Correlated Emission Laser Research Articles

Phase in the correlated-emission laser.

The linear theory of the correlated-emission laser (CEL) is studied using the quantum-mechanical definition of the phase of the electromagnetic field recently introduced by Barnett and Pegg [J. Mod. Opt. 36, 17 (1989); Phys. Rev. A 39, 1665 (1989)]. From the master equation for the density matrix of the field, a Fokker-Planck equation for the phase probability function is derived, and the phase properties of the CEL discussed. The Adler equation and the equation of motion for the variance of the phase difference are derived. The Fokker-Planck equation satisfied by the phase probability function is compared with the corresponding equations for the P, Q, and Wigner quasiprobability distributions, specialized to the case when amplitude fluctuations are negligible. We show that the phase probability function and the Wigner function satisfy the same equation, and conclude that, of the three quasiprobability functions studied, only the Wigner function is reliable for calculating directly the phase properties. The commonly used P function overestimates the laser linewidth by a factor of 2.

Correlated-emission laser: the effect of injected atomic coherence and quantum-noise quenching for Hermitian operators

We develop a quantum theory of a correlated-emission laser (CEL) with injected atomic coherence for arbitrary initial atomic conditions and arbitrary atomic decay rates. The effect of initial atomic coherence on the CEL is studied. It is shown that, with a proper form of the initial atomic coherence and equal atomic decay rates between the two upper levels of V-type three-level lasing atoms, the diffusion coefficients for the relative phase and the relative amplitude of two laser modes can vanish under certain conditions. These conditions, plus equal cavity-loss rates, lead to the vanishing of the normally ordered variances (quantum-noise quenching) of Hermitian operators corresponding to the relative phase and the relative amplitude.

Theory of photon counting for phase-dependent three-level detector systems.

We demonstrate that atomic superposition states are sensitive to phase-dependent properties of radiation fields and that atoms prepared in such states can be employed as detectors. We concentrate on three-level detectors in two configurations, \ensuremath{\lambda} and ladder systems. \ensuremath{\lambda} systems prepared in a superposition state are shown to be sensitive to the relative phase between field modes and are relevant to measurements of fields produced by correlated-emission lasers. Ladder systems prepared in a superposition state are sensitive to the overall field phase and are relevant to measurements of fields generated in squeezing experiments. Such atomic-superposition-state detectors could be of value in detecting phase-dependent properties of microwave radiation in Rydberg atom masers and for investigating the properties of optical radiation generated in correlated-emission lasers.

Polarization correlated-emission laser and the influence of pump statistics.

We propose a new kind of correlated-spontaneous-emission laser in which the electromagnetic field is driven by coherently prepared atoms. Such a system constitutes a very simple correlated-emission scheme in that it involves only single-photon transitions, whereas all previous studies were based on correlated photon pairs. We find that for low intensities the fluctuations in the photon number can be reduced below the standard limit while the phase noise is unaffected by the atomic coherence. However, the amount of noise reduction crucially depends on the fluctuations of the pump mechanism. In the high-intensity limit the photon-number fluctuations can be reduced even further. It is possible to achieve a complete quenching of the spontaneous-emission noise and even squeezing, depending on the atomic coherence and the statistical properties of the pump mechanism. Additionally we find a large reduction in the phase fluctuations. In contrast to the amplitude noise, this reduction is independent of the pump noise.

Canonical transformation and decay into phase-sensitive reservoirs.

We show that the master equation describing the dissipative evolution of a bosonic quantum system coupled to a phase-sensitive reservoir may be reduced to a standard form of dissipation for a thermal reservoir by canonical transformations. The solution to the master equation for complex phase-sensitive interaction induced, for example, by broadband squeezed light, may then be obtained by a transformation from the known solutions for the simpler thermal case. We show that canonical transformations have a particularly useful form when describing the evolution of quantum dissipative systems in phase space using the Wigner function. We illustrate these ideas with two phase-sensitive dissipative problems: that of the correlated-emission laser and of decay induced by a broadband squeezed vacuum field.

Phase-sensitive amplification in a three-level atomic system.

A linear theory of two-photon amplification by three-level atoms in the cascade configuration is developed, where a coherence is induced between the top and bottom levels, by an external classical driving field. It is shown that this system becomes an ideal parametric amplifier for sufficiently strong driving field, whereas for a weak driving field it is a phase-insensitive amplifier. In between these two extremes, one finds phase-sensitive amplification as well as squeezing for a certain range. The system does not, however, reduce to a model studied previously where the atomic coherence was treated as an initial condition. The system is also studied in a cavity configuration: It is predicted that the oscillator may behave as a two-photon correlated emission laser, i.e., its phase diffusion coefficient vanishes.

