The parameters of the micromaser field in experiments are measured by means of detection of the state of the atoms emerging from the cavity. The employment of the atoms with degenerate levels makes it possible to obtain more information about the micromaser field than in the case of two-level atoms. A way to obtain such information recorded in various Zeeman sublevels of resonant atomic levels is suggested in the present paper. This information is provided by the average quantities , where θμ are Rabi angles related to the transitions between corresponding Zeeman sublevels. At small values of the pump parameter the combinations of these quantities Fμν = zμμzνν−zμν2 are proportional to the Fano factor of the micromaser field. The examples of atomic transitions with the angular momentum changes and are considered.
The parameters of the micromaser field in experiments are measured by means of detection of the state of the atoms emerging from the cavity. The employment of the atoms with degenerate levels makes it possible to obtain more information about the micromaser field than in the case of two-level atoms. A way to obtain such information recorded in various Zeeman sublevels of resonant atomic levels is suggested in the present paper. This information is provided by the average quantities , where θμ are Rabi angles related to the transitions between corresponding Zeeman sublevels. At small values of the pump parameter the combinations of these quantities Fμν = zμμzνν−zμν2 are proportional to the Fano factor of the micromaser field. The examples of atomic transitions with the angular momentum changes and are considered.
The polarization properties of one-atom maser pumped by the coherent field via Raman transitions are studied theoretically. The three-level Λ-type atoms with degenerate Rydberg levels E b < E a < E c enter the micromaser cavity being excited to the lower level E b . The coherent microwave field drives the transition b → c , while the maser transition a → c is coupled to the cavity quantum field. The dependence of the maser field parameters, such as the mean photon number and the variance, as well as of the correlation functions of the atoms, emerging from the cavity, versus the angle ψ between the polarizations of the maser and driving fields are investigated. The case of transitions J b = 3/2 → J c = 3/2 and J a = 5/2 → J c = 3/2 in the rubidium atoms, which are exploited in micromaser experiments (see, e.g., the review [1]), is analyzed numerically. The possibility of monitoring the state of the maser field by means of driving field polarization is discussed.
The polarization properties of the micromaser field pumped by the atoms with the resonant levels, which are degenerate in the projections of the total angular momentum on the quantization axis, are studied numerically. The standard micromaser operation, when the atoms enter the cavity excited to the upper resonant level, and the micromaser operation under the coherent pump, when the atoms enter the cavity in a superposition of resonant atomic levels, are considered. The treatment is based on the master equation for the density matrix of the micromaser field, which takes into account the degeneracy of atomic levels.
The operation of one atom-maser is considered under the conditions, when the atoms enter the cavity being excited to the state, which is the mixture of Zeeman sublevels of both the upper and lower resonant atomic levels. The analytic expression for the steady state photon distribution in the cavity under such conditions is obtained. It is shown, that the micromaser parameters, such as the atomic flux and velocity of atoms, the portion of atoms at the lower maser level, the polarizations of laser excitation fields may be chosen in such a way as to obtain the sharp maximum of photon distribution function at a given number of photons, providing the possibility of creation of pure Fock states.
We present a general method for the derivation of various statistical quantities describing the detection of a beam of atoms emerging from a micromaser. The use of non-normalized conditioned density operators and a linear master equation for the dynamics between detection events is discussed as are the counting statistics, sequence statistics, and waiting time statistics. In particular, we derive expressions for the mean number of successive detections of atoms in one of any two orthogonal states of the two-level atom. We also derive expressions for the mean waiting times between detections. We show that the mean waiting times between detections of atoms in like states are equivalent to the mean waiting times calculated from the uncorrelated steady state detection rates, although like atoms are indeed correlated. The mean waiting times between detections of atoms in unlike states exhibit correlations. We evaluate the expressions for various detector efficiencies using numerical integration, reporting results for the standard micromaser arrangement in which the cavity is pumped by excited atoms and the excitation levels of the emerging atoms are measured. In addition, the atomic inversion and the Fano-Mandel function for the detection of deexcited atoms are calculated for comparison to the experimental results of Weidinger et al. [Phys. Rev. Lett. 82, 3795 (1999)], who report the observation of trapping states.
