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Chinese Physics

Theory of two-photon micromaser: competition among different transition processes

Sun Wei-Hui, Si-de Du, Chen Xiao-Shuang

Published Jan 16, 2006• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/15/2/024

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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.
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 investigate the quantum dynamics of a two-photon micromaser pumped by atoms injected in the superposition state of the upper and intermediate levels. We simulate a master equation governing the system by the Monte Carlo wavefunction approach and analyse the steady-state behaviour as a function of the atomic transit time. The atomic coherence can effectively enhance the intensity and sub-Poissonian of the cavity field as compared with the atomic mixture. It is also discovered that the phase of the cavity field can be shifted by adjusting the detuning between the atom and field. This result shows that it is possible to manipulate the phase of the cavity field by detuning, due to atomic coherence.
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.
We present the theory of a microscopic maser operating on a nondegenerate two-photon transition between two states of same parity. We start from a three-level Hamiltonian, and discuss both the one-photon resonant cascade and the two-photon regime, when the intermediate state is far off resonance. In the semiclassical limit, we derive rate equations for the field intensities and get the corresponding steady-state values. The vacuum is stable in the two-photon regime but becomes unstable for zero detuning (a clear signature of a one-photon process). Solutions displaying true two-photon operation (intermediate state unpopulated) even with zero detuning are displayed. Using the full quantum density-matrix approach, we derive a master equation for the field and discuss both operating regimes, showing that the spontaneous emission may turn the vacuum unstable in the two-photon case. In the off-resonance two-photon regime, there is a strong correlation between the fluctuations of the intensities of the two modes. We find a squeezing factor of 50% for the fluctuations in the difference of intensities.