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Physical Review A

Photon-number correlations near the threshold of microcavity lasers in the weak-coupling regime

R. Jin, Deepak Boggavarapu, M. Sargent, Pierre Meystre, H. M. Gibbs, G. Khitrova

Published May 1, 1994• 62 citations
Publisher

Abstract

The quantum-noise properties near the threshold of microcavity lasers are studied theoretically and experimentally in the weak-coupling regime. Computations based on two-level quantum theory show that the microlasers exhibit a high degree of second-order coherence compared with conventional lasers as a result of the suppression of spontaneous emission into nonlasing modes, and that there always exists a finite threshold for these lasers defined by the peak of the photon-number correlation function corresponding to the spontaneous-to-stimulated transition.

DOI
10.1103/physreva.49.4038

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The quantum-noise properties near the threshold of microcavity lasers are studied theoretically and experimentally in the weak-coupling regime. Computations based on two-level quantum theory show that the microlasers exhibit a high degree of second-order coherence compared with conventional lasers as a result of the suppression of spontaneous emission into nonlasing modes, and that there always exists a finite threshold for these lasers defined by the peak of the photon-number correlation function corresponding to the spontaneous-to-stimulated transition.
The process of zero threshold laser action in stimulated emission (StE) has been first reported by our laboratory, together with spontaneous emission (SpE) anomalies.1,2 In this work a new microcavity technique aimed at the investigation of the Bose-Einstein quantum correlations between two microlasers coupled to the same quasi plane-wave microcavity k-mode, orthogonal to the microcavity mirrors and excited by two independent beams at λ = 0.53 μm SHG by a common TEM00 Nd:YAG unstable-cavity laser. In the experiment the micrometrically controlled transverse distance s is the relevant variable of the experiment. The StE radiation at λ = 0.632 μm emerging from the microcavity on the k-mode is detected through an efficient spatial filter. The measurement of the exponential thresholdless-laser gain at various coherent-pump intensities of the overall laser system leads to the functional s-dependence of a relevant quantity: the "degree of Bose-Einstein correlation" a (s, d) among the active spots1,2 excited in the microcavity. The behavior of this quantity for microcavity spacings d = [d ≡ (λ/2, 5d, 10d], demonstrates that the rapid quantum decorrelation taking place in the condition of maximum confinement, i.e., at d = d, decreases at large d values approaching asymptotically, for a macroscopic-cavity d > d, the full correlation over the entire plane-wave phase surface expected according to the common QED notion of full photon freespace delocalization. An extended theoretical account of this novel effect of fundamental atom-field interaction physics and laser physics is given on the basis of the quantum interference taking place within the StE process among the plane waves belonging to the modal k-distribution for a microcavity of finite finesse. A region in the microcavity of interaction coherence (referred to as a photon-localization: effect) is established, giving rise to a strong dependence of the quantum-mechanical interatom correlation on the parameters of the microcavity. The theoretical results are found to be in agreement with our experimental findings. General considerations on the QED concept of transversal photon localization will be given on the basis of our results. These are apparently the first to be concerned with such a fundamental topological problem. This one is found to involve, in a new manner, relativistic retardation effects as well as a new EPR-type experimental configuration. Experimental results on the process of field interference by the partially interacting microlasers1,2 will also be reported. This topic raises (and our results answer) additional questions regarding the quantum structure of light. The QED theory of the interference process will also be given with reference to our results.
The near-zero threshold and the very high gain of the active optical microlaser are investigated both theoretically and experimentally. These properties are found to be determined by the synergy of several quantum-statistical processes taking place in the condition of extreme field confinement provided by the peculiar Casimir-type topology of the optical microcavity. The determination of the microcavity mode structure leads to a detailed study of the process of merging of the spontaneous emission with stimulated emission (StE) and of the consequent anomalous onset of the collective atomic behavior at very low excitation levels. An excitation threshold of about 50 pJ has been determined experimentally with a molecular oxazine microlaser excited by a femtosecond-pulse source. The relevance within the overall StE dynamics of the processes of mode-competition fluorescence loss, interatom transverse Bose correlations, and periodic excitation are investigated both theoretically and experimentally. A discussion of the overall process in terms of a second-order phase transition in a nonequilibrium statistical problem is given. The extension of the microcavity dynamics to quantum-dynamical systems such as the ``microscopic'' parametric oscillator and to Raman and Compton scattering is also considered.
We investigate the appearance of spontaneous coherence in the parametric emission from planar semiconductor microcavities in the strong coupling regime. Calculations are performed by means of a quantum Monte Carlo technique based on the Wigner representation of the coupled exciton and cavity-photon fields. The numerical results are interpreted in terms of a nonequilibrium phase transition occurring at the parametric oscillation threshold: below the threshold, the signal emission is incoherent, and both the first and the second-order coherence functions have a finite correlation length which becomes macroscopic as the threshold is approached. Above the threshold, the emission is instead phase coherent over the whole two-dimensional sample and intensity fluctuations are suppressed. Similar calculations for quasi-one-dimensional microcavities show that in this case the phase coherence of the signal emission has a finite extension even above the threshold, while intensity fluctuations are suppressed.
We develop a nonlinear theory of a two-photon correlated-spontaneous-emission laser (CEL) by using an effective interaction Hamiltonian for a two-level system coupled by a two-photon transition. Assuming that the active atoms are prepared initially in a coherent superposition of two atomic levels involved in the two-photon transition, we derive a master equation for the field-density operator by using our quantum theory for coherently pumped lasers. The steady-state properties of the two-photon CEL are studied by converting the field master equation into a Fokker-Planck equation for the antinormal-ordering Q representation of the field-density operator. Because of the injected atomic coherence, the drift and diffusion coefficients become phase sensitive. This leads to laser phase locking and an extra two-photon CEL gain. The laser field can build up from a vacuum in the no-population-inversion region, in contrast to an ordinary two-photon laser for which triggering is needed. We find an approximate steady-state solution of the Q representation for the laser field, which consists of two identical peaks of elliptical type. We calculate the phase variance and, for any given mean photon number, obtain the minimum variance in the phase quadrature as a function of the initial atomic variables. Squeezing of the quantum noise in the phase quadrature is found and it exhibits the following features: (1) it is possible only when the laser intensity is smaller than a certain value; (2) it becomes most significant for small mean photon number, which is achievable in the no-population-inversion region; and (3) a maximum of 50% squeezing can be asymptotically approached in the small laser intensity limit. As a by-product we also study the ordinary two-photon laser and find, e.g., photon-number variance and laser linewidth.
We detail the derivation of nanolaser models that include coherent and incoherent variables and predict the existence of a laser threshold, irrespective of cavity size and emitter number, for both single- and multielectron systems. The growth in photon number in the lasing mode is driven by an increase in correlation between absorption and emission processes, leading to the onset of self-sustained stimulated emission (laser threshold), followed in turn by a correlation decrease and ending with the dominance of coherent emission. The first-order coherence g(1){g}^{(1)}g(1) steadily increases, as the pump grows towards the laser threshold value, and reaches unity at or beyond threshold. The transition toward coherent emission becomes increasingly sharp as the numbers of emitters and coupled electromagnetic cavity modes increase, continuously connecting, in the thermodynamic limit, the physics of nano- and macroscopic lasers at threshold. Our predictions are in remarkable agreement with experiments whose first-order coherence measurements have so far been explained only phenomenologically. A consistent evaluation of different threshold indicators provides a tool for a correct interpretation of experimental measurements at the onset of laser action.