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Physical Review A

Quantum-noise quenching in the correlated spontaneous-emission laser as a multiplicative noise process. II. Rigorous analysis including amplitude noise

Wolfgang P. Schleich, Marlan O. Scully, H.-G. von Garßen

Published Apr 1, 1988• 20 citations
Publisher

Abstract

An analytical steady-state distribution for the phase difference \ensuremath{\psi} in a correlated spontaneous-emission laser (CEL) is derived based on the amplitude and phase equations of a CEL. This distribution is shown to be an excellent approximation to that obtained from a numerical simulation of the complete set of CEL equations. In particular, the effects of amplitude noise on CEL operation are considered and it is shown that fluctuations in the relative amplitude are also noise quenched.

DOI
10.1103/physreva.37.3010

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Physical Review A•May 1, 1989•69 citations
An analytical steady-state distribution for the phase difference \ensuremath{\psi} in a correlated spontaneous-emission laser (CEL) is derived based on the amplitude and phase equations of a CEL. This distribution is shown to be an excellent approximation to that obtained from a numerical simulation of the complete set of CEL equations. In particular, the effects of amplitude noise on CEL operation are considered and it is shown that fluctuations in the relative amplitude are also noise quenched.
We show, via simple geometrical arguments, the quantum-noise quenching in a correlated (spontaneous) emission laser (CEL). This noise quenching is a consequence of the correlation between noise sources which results in a multiplicative noise process. The steady-state distribution for the phase difference between the two electric fields in a CEL is compared and contrasted to that of a standard phase-locked laser. Noise quenching is shown to occur in the case of the CEL via an explicit solution of the Fokker-Planck equation.
As discussed in the last three chapters, the fundamental source of noise in a laser is spontaneous emission. A simple pictorial model for the origin of the laser linewidth envisions it as being due to the random phase diffusion process arising from the addition of spontaneously emitted photons with random phases to the laser field. In this chapter we show that the quantum noise leading to the laser linewidth can be suppressed below the standard, i.e., Schawlow–Townes limit by preparing the atomic systems in a coherent superposition of states as in the Hanle effect and quantum beat experiments discussed in Chapter 7. In such coherently prepared atoms the spontaneous emission is said to be correlated. Lasers operating via such a phase coherent atomic ensemble are known as correlated spontaneous emission lasers (CEL). An interesting aspect of the CEL is that it is possible to eliminate the spontaneous emission quantum noise in the relative linewidths by correlating the two spontaneous emission noise events. A number of schemes exist in which quantum noise quenching below the standard limit can be achieved. In two-mode schemes a correlation between the spontaneous emisson events in two different modes of the radiation field is established via atomic coherence so that the relative phase between them does not diffuse or fluctuate. In a Hanle laser and a quantum beat laser this is achieved by pumping the atoms coherently such that every spontaneously emitting atom contributes equally to the two modes of the radiation, leading to a reduction and even vanishing of the noise in the phase difference.
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.