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Physical Review A

Two-mode micromaser operating on three-level atoms

Fam Le Kien, Georg M. Meyer, Marlan O. Scully, HERBERT WALTHER, Shi-Yao Zhu

Published Feb 1, 1994• 24 citations
Publisher

Abstract

We present the quantum theory of the two-mode micromaser operating on \ensuremath{\Lambda}-type three-level atoms. The explicit expression of the detailed-balance steady-state photon distribution is derived. The photon statistics and the correlation between the modes are studied. It is shown that due to the strong anticorrelation between the modes the fluctuations in the total number of photons may be sub-Poissonian even when the fluctuations in the number of photons in each mode are super-Poissonian.

DOI
10.1103/physreva.49.1367

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We present the quantum theory of the two-mode micromaser operating on \ensuremath{\Lambda}-type three-level atoms. The explicit expression of the detailed-balance steady-state photon distribution is derived. The photon statistics and the correlation between the modes are studied. It is shown that due to the strong anticorrelation between the modes the fluctuations in the total number of photons may be sub-Poissonian even when the fluctuations in the number of photons in each mode are super-Poissonian.
We derive the master equations for the fields in the one-mode \ensuremath{\Lambda}-type micromaser and laser with injected atoms in a superposition of their states. In terms of effective parameters, these equations are equivalent to those for a two-level micromaser and laser. The interference terms in the master equations may cancel the absorption terms independent of statistical properties of the field. Due to the atomic coherence between the two degenerate lower levels, the generation of field states with sub-Poissonian photon statistics is possible in the micromaser without the need for a population inversion. If an equivalent level system is used in a laser operating without population inversion it can produce field states with Poisson distributions of the photon number.
In this dissertation, we study the quantum theory of two-photon micromaser and laser. To begin with, we study the photon statistics of the two-photon micromaser by considering the interaction of a quantized single-mode field with an effective two-level atom through intermediate states. We present an exact solution for the photon distribution function and study the behaviour of mean photon number and photon number fluctuations. A periodic "collapse" and "revival" type behaviour is predicted. We find that the photon number fluctuations exhibits a periodic sub-Poissonian behaviour with respect to the interaction time. We then discuss the photon statistics of two-photon laser and derive an exact expression for photon distribution function. We find that photon distribution function for two-photon laser is wider than the Poisson distribution function. We also calculate the natural line-width of a two-level two-photon laser by using a Fokker-Planck approach. It is shown that, apart from a constant, the gain contribution to the laser linewidth is equal to the two-photon gain parameter and is independent of the mean number of photons in the field. Finally, we study the two-photon transitions in multi-level atomic system. In this case first we discuss the photon statistics of three-level two-photon micromaser and laser. Then we consider the two-photon transition in four-level atomic system by considering dye laser as an example.
Quantum interference effects are theoretically investigated in the steady-state photon statistics of single-mode Λ- and V-type micromasers with injected three-level atoms in a superposition of their internal states. The two lower (upper) levels are nondegenerate and coherent in a general case. For the Λ-type case, we have discussed how detunings affect the photon statistics of the noninversion micromaser. Under the proper conditions strongly sub-Poissonian field states with a large number of photons can be easily produced in this novel micromaser even if there exists no coherence between the two lower levels. For the V-type case, we have analysed how the photon statistics changes with the increase of the ground-state population. Although the generation of the strongly sub-Poissonian states is always possible in the micromaser under the noninversion case, their photon intensities become very weak compared to the Λ-type case. Our results indicate that it is perfectly possible to experimentally realize a noninversion micromaser with strongly sub-Poissonian statistics in the Λ-type system.
We have established the master equation for the micromaser with the ultra-cold Λ-type three-level atoms and studied the photon statistics of the micromaser field. We find that as the atoms become colder, the change of the mean photon-number and the normalized standard deviation become more regular, and their resonance peaks become sharper. For zero-temperature cavity, there are some regions in which the photon statistics are sub-Poissonian. With the increase of the cavity temperature, both the mean photon-number and the normalized standard deviation increase. When the cavity temperature is high enough, the sub-Poissonian property may disappear.
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.
We theoretically investigate the quantum statistical properties of a two-mode cavity light generated by a ∨ -type three-level atom interacting with nondegenerate subharmonic light and coupled to a two-mode squeezed vacuum reservoir. Using the master equation, we obtain steady-state expectation values for the atomic and cavity-mode operators. Based on these results, we analyze the global and local photon number variances, intensity fluctuation spectrum, joint photon number distribution, and photon count statistics. Our results reveal that squeezing parameter and subharmonic generation significantly enhance intensity fluctuations, as well as the mean and variance of photon counts, whereas atom-field coupling and cavity decay suppress them. The system exhibits super-Poissonian photon statistics, indicating that photon number fluctuations exceed the mean photon number. Furthermore, the photon count variance, which incorporates intracavity transmission and input noise, increases with detector efficiency. These results provide a comprehensive picture of photon statistics in atom-photon systems and guide the design of advanced quantum optical devices.