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Physical Review A

Polarization correlated-emission laser and the influence of pump statistics

Claus Benkert, Marlan O. Scully

Published Sep 1, 1990• 22 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.42.2817

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Physical Review A•May 1, 1989•69 citations
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.
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.
The fundamental source of noise in laser and optical amplifier is spontaneous emission. However, it is possible to reduce this noise by preparing the gain medium (atoms) in coherent superposition of states. There are essentially two schemes for generating atomic coherence in optical amplifiers. \n \nFirst scheme involves the preparation of atoms in a coherent superposition of states before injecting them inside the cavity. In the other scheme atoms (initially pumped incoherently) are continuously driven by an external pump field inside the cavity. Almost all the studies concerning the quenching of spontaneous emission noise in optical amplifiers, based on the notion of atomic coherent superposition, ignore the finite bandwidth of the field that is responsible for generating coherence. In this dissertation, we have examined the effect of the finite bandwidth associated with the phase fluctuations of the driving field on a number of noise quenching schemes. \n \nIt is known that coherent preparation of atoms can, under certain conditions, lead to noise-free amplification and almost 50 percent phase squeezing in a two-photon correlated emission laser. We study the effect of phase fluctuations in the injected atoms on the phase noise of the field in these systems. We discuss the conditions under which squeezing is preserved in the two-photon linear amplifiers. We also show that, even for very large phase fluctuations in the injected atoms, almost 50 percent phase squeezing can be achieved. The corresponding gain is however significantly reduced. \n \nWe also study a system of phase-sensitive amplifier where atoms are prepared in a coherent superposition of states by a strong classical field. We study the role of pump phase fluctuations associated with the finite linewidth on the quantum statistical properties of the radiation field. A study of output field characteristics reveals that the presence of a weak pump field gives rise to equal variances in both the field quadratures which are independent of linewidth. On the other hand, the presence of strong pump field alters the output field characteristics with the generation of squeezing which is later on destroyed due to the presence of phase fluctuations
An intense single-mode correlated-spontaneous-emission laser or maser can be realized by driving the active atoms coherently with an injected external field. The scheme involves single-photon transitions unlike the two-photon or quantum-beat correlated-emission lasers that utilize correlations between successive photon-cascade emissions or between simultaneous emissions into modes of the field. Quenching of both the amplitude and phase noise and, in certain cases, squeezing of the amplitude fluctuations are found.
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.
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.