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Physical Review A

Stochastic model of nonclassical light emission from a microcavity

Seiji Miyashita, Hiromi Ezaki, Eiichi Hanamura

Published Mar 1, 1998• 7 citations
Publisher

Abstract

A sub-Poissonian distribution of photon numbers (photon-number squeezing) within a microcavity is theoretically shown to be possible using a realistic model of nonlinear photon dissipation. By deriving and solving a stochastic Schr\"odinger equation for a system with photons and atoms in a microcavity, we have obtained strong antibunching and a sub-Poissonian distribution of the number of emitted photons from the microcavity. The relationship among the above three statistical quantities, which describe the nonclassical nature of the quantum radiation field, are also discussed.

DOI
10.1103/physreva.57.2046

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A sub-Poissonian distribution of photon numbers (photon-number squeezing) within a microcavity is theoretically shown to be possible using a realistic model of nonlinear photon dissipation. By deriving and solving a stochastic Schr"odinger equation for a system with photons and atoms in a microcavity, we have obtained strong antibunching and a sub-Poissonian distribution of the number of emitted photons from the microcavity. The relationship among the above three statistical quantities, which describe the nonclassical nature of the quantum radiation field, are also discussed.
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.
We study spectral properties and photon statistical characteristics of a strongly driven two-level atom produced within a nonlinear photonic crystal. This study reveals that when a large discontinuity in the local photon density of states and the cavity field mode is resonant with the central component of the Mollow spectrum of atomic resonance fluorescence, there is squeezing of the cavity field below the quantum shot noise limit and the peak of the cavity field spectrum that is achieved in the nonlinear photonic crystal is higher than that in the linear photonic crystal. Furthermore, we can see the statistics of the photons emitted by the atom into the microcavity is sub-Poissonian and close to Poissonian when the frequency of the driving field is high.
The statistical fluctuations of light can, under certain circumstances, exhibit a number of interesting nonclassical features. These include photon antibunching, sub-Poissonian statistics, and squeezing, all of which exist only in a quantum field. The three effects are distinct, and do not necessarily go together, although the first two are sometimes mistakenly treated as interchangeable. Both photon antibunching and sub-Poissonian statistics have been observed in experiments on resonance fluorescence from single atoms, which is described. Squeezing has not yet been seen experimentally, although many nonlinear processes are expected to give rise to it. The squeezed state can be recognized in heterodyne or homodyne experiments, where the squeezing becomes manifest as sub-Poissonian photon fluctuations.
We theoretically study the emission statistics of a nonlinear photonic dimer during coherent Josephson-like oscillations. We show that the phase and population oscillations allow to periodically approach an optimal squeezing condition resulting in strongly nonclassical emission statistics. By considering a realistic exciton-polariton field in a appropriately designed microcavity, we show that the antibunching should emerge in such semiconductor system where nonclassical signatures have remained elusive to date.
Quantum-statistical properties such as the photon-number probability distribution and sub-Poissonian distribution are studied by considering the resonant interaction of two radiation fields, one of which is in a squeezed state with a cascade-structure three-level atom. It is noteworthy to emphasize that the direction of squeezing, i.e., the angle \ensuremath{\theta}, and the squeezing parameter r as well as the initial atomic state play important roles in the determination of the nonclassical behavior of the radiation field. At the same time we give a possible explanation for the effect of the ratio of the intensity of the two fields on the quantum-statistical properties.
The reduced density matrix method is used to calculate the quantum-statistical properties of the radiation of a quantum-dot laser operating on the whispering gallery mode of a dielectric microsphere. It is shown that under the conditions of strong coupling between the quantum dot and an electromagnetic field the radiation of such a laser can be in a nonclassical (sub-Poissonian) state. The laser scheme considered is characterized by an extremely low lasing threshold and a small number of saturation photons, as result of which lasing is possible with close to zero population inversion of the working levels, if g ≫ P ≫ γ ≫ Γ, where g is the field-matter interaction constant, P is the pumping rate, γ is the loss rate of the resonator, and Γ is the spontaneous emission rate. The largest squeezing inside the resonator-microsphere (the Fano factor F = 0.75) obtains for g ≫ P ≫ γ ≫ Γ, and the greatest squeezing in the fluctuation spectrum outside the resonator [V(ω = 0) ≈ 0.25] occurs for g ∼ P ∼ γ ≫ Γ, and in this case a substantial deviation of the photon number statistics of the radiation leaving the resonator from the Poissonian statistics is observed.