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Optimal Signal-to-Quantum Noise Ratio for Nonclassical Number States

Feng, Y, A. I. Solomon

Published Dec 15, 1997• 5 citations
OpenAlex

Abstract

We analyze the properties of nonclassical number states, specifically squeezed number states D(a)S(z)|n >, and find their maximum signal-to-quantum noise ratio. It is shown that the optimal signal-to-quantum noise ratio for these states decreases as 1/(2n+1)2, where n is the photon number, from the optimal value as derived by Yuen.

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For an arbitary quantum state of radiation with frequency the optimum signal-to-quantum noise ratio for fixed energy (or power per unit frequency) h ω N 3 has the value 4 N 3 ( N 3 +1), attainable by the squeezed coherent vacuum. The question arises as to what ρ is attainable when the vacuum is imperfect, and there are n photons present. We show that in such a situation the attainable signal-to-quantum noise ratio ρ is reduced by a factor (2 n +1) 2 . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
A continuous parameter introduced into the convolution transformation between P and Q functions leads to a measure of how nonclassical quantum states are with values ranging from 0 to 1: For photon-number states, the value is 1, the maximum possible. For squeezed vacuum states, it is a monotonically increasing function of the squeeze parameter with values varying from 0 to 1/2. This measure is identical to the minimum number of thermal photon necessary to destroy whatever nonclassical effects existing in the quantum states.
The signal-to-noise ratios (SNRs) of three Gaussian-state ghost-imaging configurations---distinguished by the nature of their light sources---are derived. Two use classical-state light, specifically a joint signal-reference field state that has either the maximum phase-insensitive or the maximum phase-sensitive cross correlation consistent with having a proper PPP representation. The third uses nonclassical light, in particular an entangled signal-reference field state with the maximum phase-sensitive cross correlation permitted by quantum mechanics. Analytic SNR expressions are developed for the near-field and far-field regimes, within which simple asymptotic approximations are presented for low-brightness and high-brightness sources. A high-brightness thermal-state (classical phase-insensitive state) source will typically achieve a higher SNR than a biphoton-state (low-brightness, low-flux limit of the entangled-state) source, when all other system parameters are equal for the two systems. With high efficiency photon-number-resolving detectors, a low-brightness, high-flux entangled-state source may achieve a higher SNR than that obtained with a high-brightness thermal-state source.
Abstract The signal-to-noise ratio is an important quantity in signal and image analysis that gives information about the quality of the signal and/or image of interest. When plasmonic biosensors are used to study how molecules interact in intermolecular binding reactions, the output signal and/or image must be of the highest quality to get the best value from our biosensors. Images of interest in this work are images of the binding region at the metal surface of the plasmonic biosensor. Improving the signal-to-noise ratio of these signals and/or images is a key area of research that can help scientists learn more about how different molecules interact with each other. Because these molecular entities can include a wide range of biomolecules, we can investigate different types of binding interactions. In this paper, we look at a theoretical two-mode image sensing framework that we use to model the signal-to-noise ratio in images generated by a plasmonic image-based biosensor. A Krestchmann configuration-based surface resonance sensor is used as a plasmonic biosensor. In the model, an example of how BSA and an antibody called IgG1 bind to the surface of a plasmonic biosensor are examined. Traditionally, classical states of light are used as probe states in the Krestchman configuration; in this paper, quantum states of light are considered alternative probe states. The effect of using quantum states of light, such as the Fock state, squeezed displaced states, and squeezed vacuum states, on the signal-to-noise ratio of images is investigated. This work also looks at the effect of losses in the sensing environment and changes in photon numbers in the input signal on the average signal-to-noise ratio of the output of the plasmonic biosensor. The novelty in the described work lies in the exploration of using a variety quantum states of light as probe states in a plasmonic image-based biosensor, specifically in the context of improving the signal-to-noise ratio of images captured from the binding region at the metal surface accounting for the impact of losses. It was found that some quantum states improve the signal-to-noise ratio of the plasmonic biosensor output image.