There are only fistful of systems in physics that can be described by an exact theory from first principles and, at the same time, can be investigated under experimental conditions approaching the idealized theoretical ones. The one-atom-maser or micromaser provides such an example, making a detailed study of the fundamental properties of the atom-field interaction possible. The situation realized in a micromaser is very close to the ideal case of a single two-level atom interacting with a single quantized mode of a cavity field. In the micromaser the atoms have a dual purpose of both pumping the field and also probing it via measurements of the outgoing atoms. Any other means of measuring the field inside the resonator has the detrimental effect of lowering its Q-factor and thereby the photon storage time. The long photon storage time of the resonator allows for the decay of the field to be negligible during the passage of an atom and its interaction with the field. The behavior of atoms in a cavity is governed by the oscillatory exchange of energy between the atoms and the field, which is called Rabi oscillation. For cavity fields in the vacuum and few photon number states (Fock states), Rabi oscillations have been measured in the past. To prevent thermal effects from polluting the pure number states these experiments were performed at low temperatures (below 1 K). However, the observed resolution of the Rabi oscillations measurements was quite disappointing (only about 2% of the predicted theoretical value) and precluded more ambitious experiments like atom-atom correlations or time resolved investigations of the maser field dynamics. The observed contrast of Rabi oscillations can be considered as a figure of merit for the experimental resolution of quantum features of a maser field. Therefore, a high resolution in the measurements of Rabi oscillations is crucial. This thesis describes the methods and improvements applied to enhance the resolution of Rabi oscillations by a factor of 8. The following upgrades and developments proved to be crucial in this work: 1) The base temperature of the cryogenic system was lowered to 0.3 K, i.e. one third of the original value. At the same time, the time during which the system remains at the base temperature was improved by almost of an order of magnitude (to more than 12 h). 2) For the promotion of the atoms to the Rydberg regime new three-step diode laser setup was constructed. The excitation efficiency compared to the old dye laser was increased by two orders. Using top-of-fringe stabilization with new spectroscopic methods, specially designed error detection and feedback schemes as well as state-of-the-art PID regulators the continuous locking of lasers is about 8 h (compared to about 20 min with the old dye laser system). 3) The flexibility of using the three step excitation allows to excite different maser states and for the first time to investigate pure maser transition. 4) Various improvements on the atomic oven and the channeltron detection unit led to the reliable and stable production and detection of the atomic beam. Observed distribution of the atomic beam statistics reaches to within 6% the Poisson limit which is expected in the absence of experimental imperfections. 5) New developed techniques in magnetic field compensation allow to perform such measurements with two orders of magnitude better accuracy compared to the previous experiments. To demonstrate the new capabilities of the apparatus and to apply its improved resolution of quantum fields we performed a previously impossible in-depth analysis of mean photon number and the atomic inversion produced by a micromaser for various detunings between the cavity- and atomic resonance frequency.
The development of a single-atom maser or a micromaser allows a detailed study of the atom–field interaction. The situation realized is very close to the ideal case of a single two-level atom interacting with a single-mode quantized field as treated in Section 6.2. In a micromaser a stream of two-level atoms is injected into a superconducting cavity with a high quality factor. The injection rate can be such that only one atom is present inside the resonator at any time. Due to the high quality factor of the cavity, the radiation decay time is much larger than the characteristic time of the atom–field interaction, which is given by the inverse of the single-photon Rabi frequency. Therefore, a field is built up inside the cavity when the mean time between the atoms injected into the cavity is shorter than the cavity decay time. A micromaser, therefore, allows sustained oscillations with less than one atom on the average in the cavity. The realization of a single-atom maser or a micromaser has been made possible due to the enormous progress in the construction of superconducting cavities together with the laser preparation of highly excited atoms called Rydberg atoms. The quality factor of the superconducting cavities is high enough for periodic energy exchanges between atom and cavity field to be observed. The interesting properties of the Rydberg atoms make them ideal for micromasers. In Rydberg atoms the probability of induced transitions between adjacent states becomes very large and scales as n 4 , where n denotes the principle quantum number.