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Journal of Experimental and Theoretical Physics

Generation of sub-Poissonian light by a four-level microlaser with a high-Q cavity

Yu. M. Golubev, Berthold‐Georg Englert, Hwang Lee, Marlan O. Scully, HERBERT WALTHER

Published Aug 1, 1999• 0 citations
Publisher

Abstract

We develop a kinetic theory that describes the behavior of a monatomic four-level laser when the atom is fixed inside a high- Q optical cavity. Such a statement of the problem is similar to that used in the experiment of G. M. Meyer, H.-J. Briegel, and H. Walther [Europhys. Lett. 37 , 317 (1997)]. The condition that the number of photons is large and the photon fluctuations are small is employed. We show that by selecting the parameters of the periodic electromagnetic pulses exciting the atom one can achieve regular pumping of the upper laser level and generate sub-Poissonian laser light. We also discuss the reasons why the statistical pattern of the radiation differs from the micromaser pattern with regular injection of atoms.

DOI
10.1134/1.558978

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We develop a kinetic theory that describes the behavior of a monatomic four-level laser when the atom is fixed inside a high- Q optical cavity. Such a statement of the problem is similar to that used in the experiment of G. M. Meyer, H.-J. Briegel, and H. Walther [Europhys. Lett. 37 , 317 (1997)]. The condition that the number of photons is large and the photon fluctuations are small is employed. We show that by selecting the parameters of the periodic electromagnetic pulses exciting the atom one can achieve regular pumping of the upper laser level and generate sub-Poissonian laser light. We also discuss the reasons why the statistical pattern of the radiation differs from the micromaser pattern with regular injection of atoms.
We present a theory which can explain the micromaser as well as its optical counterpart, the microlaser, for appropriate values of dissipative parameters. We show that, in both the the cases, the cavity radiation fields can have sub-Poissonian photon statistics. We further analyse if it is possible to attain a Fock state of the radiation field. The microlaser is precluded for such analysics due to the damping of its lasing levels making transitions at optical frequencies. Hence, we focus our attention on the micromaser and our exact simulation of the dynamics shows that it is not possible to generate a Fock state of the cavity radiation field.
We have achieved the first realization of a single atom microlaser, a laser oscillator with only one atom in an optical resonator. In the experiment a beam of two-level barium atoms traverses an ultrahigh Q single-mode cavity. The atoms are inverted by a (pi) -pulse field before they enter the cavity. Laser oscillation ((lambda) equals 791 nm) has been observed, with the mean number of atoms inside the mode <N> as small as 0.1, resulting in the mean number of photons in the mode <N> or 0.14. To understand the results quantitatively we used a fully-quantized one-atom microlaser theory adapted from its counterpart micromaser theory. The present theory was found to be in good agreement with the data for small <N> and <n>. Discrepancy between experiment and theory was observed for <n> very much greater than 1 and <N> approximately equal to 1. This discrepancy may be explained by the standing-wave nature of the cavity mode, in combination with the saturation effect occurring at large cavity photon number, as well as by the breakdown of single-atom interaction assumption in the theory for <N> greater than or equal to 1.
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.
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.
We perform quantum trajectory simulations of the micromaser/laser with Poissonian pump, lifting all restriction on the number of simultaneously interacting atoms. For mean numbers of intracavity atoms between zero and two, highly sub-Poissonian fields are obtained from the Poissonian pumping, with a Mandel QQQ parameter inside the cavity below −0.6-0.6−0.6 under suitable conditions. Simulation of a Hanbury Brown and Twiss-type measurement performed on the cavity emissions recovers the intracavity value of the Mandel QQQ parameter from the intensity correlation function of the output photon stream.
Sub-Poisson field with much reduced fluctuations in a cavity can boost quantum precision measurements via cavity-enhanced light-matter interactions. Strong coupling between an atom and a cavity mode has been utilized to generate highly sub-Poisson fields. However, a macroscopic number of optical intracavity photons with more than 3 dB variance reduction has not been possible. Here, we report sub-Poisson field lasing in a microlaser operating with hundreds of atoms with well-regulated atom-cavity coupling and interaction time. Its photon-number variance was 4 dB below the standard quantum limit while the intracavity mean photon number scalable up to 600. The highly sub-Poisson photon statistics were not deteriorated by simultaneous interaction of a large number of atoms. Our finding suggests an effective pathway to widely scalable near-Fock-state lasing at the macroscopic scale.