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Physical Review Letters

Quenching Quantum Phase Noise: Correlated Spontaneous Emission versus Phase Locking

Ingo Steiner, P. E. Toschek

Published Jun 5, 1995• 37 citations
Publisher

Abstract

Measuring the phase dynamics of the beat note in the output of a HeNe Zeeman laser, we (i) unravel the interplay of phase locking and correlated spontaneous emission, (ii) observe the phase-diffusion noise reduced to $\frac{1}{14}$ of the Schawlow-Townes quantum level (the largest reduction of quantum noise reported so far), and (iii) show that balanced pumping of the two upper laser levels would achieve correlation of the laser phase noise with no locking at all. The resulting reduction in the phase noise of the beat note allows interferometric measurements of vastly enhanced sensitivity.

DOI
10.1103/physrevlett.74.4639

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Measuring the phase dynamics of the beat note in the output of a HeNe Zeeman laser, we (i) unravel the interplay of phase locking and correlated spontaneous emission, (ii) observe the phase-diffusion noise reduced to 114\frac{1}{14}141​ of the Schawlow-Townes quantum level (the largest reduction of quantum noise reported so far), and (iii) show that balanced pumping of the two upper laser levels would achieve correlation of the laser phase noise with no locking at all. The resulting reduction in the phase noise of the beat note allows interferometric measurements of vastly enhanced sensitivity.
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.
Current laser systems have phase and amplitude fluctuations which are partially quantum in origin. The amplitude fluctuations of a highly stabilized laser are shot noise limited, that is they have quantum fluctuations due to the Poissonian fluctuations of photons in a coherent state. These photon number fluctuations have been shown to have an origin in the incoherent pumping mechanism used for standard lasers. It has recently been demonstrated experimentally that by suppressing the amplitude fluctuations of the pump a laser output with reduced amplitude fluctuations is possible. The phase fluctuations in a laser are due to phase diffusion and are substantially above the quantum limit. Techniques to reduce the laser phase fluctuations have been proposed making use of correlated spontaneous emission.
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.
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.