A Heuristic Analysis of Quantum Noise Quenching in the Two‐Photon Correlated Emission Laser

AbstractWe demonstrate how the two‐photon correlated emission laser (CEL) can be understood from a simple physical picture in a quasirigorous fashion. We use semiclassical arguments to derive correct expressions for the phase and amplitude diffusion in a simple way. We then illustrate how noise suppression is achieved in the two‐photon CEL.

Comparative study of various quasiprobability distributions in different models of correlated-emission lasers.

We make a comparative study of various quasiprobability distributions in phase-sensitive quantum-optical systems. Starting from a general, linear master equation for the field, which emerges in different models of correlated-emission lasers, we derive the Fokker-Planck equations in the CJlauber-Sudarshan P, the antinormal ordering Q, the Wigner W, the complex P, and the positive P representations and find the steady-state solutions for the five distributions. Simple relations between the complex and positive P functions are discovered for the first time. Various moments calculated by using these distributions are found to be identical, as expected. An application of these distributions to the two-photon correlated-emission laser shows that the intracavity field can be near-perfectly squeezed in the phase quadrature and the maximum quadrature squeezing is reached when the mean laser amplitude vanishes. I. INTRODUCTION Recently, several mechanisms for the correlatedemission laser (CEL) have been considered. ' The correlated emission is based on using atoms prepared in a coherent superposition of the states between which the laser emission takes place. The initial atomic coherence can lead to the reduction in either phase or amplitude noise. It can even lead to the squeezing in one of the quadratures of the field. The microscopic theories of the (single-mode) CEL show that the dynamical equation for the density matrix for the field mode a can be written in the form'

Squeezing and quantum-noise quenching in phase-sensitive optical systems.

We present a systematic account of the different relations between squeezing, correlated-emission-laser (CEL) quantum-noise quenching, and general phase-diffusion noise expressed in terms of quadrature amplitudes. For a wide class of optical devices as described by a general Fokker-Planck equation, we establish conditions that lead to squeezing and CEL quantum-noise quenching.

Nonlinear theory of a correlated emission laser.

A nonlinear theory of correlated emission lasers is presented. It is shown that if three-level atoms in the V configuration are injected in a coherent superposition of the upper two states in a doubly resonant cavity, the diffusion coefficient for the relative phase vanishes under certain conditions.

Correlated-emission laser: Nonlinear theory of the quantum-beat laser.

A nonlinear quantum theory of the quantum-beat laser is developed using a ``dressed-atom--dressed-mode'' master-equation approach. The theory is valid under the detuning conditions which led to correlated spontaneous emission in a linear theory. It is shown that the quenching of the quantum noise remains valid in the nonlinear theory and this operation is stable above threshold.

Correlated-emission laser: Phase noise quenching via coherent pumping and the effect of atomic motion.

We show that in a three-level system, if the atoms are initially prepared in a coherent superposition of the two upper states, as in Hanle experiments, the spontaneous-emission events from these two states to the lowest one can, under certain conditions, be strongly correlated, with a vanishing diffusion constant for the relative phase. The conditions under which correlated spontaneous emission occurs in a Hanle laser remain essentially unchanged if atomic motion is included.

Correlated-emission laser: Theory of the quantum-beat micromaser.

We show that if we inject three-level atoms, at a low rate, through a double cavity, with the two upper levels strongly coupled, and if, in the theoretical analysis, one makes the rotating-wave approximation, this problem is formally equivalent to the ordinary two-level micromaser. We also obtain the relevant master equation and the photon statistics.

Dynamically correlated spontaneous-emission laser: theory and comparison with experiment

A higher-order correlated-emission laser (CEL) effect is found theoretically in a Doppler-broadened medium. A full quantum-mechanical account of the CEL in the nonlinear regime shows a large reduction in the beat-signal linewidth. This behavior is confirmed by a recent experiment.

Correlated-emission laser gyroscope

We show that correlated-emission noise quenching can be achieved in a ring laser via a spatially modulated active medium. A gyroscope based on such a correlated-emission laser has a potential sensitivity superseding the usual quantum limit.