. The mean photon number, photon-number correlations, second-order coherence, and quadrature fluctuations are examined as functions of the stimulated-emission decay constant and the squeezing parameter. The system exhibits two distinct regimes: a squeezing-dominated regime, governed by reservoir-induced correlations, and a cavity-dynamics-dominated regime, characterized by strong gain–loss competition. Enhanced squeezing increases photon generation, intermodal correlations, and intracavity energy through correlated photon-pair injection while reducing vacuum fluctuations. Conversely, stronger stimulated emission induces nonlinear amplification, asymmetric photon distributions, and sequential emission dynamics. A transition from super-Poissonian to sub-Poissonian statistics is observed, indicating the coexistence of photon antibunching and continuous-variable quantum correlations. Furthermore, atom–cavity interactions modify the generalized uncertainty bounds, revealing fundamental limitations on achievable squeezing imposed by higher-order noise processes. These findings demonstrate that engineered reservoirs and cascade atomic systems provide versatile control of nonclassical light for quantum communication, precision metrology, and continuousvariable quantum information processing.
We derive the dressed states for the interaction of a cascade three-level atom with a quantum cavity field, suggest using ultra-cold cascade three-level atoms in micromasers, put forward the idea of the two-photon mazer, establish its general quantum theory and study its emission probability and photon statistics. We examine the effects of the atomic centre-of-mass momentum, the atom-field detuning, the photon number in thermal equilibrium, the ratio of the atomic injection rate to the cavity decay rate and the interaction length on the emission probability and the photon statistics.
The properties of the two-mode mazer operating on V-type three-level atoms are studied. The effect of the one-atom pumping on the two modes of the cavity field in number-state is asymmetric, that is, the atom emits a photon into one mode with some probability and absorbs a photon from the other mode with some other probability. This effect makes the steady-state photon distribution and the steady-state photon statistics asymmetric for the two modes. The diagram of the probability currents for the photon distribution, given by the analysis of the master equation, reveals that there is no detailed balance solution for the master equation. The computations show that the photon statistics of one mode or both modes can be sub-Poissonian, that the two modes can have anticorrelation or correlation, that the photon statistics increases with the increase of thermal photons and that the resonant position and strength of the photon statistics are influenced by the ratio of the two coupling strengths of the two modes. These properties are also discussed physically.