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Journal of Physics B Atomic Molecular and Optical Physics

Coherence and statistics of a one-atom laser in a photonic crystal microcavity

Xiaoyong Guo, Shuchen Lü, Zhongzhou Ren

Published Oct 29, 2010• 5 citations
Publisher

Abstract

Through calculating the quantum degree of second-order coherence and photon number distribution numerically, we investigate the coherence and statistics of a one-atom laser where a coherently driven two-level atom is coupled to a photonic crystal microcavity. By going beyond the previous theoretical studies, we show that in the presence of non-secular terms the cavity field displays a variable degree of second-order coherence as a function of discontinuities in the photonic density of states. The cavity field is characterized by photon antibunching and sub-Poissonian statistics for large discontinuities. In the case of a vanishing photonic density of states on the lower Mollow sideband, we can obtain only weak antibunching. If the jump in the photonic density of states is small, the bunching and super-Poissonian statistics field is generated in the cavity. Consequently, the cavity field exhibits certain non-classical features when non-secular interaction is included into the dynamics of the system. The theoretical analysis and numerical calculations presented here coincide with recent experimental observations.

DOI
10.1088/0953-4075/43/22/225401

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Through calculating the quantum degree of second-order coherence and photon number distribution numerically, we investigate the coherence and statistics of a one-atom laser where a coherently driven two-level atom is coupled to a photonic crystal microcavity. By going beyond the previous theoretical studies, we show that in the presence of non-secular terms the cavity field displays a variable degree of second-order coherence as a function of discontinuities in the photonic density of states. The cavity field is characterized by photon antibunching and sub-Poissonian statistics for large discontinuities. In the case of a vanishing photonic density of states on the lower Mollow sideband, we can obtain only weak antibunching. If the jump in the photonic density of states is small, the bunching and super-Poissonian statistics field is generated in the cavity. Consequently, the cavity field exhibits certain non-classical features when non-secular interaction is included into the dynamics of the system. The theoretical analysis and numerical calculations presented here coincide with recent experimental observations.
We present a quantum theory of a coherently pumped two-level atom in a photonic band gap (PBG), coupled to both a multimode waveguide channel and a high-quality microcavity embedded within a photonic crystal. One mode is engineered to exhibit a sharp cutoff within the PBG, leading to a large discontinuity in the local photon density of states near the atom, and the cavity field mode is resonant with the central component of the Mollow spectrum of atomic resonance fluorescence. Another mode of the waveguide channel is used to propagate the pump beam. We derive analytical expressions for the optical amplitude, intensity, second-order correlation functions, and conjugate quadrature variances for the light emitted by the atom into the microcavity. The quantum degree of second-order coherence in the cavity field reveals enhanced, inversionless, nearly coherent light generation when the photon density of states jump between the Mollow spectral components is large. The cavity field characteristics are highly distinct from that of a corresponding high-QQQ cavity in ordinary vacuum. In the case of a vanishing photon density of states on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian, and the cavity field exhibits quadrature coherence.
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.
We present a quantum theory of a coherently pumped two-level atom in a photonic crystal, coupled to both a multi-mode wave-guide channel and a high quality micro-cavity embedded within the photonic crystal. The cavity field characteristics are highly distinct from that of a corresponding high Q cavity in ordinary vacuum. If the cavity field mode is resonant with the central component of the Mollow spectrum of atomic resonance fluorescence, enhanced, inversionless, nearly coherent light generation occurs when the photon density of states jump between the Mollow spectral components is large. The spectrum of the cavity field is also investigated and showed to be narrower than in the case of a conventional cavity. Moreover, enhanced, non-classical light generation is possible, if the cavity field is tuned on resonance with a Mollow sideband.
The emission spectrum of a single-emitter laser in a photonic crystal is presented. We consider a coherently pumped two-level emitter strongly coupled to a high-quality microcavity engineered within a photonic crystal. We show that the cavity spectrum consists of both elastic and inelastic components, for which we derive analytical expressions. Our study reveals enhanced, spectrally narrower emission resulting from the radiation reservoir of the photonic crystal. The cavity field spectral characteristics are fundamentally distinct from those of a corresponding microcavity in ordinary vacuum. At high pump intensities and for large discontinuities in the photon density of states between Mollow spectral components of atomic resonance fluorescence, the emitted intensity originating from the elastic spectral component increases with the intensity of the pump and the elastic component dominates the spectrum. In the case of a vanishing photon density of states in the spectral range surrounding the lower Mollow sideband and no dipolar dephasing, the cavity spectrum is elastic.
We investigate the transient and the steady-state behaviour of the photon statistics of a single-atom laser, consisting of a three-level Λ system, driven by an incoherent external pump field and strongly coupled to a single mode of an optical cavity. For several limiting cases we are able to obtain analytical results. A comparison with standard multi-atom laser theory reveals a surprisingly good agreement down to very small intracavity photon numbers. Under appropriate operating conditions a calculation of the second-order intensity correlation function yields sub-Poissonian statistics as well as strong antibunching induced by the nonlinear dynamics of the atom.