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Journal of Modern Optics

Production of Sub-poissonian Light in A Quantum Optical Oscillator

Tran Quang, Helen S. Freedhoff

Published Jan 1, 1993• 3 citations
Publisher

Abstract

In this paper we investigate theoretically the behaviour of a quantum optical oscillator, consisting of two-level atoms strongly coupled to a cavity mode, in the optical domain. In contrast with the usual laser theory, we include explicitly the effects of atomic spontaneous emission and of cavity decay in the interaction of the atoms with the cavity field, using a quantum mechanical master equation approach. It is shown that such an oscillator produces sub-Poissonian light with a large degree of noise reduction even for the case when the atom–field coupling constant is only marginally larger than the spontaneous decay rate.

DOI
10.1080/09500349314550071

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In this paper we investigate theoretically the behaviour of a quantum optical oscillator, consisting of two-level atoms strongly coupled to a cavity mode, in the optical domain. In contrast with the usual laser theory, we include explicitly the effects of atomic spontaneous emission and of cavity decay in the interaction of the atoms with the cavity field, using a quantum mechanical master equation approach. It is shown that such an oscillator produces sub-Poissonian light with a large degree of noise reduction even for the case when the atom–field coupling constant is only marginally larger than the spontaneous decay rate.
The author reviews methods for generating sub-Poissonian light and related concepts. This light has energy fluctuations reduced below the level which corresponds to a classical Poissonian process (shot-noise level). After an introduction to the concept of nonclassical light, an overview is given of the main methods of quantum-noise reduction. Sub-Poissonian processes are exemplified in different areas of optics, ranging from single-atom resonance fluorescence to nonlinear optics, laser physics, and cavity quantum electrodynamics. Emphasis is placed on the conceptual foundations, and on developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-Poissonian light generation in lasers and masers. The sources of quantum noise in these devices are analyzed, and four noise-suppression methods are discussed in detail: regularization of the pumping, suppression of spontaneous-emission noise, nonadiabatic evolution of the atomic variables, and twin-beam generation.
We show that the injection of an external field in a laser helps to improve amplitude squeezing and sub-Poissonian light generation close to threshold, but spoils quantum noise reduction for very high pumping rates. A general nonlinear theory is developed for the resonant case (no detunings), without any assumption on the relative magnitudes of field and atomic decay constants, thus encompassing a large class of lasers. Several possible pumping schemes are accommodated, ranging from regular to Poissonian. We carry out a detailed stability analysis of the general equations of motion, relating it to the noise-reduction problem. Both the photon-number variance inside the cavity and the homodyne spectra of the output are discussed.
It is shown that the Λ quantum beat system, into which a new atomic coherence is introduced, can produce bright two-mode sub-Poissonian light. The Mandel Q parameter is calculated using Scully-Lamb theory. On one hand, when quantum noises of the relative amplitude and relative phase drop to vaccum noise levels, the average mode exhibits sub-Poissonian photon distribution; when quantum noises of the average amplitude and average phase drop to vaccum noise levels, the relative mode exhibits sub-Poissonian photon statistics; the optimum Mandel Q parameter is -0.5. On the other hand, in the above two cases, each of the correlated spontaneous emission laser modes exhibits sub-Poissonian photon statistics with optimum Mandel Q parameter of -0.25.
A quantum theory of spontaneous emission from an initially excited two-level atom in a one-dimensional optical cavity with output coupling from both sides is developed. Orthonormal mode functions with a continuous spectrum are employed, which are derived by imposing a periodic boundary condition on the whole space with a period much larger than the cavity length. The delay differential equation of the atomic state of Cook and Milonni [Phys. Rev. A 35, 5081 (1987)] is re-derived in a strict manner, where the reflectivity of the cavity mirrors is included naturally in the mode functions. An approximate solution at a single-resonant-mode limit shows the results of ``vacuum'' Rabi oscillation in an underdamped cavity and enhanced spontaneous emission rate in an overdamped cavity. For the latter case, it is found that in the optical range the spontaneous emission rate is enhanced by a factor F (finesse of the cavity).
We investigate the effects of sub-Poissonian photon statistics and photon antibunching in the light generation by a photonic-crystal one-atom laser. The physical system consists of a two-level light emitter strongly coupled to a high-quality microcavity engineered within a photonic crystal and coherently driven by a strong external laser field. This study reveals that the electromagnetic environment provided by the photonic crystal facilitates light generation characterized by pronounced sub-Poissonian photon statistics and photon antibunching, and strongly enhanced relative to that from a one-atom laser in a conventional optical cavity. The characteristics of the cavity photon statistics are fundamentally distinct from those of a corresponding microcavity in ordinary vacuum. For large discontinuities in the photon density of states between Mollow spectral components of atomic resonance fluorescence, in the good cavity regime, the photon statistics is sub-Poissonian, in contrast to the case of a conventional cavity where sub-Poissonian photon statistics is present only for a bad cavity. These results suggest the possibility of using a photonic-crystal one-atom laser as an efficient source of nonclassical light.
According to the exact solution of a two-level atomic system interacting with a single-mode field in a cavity and including a pumping mechanism, sub-Poissonian photon statistics can be generated either by regular pumping or by resonance absorption of the lower level. When the atomic lifetime is much smaller than the interaction time (${\ensuremath{\gamma}}_{\mathit{a}\mathit{b}}$\ensuremath{\tau}\ensuremath{\gg}1), which corresponds to a usual laser system, the sub-Poissonian photon distribution can be obtained only by regular pumping. On the other hand, if the atomic lifetime is comparable with the interaction time (${\ensuremath{\gamma}}_{\mathit{a}\mathit{b}}$\ensuremath{\tau}\ensuremath{\le}1), the sub-Poissonian photon distribution can be generated by both mechanisms.