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Physica Scripta

Quantum phase fluctuations in a three-level laser

Javaid Anwar

Published Jun 1, 2007• 0 citations
Publisher

Abstract

A scheme of a three-level laser in the presence of usual transmission losses is presented. It is proposed that, if the spontaneous emission between the lasing levels is coupled to a 'squeezed vacuum' reservoir, stability of phase locking can be achieved. The phase diffusion coefficient decreases below the Schawlow–Townes limit and vanishes for larger squeezing.

DOI
10.1088/0031-8949/76/1/007

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A scheme of a three-level laser in the presence of usual transmission losses is presented. It is proposed that, if the spontaneous emission between the lasing levels is coupled to a 'squeezed vacuum' reservoir, stability of phase locking can be achieved. The phase diffusion coefficient decreases below the Schawlow–Townes limit and vanishes for larger squeezing.
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.
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.
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.
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.
The squeezing, entanglement, and statistical properties of cavity modes produced by V-type three-level laser coupled to squeezed vacuum reservoir were studied employing the steady state solutions of the expectation values of the cavity mode operators. The study showed that a light in squeezing state can be produced by the system under consideration under the condition that the cavity decay constant is larger than linear gain coefficient and the squeezing occurs in the plus-quadrature. The cavity modes do not exhibit entanglement properties. It is also observed that the degree of squeezing increases with the linear gain coefficient and squeezing parameter. We also determined the mean and variance of the photon number, intensity difference fluctuations, and the second order correlation function of the two modes. The mean and variance of the photon number as well as the correlation function of two modes decrease as the difference of the probability of the two states at initial time increases. The photons have super-poissionian statistics. The point, η, at which the maximum intensity difference fluctuation occurred depends on linear gain coefficient but not squeezing parameter. The result shows that the correlation of the two modes decreases as η the linear gain coefficient and squeezing parameter.
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.