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Physical Review A

Memory correlation effects on quantum noise in lasers and masers

Claus Benkert, Marlan O. Scully, Georg Süssmann

Published Jun 1, 1990• 22 citations
Publisher

Abstract

We demonstrate how spontaneous-emission noise in lasers and masers can be reduced through memory effects of the lasing atoms. We show that for short measurement times the spontaneous-emission noise can be smaller than the usual Schawlow-Townes limit. We discuss a general model for atomic memory effects and derive expressions for the noise correlation function, phase diffusion, and the emitted spectrum. Furthermore, we allow for a frequency distribution over the lasing atoms and hence account for Doppler broadening or a selective excitation of the atoms.

DOI
10.1103/physreva.41.6119

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We demonstrate how spontaneous-emission noise in lasers and masers can be reduced through memory effects of the lasing atoms. We show that for short measurement times the spontaneous-emission noise can be smaller than the usual Schawlow-Townes limit. We discuss a general model for atomic memory effects and derive expressions for the noise correlation function, phase diffusion, and the emitted spectrum. Furthermore, we allow for a frequency distribution over the lasing atoms and hence account for Doppler broadening or a selective excitation of the atoms.
We discuss the influence of atomic memory effects on the field fluctuations of a laser in a general context. We derive a Fokker-Planck equation for the field that takes into account the long lifetime of the lasing atoms. Using this equation, we discuss two consequences of atomic memory. First, we find that even in the presence of saturation, memory effects can lead to a reduction of spontaneous-emission noise for short measurement times. Second, we quite generally show that atomic memory effects lead to time-dependent diffusion coefficients.
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 investigate different kinds of polarization-correlated-emission schemes, including a maser and a laser concept. In these systems, coherently prepared atoms drive the electromagnetic field. We demonstrate that the atomic coherence can lead to a reduction of noise fluctuations within a linear theory. In the homogeneously broadened case the amplitude noise is strongly affected by the atomic coherence, leading to noise quenching in the laser and even squeezing in the maser. On the other hand, the phase fluctuations are unaffected by the coherence between the lasing levels. We then study the effect of inhomogeneous broadening of the atomic transition frequency. We find the interesting result that the noise reduction due to the atomic coherence is not destroyed but redistributed between the phase and amplitude of the electromagnetic field.
We consider the problem of reducing the contributions of pump and spontaneous-emission noise to the output noise of a laser field. We consider two models based on an atomic medium, one analytic, the other involving numerical simulation of a sequence of pump cycles. The predictions of both models are shown to agree. For regular pump excitation the intensity fluctuations of a laser well above threshold may be reduced to zero at the cavity resonance frequency if the ratio of the lifetimes of the upper and lower lasing levels is sufficiently large that spontaneous emission is suppressed. When the atomic lifetimes are comparable, spontaneous emission reduces the amount of noise reduction. For example, for equal atomic lifetimes regular pump excitation will result in a maximum noise reduction in the output field of one-half the shot-noise limit.
It is predicted that a laser's phase-diffusion rate (its Schawlow-Townes linewidth) may be reduced by as much as one-half when the laser is coupled out to ``squeezed vacuum'' as opposed to ordinary vacuum. The effect is important because it is directly related to spontaneous emission in a squeezed vacuum. It shows that a part of spontaneous emission is due to amplified zero-point noise and that, therefore, in a squeezed field the random phases of the spontaneously emitted photons are no longer uniformly distributed.