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Physical Review A

Field dynamics, instabilities, and phase squeezing in the two-photon correlated-emission laser

János A. Bergou, J. Zhang, C. Su

Published Oct 1, 1995• 2 citations
Publisher

Abstract

Both stationary and time-dependent regimes of operation, instabilities, and phase squeezing are investigated in the off-resonant two-photon correlated-spontaneous-emission laser by numerical calculation. Initial atomic coherence plays an essential role in lasing without population inversion, phase locking, and phase noise squeezing in the system. Under certain conditions, in the inverted and noninverted regimes alike, the output intensity exhibits bistable behaviors against the initial atomic coherence. Depending on the parameters, the whole or a portion of the upper or lower branch gives stable operations. In the inverted regime, even tristable behavior can be found in a narrow range of parameters. The field evolution and dynamics are studied. Furthermore, phase noise reduction near bistable areas is also investigated. In addition to the lower branch, where from previous studies, it has been known to exist, phase squeezing is also found on the upper branch both with and without population inversion, thus generating a bright source of phase noise squeezed light.

DOI
10.1103/physreva.52.3183

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ROLE OF PUMP PHASE FLUCTUATIONS IN CORRELATED SPONTANEOUS EMISSION LASER

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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

•Jan 1, 1995•0 citations
Both stationary and time-dependent regimes of operation, instabilities, and phase squeezing are investigated in the off-resonant two-photon correlated-spontaneous-emission laser by numerical calculation. Initial atomic coherence plays an essential role in lasing without population inversion, phase locking, and phase noise squeezing in the system. Under certain conditions, in the inverted and noninverted regimes alike, the output intensity exhibits bistable behaviors against the initial atomic coherence. Depending on the parameters, the whole or a portion of the upper or lower branch gives stable operations. In the inverted regime, even tristable behavior can be found in a narrow range of parameters. The field evolution and dynamics are studied. Furthermore, phase noise reduction near bistable areas is also investigated. In addition to the lower branch, where from previous studies, it has been known to exist, phase squeezing is also found on the upper branch both with and without population inversion, thus generating a bright source of phase noise squeezed light.
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.
A quantum theory of two-photon correlated-spontaneous-emission lasers (CEL's) is developed, starting from the exact atom-field interaction Hamiltonian for cascade three-level atoms interacting with a single-mode radiation field. We consider the situation where the active atoms are prepared initially in a coherent superposition of three atomic levels and derive a master equation for the field-density operator by using a quantum theory for coherently pumped lasers. The master equation is transformed into a Fokker-Planck equation for the antinormal-ordering Q function. The drift coefficients of the Fokker-Planck equation enable us to study the steady-state operation of the two-photon CEL's analytically. We have studied both resonant two-photon CEL for which there is no threshold, and off-resonant two-photon CEL for which there exists a threshold. In both cases the initial atomic coherences provide phase locking, and squeezing in the phase quadrature of the field is found. The off-resonant two-photon CEL can build up from a vacuum when its linear gain is larger than the cavity loss (even without population inversion). Maximum squeezing is found in the no-population-inversion region with the laser intensities far below saturation in both cases, which are more than 90% for the resonant two-photon CEL and nearly 50% for the off-resonant one. Approximate steady-state Q functions are obtained for the resonant two-photon CEL and, in certain circumstances, for the off-resonant one.
The influence of injected atomic coherence on a laser's operation is discussed by analyzing the semiclassical equations of motion of this system. Both stationary-steady-state and time-dependent regimes of operation are investigated. We present the dependence of the stationary laser intensity and phase on the external parameters (population inversion, amplitude of atomic coherence, and detuning). For small cavity-field detuning and large atomic coherence, both frequency and phase locking occurs. The laser frequency is locked to the atomic frequency, and the phase is locked to a value determined primarily by the phase of the atomic coherence. Under certain conditions, in the inverted regime, the output intensity is an ssS-shaped function of the atomic coherence, leading to the possibility of a bistable behavior. However, only a portion of the bistable curve gives stable stationary operation, and in critical points (the location of which depends crucially on the external parameters) time-dependent instabilities branch away. When the detuning is larger than a critical value there is neither phase nor frequency locking. We find that the time-dependent behavior of the laser intensity in this case is oscillatory (quasiperiodic), and show that there is a stable limit cycle in the phase plane of the quadratures. There is a small parameter region where a stationary steady state and an oscillatory state may coexist. We also consider the nonlinear quantum theory of a laser with injected atomic coherence, and include the effect of pumping statistics. We derive the Fokker-Planck equation for the P representation, and express the noise in terms of moments. We find that in the steady state the intensity noise can be suppressed below the shot-noise limit but that the phase fluctuations are not affected by pump regularity. For nonzero detuning, we find that transient squeezing of the phase fluctuations is possible.
We show in this paper that phase fluctuations of active atoms in many two-photon correlated spontaneous-emission lasers will reduce field squeezings and brightness of the squeezed light. But, under certain conditions of laser operation, the fluctuations of atomic phases between lower almost degenerate atomic levels could increase the squeezings and the brightness. We also show that, even for large phase fluctuations of the active atoms, almost perfect field squeezings and substantial brightness of the squeezed light can be obtained.
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