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Physical Review Letters

Squeezing of spontaneous emission in a laser

Julio R. Gea-Banacloche

Published Aug 3, 1987• 68 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.59.543

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It is shown by Gea-Banacloche [Phys. Rev Lett. 59, 543 (1987)] that the Laser Phase diffusion rate may be reduced by as much as one-half when laser is coupled out through a partially transmitting mirror to ``squeezed vacuum'' as opposed to ordinary vacuum. This happens for a particular choice of the phase of the squeezed field. However, phase stability is not achieved for this choice of phase. In this paper, this analysis is extended by including a separate squeezed vacuum reservoir which couples the spontaneous decay between the lasing levels. The results show that, it is possible to obtain the phase stability as well as phase noise quenching in this system.

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We investigate the effect of injected squeezed vacuum on the phase and intensity fluctuations of a laser. By using a stochastic simulation of the Langevin equations, we find that the phase diffusion noise of a laser with injected squeezed vacuum can be transiently reduced by a factor of 2, in agreement, with earlier predictions. Further, we find that the laser linewidth is broadened. The key observation is that the phase-diffusion rate is time dependent. We find that the steady-state intensity fluctuations are increased by the injected squeezing, in qualitative (but not quantitative) agreement with an earlier prediction. The problem of locking is examined. We find that the injected squeezed vacuum does not cause the laser to lock to any particular phase. We present an approximate solution of the Fokker-Planck equation in steady state, and a simple geometrical, vector kick model from which most of our results can be obtained.

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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.

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Effects of a squeezed vacuum on a laser exhibiting phase locking: An application to a laser with injected atomic coherence

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We study the steady-state operation and noise properties of a laser (or maser) exhibiting phase locking when an ordinary vacuum is replaced by a squeezed vacuum. Such a phase-sensitive laser can be realized by preparing the active medium initially in a coherent superposition of levels involved in the laser transition. We develop a general formalism to treat number-phase fluctuations and quadrature fluctuations. When applied to a one-photon laser with injected atomic coherence, we find that not only is a complete quenching of the (spontaneous-emission) quantum noise possible, but the field can actually be in a squeezed state. The variance in either amplitude or phase quadrature can be below the vacuum noise level by a factor of 2 (50%) at the expense of enhanced fluctuations in the other quadrature.

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In the presence of usual transmission losses, it is shown that phase noise in a four-level laser can be reduced below the Schawlow–Townes limit when lasing levels are coupled to a squeezed vacuum reservoir. The squeezed vacuum coupled to the lasing mode modifies the phase diffusion rate and dominates the contribution from transmission losses. It is predicted to obtain phase stability in the system and phase noise vanishes for larger squeezing. Gain of the laser remains positive under these conditions.

Chinese Physics Letters•Mar 1, 2010•0 citations
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.
It is shown by Gea-Banacloche [Phys. Rev Lett. 59, 543 (1987)] that the Laser Phase diffusion rate may be reduced by as much as one-half when laser is coupled out through a partially transmitting mirror to ``squeezed vacuum'' as opposed to ordinary vacuum. This happens for a particular choice of the phase of the squeezed field. However, phase stability is not achieved for this choice of phase. In this paper, this analysis is extended by including a separate squeezed vacuum reservoir which couples the spontaneous decay between the lasing levels. The results show that, it is possible to obtain the phase stability as well as phase noise quenching in this system.
We investigate the effect of injected squeezed vacuum on the phase and intensity fluctuations of a laser. By using a stochastic simulation of the Langevin equations, we find that the phase diffusion noise of a laser with injected squeezed vacuum can be transiently reduced by a factor of 2, in agreement, with earlier predictions. Further, we find that the laser linewidth is broadened. The key observation is that the phase-diffusion rate is time dependent. We find that the steady-state intensity fluctuations are increased by the injected squeezing, in qualitative (but not quantitative) agreement with an earlier prediction. The problem of locking is examined. We find that the injected squeezed vacuum does not cause the laser to lock to any particular phase. We present an approximate solution of the Fokker-Planck equation in steady state, and a simple geometrical, vector kick model from which most of our results can be obtained.
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 study the steady-state operation and noise properties of a laser (or maser) exhibiting phase locking when an ordinary vacuum is replaced by a squeezed vacuum. Such a phase-sensitive laser can be realized by preparing the active medium initially in a coherent superposition of levels involved in the laser transition. We develop a general formalism to treat number-phase fluctuations and quadrature fluctuations. When applied to a one-photon laser with injected atomic coherence, we find that not only is a complete quenching of the (spontaneous-emission) quantum noise possible, but the field can actually be in a squeezed state. The variance in either amplitude or phase quadrature can be below the vacuum noise level by a factor of 2 (50%) at the expense of enhanced fluctuations in the other quadrature.
In the presence of usual transmission losses, it is shown that phase noise in a four-level laser can be reduced below the Schawlow–Townes limit when lasing levels are coupled to a squeezed vacuum reservoir. The squeezed vacuum coupled to the lasing mode modifies the phase diffusion rate and dominates the contribution from transmission losses. It is predicted to obtain phase stability in the system and phase noise vanishes for larger squeezing. Gain of the laser remains positive under these conditions.