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CRC Press eBooks

Models for Phase-Insensitive Quantum Amplifiers

G. L. Mander, R. Loudon, Terence J. Shepherd

Published Aug 12, 2020• 0 citations
Publisher

Abstract

This chapter reviews and extends the work on the particular class of linear amplifiers known as inverted population amplifiers. It discusses first the fundamental requirements demanded by quantum mechanics from any theory of linear amplifiers, and then describes the basic model for the atomic amplifier in a closed cavity. The chapter considers the extension of this model to allow explicit incoherent coupling of the internal cavity field to external fields, and treats finally an open system with coherent field coupling. It investigates in particular the conditions under which the amplified field retains quantum properties such as squeezing. The chapter examines the ability of the phase-insensitive systems to enhance the signal-to-noise ratio of an injected signal, and finds that in general any signal is degraded by the amplification process. Phase-insensitive atomic amplifiers destroy all quantum statistical properties of the field if the gain exceeds the low value of two.

DOI
10.1201/9781003069539-10

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arXiv:1309.4443•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 6, 2013•0 citations
This chapter reviews and extends the work on the particular class of linear amplifiers known as inverted population amplifiers. It discusses first the fundamental requirements demanded by quantum mechanics from any theory of linear amplifiers, and then describes the basic model for the atomic amplifier in a closed cavity. The chapter considers the extension of this model to allow explicit incoherent coupling of the internal cavity field to external fields, and treats finally an open system with coherent field coupling. It investigates in particular the conditions under which the amplified field retains quantum properties such as squeezing. The chapter examines the ability of the phase-insensitive systems to enhance the signal-to-noise ratio of an injected signal, and finds that in general any signal is degraded by the amplification process. Phase-insensitive atomic amplifiers destroy all quantum statistical properties of the field if the gain exceeds the low value of two.
We calculate the input-output characteristics of an optical amplifier that consists of an inverted-population medium placed inside a high-Q Fabry-P\'erot cavity. Expressions are derived for the output second- and fourth-order spectral and temporal correlation functions, and more generally for the output characteristic functional, in terms of the corresponding input quantities. The photocount first and second factorial moments are obtained for both homodyne and direct detection of the amplifier input and output. The general results are applied to several cases of practical interest, including inputs that have coherent or chaotic coherence properties. Particular attention is paid to the effects of amplification on specific nonclassical varieties of input light. It is shown that a maximum of only twofold amplification is permitted if any squeezing present in the input is to survive as squeezing in the output light. Similarly, for the preservation of photon antibunching in amplification, we show, by consideration of a kind of free-space number-state input, that only small gains are allowed. The amplifier model treated here provides a detailed example of the limitations imposed by quantum mechanics on the minimum noise generated by a multimode linear amplifier. In particular, we show that minimum noise occurs in a cavity that is asymmetric with respect to mirror reflectivities, for which we derive the corresponding conditions. In addition, we demonstrate the ability of the amplifier to improve upon signal-to-noise ratio, otherwise limited by low detector quantum efficiency.
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.
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
We examine the effects of linear amplification and attenuation on the quantum-mechanical phase properties of light for fields with mean photon numbers of at least the order of 10. The phase probability density is found to satisfy a diffusion equation for both phase-insensitive and phase-sensitive amplifiers and attenuators. The solution is a convolution of the initial phase probability density with an infinite series of expanding Gaussians which clearly illustrates the diffusion of the phase. In particular, we find that for phase-insensitive amplification the phase of the field undergoes time-dependent uniform diffusion. In the limit of large amplification the diffusion ceases and the phase variance of the amplified light is given by the input phase variance plus an extra term which is equal to the phase variance of a coherent state of the same intensity as the initial field. We show that the reduced phase variance of phase-optimized states (relative to coherent states of the same intensity) is lost for power gains greater than the photon-cloning value of 2. In contrast, phase-sensitive amplifiers give rise to time-dependent nonuniform phase diffusion. The amount of phase diffusion depends on the relative phase angle between the light and the amplifier. If the peak of a relatively narrow phase probability density is near a minimum in the phase diffusion coefficient, then the phase noise added by the amplifier will be less than that found for a phase-insensitive amplifier. Further squeezing of the amplifier reduces the added phase noise proportionally. We find that it is possible, using phase-sensitive amplifiers, to amplify phase-optimized states by power gains considerably larger than 2 and still retain a reduced phase variance.
The properties of a linear optical amplifier or attenuator in which the input light is coupled to a collection of non-saturable atoms are considered. The photon-number factorial moments and probability distribution of the amplifier output are derived for arbitrary input statistics. Relations are obtained between the output and input variances in photon number, phase-angle cosine, and electric-field magnitude. The effects of amplification and attenuation on signal-to-noise ratio are obtained for both direct and homodyne detection. Particular attention is paid to the extents to which the non-classical properties of photon antibunching and squeezing are preserved by amplification and attenuation. It is found that both properties can at best survive only twofold intensity amplification.
According to the fundamental laws of quantum optics, noise is necessarily added to the system when one tries to clone or amplify a quantum state. However, it has recently been shown that the quantum noise related to the operation of a linear phase-insensitive amplifier can be avoided when the requirement of a deterministic operation is relaxed. Nondeterministic noiseless linear amplifiers are therefore realizable. Usually nondeterministic amplifiers rely on using single photon sources. We have, in contrast, recently proposed an amplification scheme in which no external energy is added to the signal, but the energy required to amplify the signal originates from the stochastic fluctuations in the field itself. Applying our amplification scheme, we examine the amplifier gain and the success rate as well as the properties of the output states after successful and failed amplification processes. We also optimize the setup to find the maximum success rates in terms of the reflectivities of the beam splitters used in the setup. In addition, we discuss the nonidealities related to the operation of our setup and the relation of our setup with the previous setups.