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Physical Review A

Quantum-statistical properties of noise in a phase-sensitive linear amplifier

Javed Anwar, Muhammad Suhail Zubairy

Published Jan 1, 1994• 53 citations
Publisher

Abstract

We present a model for a two-photon phase-sensitive linear amplifier in which the phase sensitivity is introduced by injecting three-level atoms initially prepared in a coherent superposition of upper and lower levels. We have studied the quantum-statistical properties of noise and show that, under certain conditions, the additive noise is in a squeezed vacuum state whose squeezing parameter depends on the atomic variables.

DOI
10.1103/physreva.49.481

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We present a model for a two-photon phase-sensitive linear amplifier in which the phase sensitivity is introduced by injecting three-level atoms initially prepared in a coherent superposition of upper and lower levels. We have studied the quantum-statistical properties of noise and show that, under certain conditions, the additive noise is in a squeezed vacuum state whose squeezing parameter depends on the atomic variables.
We consider a phase-sensitive amplifier that consists of a system of three-level atoms in a cascade configuration that is prepared in a coherent superposition of upper and lower states by a strong classical field. We have studied the role of pump phase fluctuations associated with the finite linewidth on the quantum-statistical properties of the radiation field. A study of the output field characteristics reveals that the presence of a very weak pump field gives rise to equal variances in both field quadratures which are independent of linewidth. On the other hand, the presence of a 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.
It has been shown that a coherent preparation of atoms can, under certain conditions, lead to noise-free amplification and almost 50% phase squeezing in a two-photon correlated-emission laser. In this paper, 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% phase squeezing can be achieved. The corresponding gain is, however, significantly reduced.
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.
A linear theory of two-photon amplification by three-level atoms in the cascade configuration is developed, where a coherence is induced between the top and bottom levels, by an external classical driving field. It is shown that this system becomes an ideal parametric amplifier for sufficiently strong driving field, whereas for a weak driving field it is a phase-insensitive amplifier. In between these two extremes, one finds phase-sensitive amplification as well as squeezing for a certain range. The system does not, however, reduce to a model studied previously where the atomic coherence was treated as an initial condition. The system is also studied in a cavity configuration: It is predicted that the oscillator may behave as a two-photon correlated emission laser, i.e., its phase diffusion coefficient vanishes.
Abstract We investigate the quantum statistical and squeezing properties of radiation generated by a coherently driven three-level laser system coupled to a squeezed vacuum reservoir. The analysis is carried out using c-number Langevin equations for normally ordered operator moments, allowing a transparent description of the interplay among atomic coherence, coherent driving, and reservoir-induced correlations. We show that significant quadrature squeezing can be achieved under appropriate conditions, with the degree of squeezing strongly influenced by the linear gain coefficient of the squeezed-vacuum reservoir, the strength of the coherent driving, and the initial atomic preparation. In particular, we find that maximal initial atomic coherence alone does not lead to squeezing in the absence of coherent driving, highlighting the essential role of phase-sensitive amplification. The results further reveal a shift of optimal squeezing toward lower values of the atomic coherence parameter and higher values of the driving strength as the gain and reservoir squeezing increase. In addition, we demonstrate the coexistence of strong quadrature squeezing with super-Poissonian photon statistics, reflecting the distinct roles of phase-sensitive and intensity fluctuations. The squeezing spectrum is also analyzed to provide frequency-resolved insight into noise suppression, directly relevant to homodyne-detection measurements. These findings clarify the trade-off between coherent excitation, which enhances phase-sensitive correlations, and photon population growth, which tends to increase intensity fluctuations, and they highlight parameter regimes where strong nonclassical effects can be realized under parameter regimes consistent with experimentally demonstrated cavity-QED and squeezed-light implementations.