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arXiv:0807.4773 · Physical Review A

Thresholdless dressed-atom laser in a photonic band-gap material

Gao‐xiang Li, Min Luo, Z. Ficek

Published May 26, 2009• 9 citations
arXivHTMLPDF

Abstract

We demonstrate the capability of complete thresholdless lasing operation between dressed states of a two-level atom located inside a microscopic cavity engineered in a photonic band-gap material. We distinguish between threshold and thresholdless behaviors by analyzing Mandel's $Q$ parameter for the cavity field. We find that the threshold behavior depends on whether the spontaneous emission is or is not present on the lasing transition. In the presence of the spontaneous emission, the mean photon number of the cavity field exhibits threshold behavior, indicating that the system may operate as an ordinary laser. When the spontaneous emission is eliminated on the lasing transition, no threshold is observed for all values of the pumping rate, indicating the system becomes a thresholdless laser. Moreover, we find that, under a thresholdless operation, the mean photon number can increase nonlinearly with the pumping rate, and this process is accompanied by a sub-Poissonian statistics of the field. This suggests that the nonclassical statistics can be used to distinguish a nonlinear operation of the dressed-atom laser.

DOI
10.1103/physreva.79.053847

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We demonstrate the capability of complete thresholdless lasing operation between dressed states of a two-level atom located inside a microscopic cavity engineered in a photonic band-gap material. We distinguish between threshold and thresholdless behaviors by analyzing Mandel's QQQ parameter for the cavity field. We find that the threshold behavior depends on whether the spontaneous emission is or is not present on the lasing transition. In the presence of the spontaneous emission, the mean photon number of the cavity field exhibits threshold behavior, indicating that the system may operate as an ordinary laser. When the spontaneous emission is eliminated on the lasing transition, no threshold is observed for all values of the pumping rate, indicating the system becomes a thresholdless laser. Moreover, we find that, under a thresholdless operation, the mean photon number can increase nonlinearly with the pumping rate, and this process is accompanied by a sub-Poissonian statistics of the field. This suggests that the nonclassical statistics can be used to distinguish a nonlinear operation of the dressed-atom laser.
We investigate spectral properties of the atomic fluorescence and the output field of the cavity-mode of a single-atom dressed-state laser in a photonic crystal. We pay particular attention to the behavior of the spectra in the presence of the frequency dependent reservoir and search for signatures of the thresholdless lasing. Although the thresholdless behavior has been predicted by analyzing the photon statistics of the cavity field, we find that the threshold behavior still exists in the spectrum of the cavity field. We find that the structure of cavity field spectrum depends strongly on the range of the pumping rate. For low pumping rates, the spectrum is not monochromatic, it is composed of a set of discrete lines revealing the discrete (quantum) structure of the combined dressed-atom plus the cavity field system. We find that for a certain value of the pumping rate, the multi-peak structure converts into a single very narrow line centered at the cavity field frequency. A physical explanation of the behavior of the spectra is provided in terms of dressed states of the system.
Although conventional lasers operate with a large number of intracavity atoms, the lasing properties of a single atom in a resonant cavity have been theoretically investigated for more than a decade. Here we report the experimental realization of such a one-atom laser operated in a regime of strong coupling. Our experiment exploits recent advances in cavity quantum electrodynamics that allow one atom to be isolated in an optical cavity in a regime for which one photon is sufficient to saturate the atomic transition. In this regime the observed characteristics of the atom-cavity system are qualitatively different from those of the familiar many atom case. Specifically, we present measurements of intracavity photon number versus pump intensity that exhibit "thresholdless" behavior, and infer that the output flux from the cavity mode exceeds that from atomic fluorescence by more than tenfold. Observations of the second-order intensity correlation function demonstrate that our one-atom laser generates manifestly nonclassical light that exhibits both photon antibunching and sub-Poissonian photon statistics.
Summary form only given. Unlike semiconductors which facilitate the coherent propagation of electrons, photonic band gap (PBG) materials execute their novel functions through the coherent localization of photons. When a PBG material is doped with impurity atoms which have an electronic transition that lies within the gap, spontaneous emission of light from the atom is inhibited. Inside the gap, the photon forms a bound state to the atom. Outside the gap, radiative dynamics in the colored vacuum is highly nonMarkovian. I discuss the influence of these memory effects on laser action. When spontaneous emission is absent, the next order radiative effect (resonance dipole-dipole interaction between atoms) must be incorporated, leading to anomalous nonlinear optical effects which occur at a much lower threshold than in ordinary vacuum. I describe the collective switching of two-level atoms near a photonic band edge, by external laser field, from a passive stare to one exhibiting population inversion. This effect is forbidden in ordinary vacuum. Finally, I discuss the prospects for a phase sensitive, single (3-level) atom quantum memory device, onto which information may be written by an external laser pulse. By scattering polarized photons (flying qubit) this system may execute certain quantum logic operations.
We present a comprehensive quantum electrodynamical analysis of the interaction between a continuum with photonic band gaps (PBGs) or frequency cut-off and an excited two-level atom, which can be either ‘bare’ or ‘dressed’ by coupling to a near-resonant field mode. A diversity of novel features in the atom and field dynamics is shown to arise from the non-Markovian character of radiative decay into such a continuum of modes. Firstly the excited atom is shown to evolve, by spontaneous decay, into a superposition of non-decaying single-photon dressed states, each having an energy in a different PBG, and a decaying component. This superposition is determined by the atomic resonance shift, induced by the spontaneously emitted photon, into or out of a PBG. The main novel feature exhibited by the decaying excited-state component is the occurrence of beats between the shifted atomic resonance frequency and the PBG cut-off frequencies, corresponding to a non-Lorentzian emission spectrum. Secondly the induced decay of a resonantly driven atom into such a continuum exhibits a cascade of transitions down the ladder of dressed states, which are labelled by decreasing photon numbers of the driving mode. Remarkably, this cascade is terminated at the dressed-state doublet, from which all subsequent transitions to lower doublets are forbidden because they fall within the PBG. This doublet then becomes an attractor state for the populations of higher-lying doublets. As a result, the photon-number distribution of the driving mode becomes strongly sub-Poissonian.
We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as \ensuremath{\beta}, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for \ensuremath{\beta} are $0.01<\ensuremath{\beta}<1.0.$ We find that for large enough \ensuremath{\beta}, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as \ensuremath{\beta} is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with \ensuremath{\beta} values in the range considered here. As \ensuremath{\beta} is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results.
The radiative emission of strongly driven, two-level-like barium atoms into the modes of a confocal optical cavity is studied as a function of barium density. As the barium density is increased, the spatial profile, intensity, and spectrum of light emitted out the ends of the confocal cavity display dramatic changes indicative of a transition from fluorescence to lasing. In this novel two-level system, laser action can be explained in terms of an inversion between the dressed atom-field states or in terms of a type of stimulated hyper-Raman scattering in which atoms lase from the ground to the excited atomic state. A simple dressed-atom rate-equation analysis of this two-level-atom laser is presented. It is pointed out that this same system may provide a means of realizing two-photon-like laser action.