The model commonly used to describe non-Poissonian pumping of micrornasers refers to periodic pumping where the possible arrival times of the pump atoms are separated by constant time intervals.1 In contrast to this, we study a micromaser with strictly stationary pumping.2 We investigate the level-selective statistics of the atoms leaving the cavity as well as the photon statistics of the cavity field. Our method is based on treating the statistics of the arrival times of the individual pump atoms, which are in the upper state of the microwave transition, with the help of the theory of stochastic point processes.
The model commonly used to describe non-Poissonian pumping of micrornasers refers to periodic pumping where the possible arrival times of the pump atoms are separated by constant time intervals.1 In contrast to this, we study a micromaser with strictly stationary pumping.2 We investigate the level-selective statistics of the atoms leaving the cavity as well as the photon statistics of the cavity field. Our method is based on treating the statistics of the arrival times of the individual pump atoms, which are in the upper state of the microwave transition, with the help of the theory of stochastic point processes.
A method is presented for theoretically investigating the properties of a one-atom micromaser with stationary non-Poissonian pumping. The method is based on treating the statistics of the arrival times of the individual pump atoms with the help of the theory of stochastic point processes. Considerable simplification is achieved by assuming the pump statistics to be described by a stationary renewal process. Thus the influence of super- as well as sub-Poissonian pumping with different strengths of correlation between the pump atoms and different correlation decay times may be studied quantitatively. The level-selective statistics of the atoms leaving the cavity is investigated as well as the photon statistics of the cavity field. Moreover, the relation to the other models used in the literature for describing the micromaser pump statistics is discussed. It is found that for sub- (super-)Poissonian pumping, the stationary expectation value of the cavity photon number (which corresponds to its time-averaged value) is larger (smaller) than the conditioned mean photon number that would result from averaging over the number of photons present in the cavity at the time instants immediately before the injection of the individual pump atoms. For Poissonian pumping, both quantities are shown to be equal. The relative standard deviation of the stationary cavity photon number is decreased (increased) for sub- (super-) Poissonian pumping, in comparison to the corresponding values that would result from Poissonian pumping. Moreover, it turns out that for sub- (super-)Poissonian pumping, the normalized coincidence probability density for the detection of the outgoing deexcited atoms is smaller (larger) than the normalized cavity field intensity correlation function at zero time delay. The difference decreases with increasing lifetime of the pump-atom correlations. Finally, the level-selective delayed coincidence probability densities of the outgoing atoms and their waiting-time distributions are found to be affected greatly by the correlation strength as well as the correlation decay time of the incoming pump atoms.
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.
We investigate the effect of non-Poissonian pump fluctuations on the micromaser dynamics. Non-Poissonian micromaser pumping has been described by two, seemingly unrelated, theoretical approaches. The first employs a discrete pumping process where the pump atoms are allowed to arrive, with certain probability p, only at regularly spaced instants of time, whereas the second refers to continuously distributed arrival times of the pump atoms. Based on a generalization of the latter, we present a unified approach that can handle both situations on an equal footing. We find that for any kind of non-Poissonian pumping the resulting dynamics of the micromaser field is a non-Markovian one. For a micromaser with discrete non-Poissonian pumping, we show the equivalence of ensemble averaging and time averaging, providing a rare example where the validity of the ergodic hypothesis can be explicitly demonstrated. Moreover, we investigate the time-delayed field-field correlation function and a generalized k-photon spectrum of the cavity field, which for k=1 corresponds to the usual power spectrum. For the case that the micromaser is operated under the k-photon trapping condition, we derive exact analytical expressions for the k-photon spectrum and the corresponding correlation functions that result from the exact solution of a non-Markovian evolution problem. Provided that p>1/2, the spectrum is found to be split into several equidistant peaks for certain values of the interaction parameters. \textcopyright{} 1996 The American Physical Society.
We describe the first investigation of the nonclassical radiation field of a micromaser. The maser cavity is cooled to 0.5 K to exclude thermal photons and has a quality factor 3\ifmmode\times\else\texttimes\fi{}1010. Velocity-selected Rydberg atoms pump the maser. The photon statistics in the cavity are measured via the statistics of the atoms leaving the cavity in the lower maser level. Taking into account a detection efficiency of 10%, their fluctuations are reduced up to 40% below the Poisson level. This corresponds to photon-number fluctuations in the cavity of up to 70% below the vacuum-state limit.
An exact method for the simulation of micromaser action is presented. The equation of motion governing the atom–field interaction is solved by inclusion of the effect of cavity dissipation at finite temperature. When the cavity is without an atom, the cavity–reservoir equation as it appears in quantum optics is solved analytically, which is valid for any photon-distribution function required by the initial conditions. The solutions can be fitted into any statistical input of atoms with the condition that, at most, one atom passes through the cavity at any time, and the field as well as the atomic statistics can be obtained. Numerical results are discussed for a Poissonian arrival of atoms at the cavity, and it is observed that the fluctuations in the photon-distribution function, caused solely by the randomness of the pump mechanism, may make the attainment of a Fock state of the cavity field a difficult task experimentally.
The realization of the micromaser prompted theoretical interest in the fundamental problems of laser physics. In particular, it has been shown that the usual quantum theory of the laser can be recovered from the micromaser theory if a Poissonian average with respect to the time intervals between subsequent injections is taken. The problem of general injection statistics has not been fully resolved but, instead, has been circumvented in the following ways. Instead of the time period between successive injections, the number of injected atoms during a fixed time interval was considered as a stochastic variable and was averaged with respect to a general sub-Poissonian distribution. This led to a closed-form master equa tion, but correction terms arise when the effect of cavity damping is significant. In another approach a stroboscopic theory has been developed: The system is observed when a full cycle of pumping, firing, and decay is completed. This assumes observation of the system on a nonuniform time scale. Here we carry out the averaging over the time interval between subsequent injections with sub-Poissonian distribution, suggest a new compact master equation, and exploit some of its consequences. We show that this approach reproduces the previous ones if the cavity damping is negligible. The surprising result of our approach is that altering the pump statistics affects both the gain and the loss part of the laser dynamics.