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Physical Review A

Micromaser as a maser without inversion

Paweł Masiak, Kazimierz Rza̧żewski, L. Roso

Published Apr 1, 1995• 6 citations
Publisher

Abstract

We show that the micromaser, widely studied for its distinct quantum features, has one more remarkable property: unlike conventional lasers and masers it works without population inversion. We study the time-averaged inversion of a single atom passing through a cavity with a field in its stationary state. The result is shown to hold also for the regularly pumped micromaser and for the two-photon micromaser. It even remains partially valid for a semiclassical description of the field.

DOI
10.1103/physreva.51.3267

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We show that the micromaser, widely studied for its distinct quantum features, has one more remarkable property: unlike conventional lasers and masers it works without population inversion. We study the time-averaged inversion of a single atom passing through a cavity with a field in its stationary state. The result is shown to hold also for the regularly pumped micromaser and for the two-photon micromaser. It even remains partially valid for a semiclassical description of the field.
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.
The one-atom maser or micromaser is, in contrary to ordinary masers and lasers, a pure quantum device operating with only a few photons and less than one pump atom on the average in the maser cavity. It is thus an ideal device to study quantum phenomena such as the generation of nonclassical light. The cavity is a superconducting niobium microwave resonator with a high quality factor (up to 3 × 1010). Using a single trapped ion related experiments can now also be performed in the infrared spectral region.
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.
Trapping states in the one-atom maser or micromaser are predicted by maser theory and are a direct consequence of the quantization of the electromagnetic field. They have been found in our experiment when the inversion of atoms leaving the cavity is observed while the interaction time is scanned. They correspond to quantum states of the atom-cavity system and under certain conditions represent Fock states. The trapping states occur when the atom-field dynamics complete a full evolution (or multiples thereof). Owing to feedback through the maser dynamics, a stabilization of the photon number in the steady state field of the maser cavity is achieved.
We present the theory of a truly microscopic maser consisting of a single-mode high-Q resonator in which a monoenergetic beam of excited two-level atoms is injected at such a low flux that at most one atom at a time is present inside the cavity. Both a microscopic theory and a heuristic Fokker-Planck approach are presented. We show that the micromaser exhibits a number of novel features that are averaged out in usual masers and lasers. First, the field is in general sub-Poissonian, which reflects the quantization of both the field and its sources. Second, the onset of maser oscillations may be followed by a succession of abrupt transitions in the state of the field. Finally, as the atomic flux through the resonator is increased, the maser threshold acquires characteristics of a continuous phase transition, whereas the subsequent changes in the field distribution become analogous to first-order phase transitions.