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Physical Review A

Photon amplification in a two-photon lossless micromaser

H. M. Moya-Cessa, P. L. Knight, Avia Rosenhouse‐Dantsker

Published Aug 1, 1994• 36 citations
Publisher

Abstract

We investigate the interaction of atoms through two-photon resonant transitions, with quantized cavity radiation, in the framework of a lossless micromaser theory. Taking advantage of the fact that the atomic inversion is quasiregular in time in this model, with quite precise revivals, we find a very strong amplification of the average photon number. At the two-photon revival time, the atom leaves the cavity in an almost pure state. This leads to an essentially noise-free process that results in a shift of two photons of the initial photon distribution each time an atom passes through the cavity, while the width of the photon distribution remains constant. This leads to strongly sub-Poissonian field statistics.

DOI
10.1103/physreva.50.1814

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We investigate the interaction of atoms through two-photon resonant transitions, with quantized cavity radiation, in the framework of a lossless micromaser theory. Taking advantage of the fact that the atomic inversion is quasiregular in time in this model, with quite precise revivals, we find a very strong amplification of the average photon number. At the two-photon revival time, the atom leaves the cavity in an almost pure state. This leads to an essentially noise-free process that results in a shift of two photons of the initial photon distribution each time an atom passes through the cavity, while the width of the photon distribution remains constant. This leads to strongly sub-Poissonian field statistics.
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.
For an arbitrary initial photon probability distribution in a micromaser cavity, it is shown that photon-number eigenstates can be induced by passing excited atoms, one at a time, through the cavity. The photon number can be predicted for a given velocity of excited atoms. It is found that the total photon energy inside a lossless cavity becomes saturated once a photon number state is achieved. It is also possible to find more than one number states, each occurs with a certain probability under particular initial conditions. If the injected atoms have a small velocity distribution Av around v, then only a near-number state with the predicted photon number is possible. For Av/v - 0.1, the photon probability in the cavity can still maintain subpoisson distribution until sufficiently large number of excited atoms have passed. Other novel phenomena are also found in two-photon processes.
A distinctive signature of the granulated nature of the electromagnetic field is the revivals known to occur in the dynamics of a two-level atom interacting with a single-field mode (Jaynes-Cummings model). The development of high-Q single-mode cavities combined with progress in Rydberg atom spectroscopy has led to a possibility of verifying these predictions. Revival experiments using micromasers have been performed by Walther et al. Here the cavity mode is first allowed to reach a steady state, and then probe atoms are injected into the resonator. By measuring their state as they exit the cavity, one can infer the state of the field. We show that the micromaser experiences Jaynes-Cummingslike revivals when the pump parameter θ is varied. However, in contrast to the conventional Jaynes-Cummings situation, which considers initially coherent fields, the micromaser photon statistics are usually not Poissonian and depend sensitively on θ. The micromaser revivals cannot be explained by a semiclassical theory or linearized quantum fluctuations about the semiclassical solution. Rather, an exact quantum treatment, considering fully the granularity of the cavity mode, is required.
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.
We show that the resonant interaction between a two-level atom and a quantized field mode via two-photon transitions leads to extreme quantum entanglement between the atom and quantum field. Nevertheless during the time evolution there are moments at which the atom-field system becomes asymptotically disentangled. We investigate statistical properties of the pure-field states generated at such times. We show that at the quarter of the revival time the field is produced in the pure superposition state (Schrödinger cat state) composed of two coherent states with the same amplitude but which are out of phase by 90° (we obtain approximate analytical solution for this superposition state). We show that the interference between component states leads to non-classical oscillations in the photon number distribution. At the revival time the field is again in the pure state (we present an approximate analytical solution for the corresponding state vector). This pure state is not a superposition state. Nevertheless it exhibits a certain degree of sub-Poissonian photon statistics. We briefly discuss the influence of the Stark shift on the production of superposition states.
The excitation of Rydberg atom transitions by submillimeter-wavelength radiation in high-Q cavities forms the basis of the micromaser. The excitation dynamics of a micromaser is known to be dependent on the detailed photon statistics in the interaction cavity and can exhibit well-known collapses and revivals of the atomic inversion, dipole moment, and photon number. We study these effects in a two-photon model in which the time evolution is exactly periodic. We study the field entropy in two two-photon cases and link the fluctuations in the field phase to the changes in the field entropy. We also calculate the statistical Q function of the field and show how the periodicity of the two-photon dynamics is linked to a periodic splitting of the Q function in phase space. Finally this periodicity is linked to the nature of the atom-field dressed states involved in two-photon resonance.