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Physical Review A

Influence of spontaneous emission on trapping states and start-up times of degenerate two-photon micromasers

E. S. Guerra, S. M. Dutra, P. L. Knight, Nicim Zagury

Published Aug 1, 1995• 3 citations
Publisher

Abstract

We study degenerate two-photon micromasers pumped by cascade three-level atoms, where each atomic energy level has a different linewidth. Our model allows us to recover the ordinary two-photon micromaser situation when these widths vanish. In the limit of large linewidths we obtain a two-photon laser model. We show that trapping states are extremely sensitive to atomic decay, even when the decay time is small in comparison to the transit time through the cavity. Unlike the one-photon micromaser, they are sensitive to the linewidth of the upper, as well as the lower energy level. We have also studied the effects of atomic decay on the starting time of micromasers and on the noise. We found that there is a significant difference between the behavior of two-photon micromasers and lasers as we change the ratio of the widths of the upper and lower levels.

DOI
10.1103/physreva.52.1651

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We study degenerate two-photon micromasers pumped by cascade three-level atoms, where each atomic energy level has a different linewidth. Our model allows us to recover the ordinary two-photon micromaser situation when these widths vanish. In the limit of large linewidths we obtain a two-photon laser model. We show that trapping states are extremely sensitive to atomic decay, even when the decay time is small in comparison to the transit time through the cavity. Unlike the one-photon micromaser, they are sensitive to the linewidth of the upper, as well as the lower energy level. We have also studied the effects of atomic decay on the starting time of micromasers and on the noise. We found that there is a significant difference between the behavior of two-photon micromasers and lasers as we change the ratio of the widths of the upper and lower levels.
In this paper, we study the influence of atomic decay on the linewidth of a two-photon micromaser using an exact Hamiltonian approach. We consider a three-level cascade atomic system (where each level has a finite lifetime) interacting with a single mode of the radiation field. The intermediate level is considered to be off resonant with the field. We calculate the linewidth for both small- and large-detuning limits. In both cases, the well known oscillatory behaviour of the linewidth vanishes for large decay rates. We also find a reduction in the linewidth in certain regions of interaction times. In the limit of small decay rates, we recover the linewidth of the ordinary two-photon micromaser. We also compare the results under the large-detuning limit with the results obtained using a phenomenological Hamiltonian approach.
We analyze the quantum theory of the two-mode micromaser pumped by cold three-level atoms with a $\ensuremath{\Lambda}$-configuration under the two-photon resonance condition. We focus more specifically on the large detuning limit where the detuning between the two cavity mode frequencies and the two atomic transition frequencies is large in comparison with the atom-cavity coupling constants. We show that this regime can mimic a virtual two-level atom micromaser without spontaneous emission where the cavity acts for the atoms as a potential barrier or a potential well (depending on the sign of the detuning) and a zero potential but no more both as a potential barrier and a potential well as it is the case for the usual cold two-level atom micromaser [M. O. Scully, G. M. Meyer, and H. Walther, Phys. Rev. Lett. 76, 4144 (1996)]. This introduces interesting options for engineering the interaction between the cold atoms and the cavity. The elimination of the spontaneous emission solves a major issue of the conventional cold two-level atom micromaser as the transit time of cold atoms inside and in the vicinity of the cavity is usually much larger than the atomic level lifetimes. It is also shown that the cold atom regime is very sensitive to the sign of the detuning (in contrast to the hot atom regime) and that, according to this sign, the cavity may speed up or slow down the incident three-level atoms after their interaction with the field.
We have investigated the steady-state cavity-field properties of a single-mode two-photon micromaser when the atoms in a cascade three-level configuration are initially prepared in a mixture of the upper and intermediate states. The mean photon number, trapping state and sub-Poissonian effect are discussed with upper (intermediate)-state population changing from 1(0) to 0(1). These properties are very different from those in a pure two- or one-photon transition process, due to the competition among different transition processes. In particular, the trapping states of nonzero photons are discovered in this system under some conditions, which is contrary to the previous findings.
In this paper, we study the linewidth of a two-photon micromaser by using an exact Hamiltonian approach. We consider a three-level atomic system interacting with a single-mode radiation field. The intermediate level is considered to be off resonant with the field. In this model, under the large detuning limit, two-photon transitions result. We calculate the linewidth of a two-photon micromaser and present results in the small and large detuning limits. In the small detuning limit, single-photon behavior is evident, whereas in the large detuning limit, true two-photon behavior is exhibited. We compare the results for the linewidth, under a large detuning limit, with the results obtained by using a phenomenological, effective Hamiltonian approach. The absence of the dynamic Stark shift in a phenomenological, effective Hamiltonian leads to qualitatively different results in the two approaches. \textcopyright{} 1996 The American Physical Society.
We use standard quantum laser theory to examine the linewidth of lasers with a four-level atomic gain medium as a function of the spontaneous emission rate into the lasing mode and the decay rates from the upper and lower lasing levels. We find that the laser linewidth ceases to exhibit the customary decrease with increased photon number when a critical photon number, proportional to the ratio of the decay rate from the lower lasing level to the rate of spontaneous emission into the lasing mode, is reached. This critical photon number would decrease as the size of the optical cavity is decreased. In addition we show that, in general, the laser linewidth depends critically on the ratio of the overall decay rates from the upper and lower lasing levels.
We present the theory of a micromaser operating on a cascade three-level atomic transition, which is coupled to two cavity modes satisfying the resonance condition. A numerical approach is employed to integrate the master equation describing the microwave field, allowing us to obtain the semiclassical regime in the limit of large mean photon numbers. We show that the transfer rate from the excited atomic state is very close to 100% over a large interval of variation of the interaction time. The atom - field interaction time may be chosen so as to avoid transitions to the intermediate atomic state when in steady-state operation. In this case, the two cavity modes have nearly the same photon statistics, and the fluctuations in the difference of intensities may be reduced by up to 50% below the classical limit. The intensity correlation between the two cavity modes originates from the possibility of controlling the interaction time, rather than from the simultaneous generation of `twin' photons in a two-photon transition.