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Journal of Modern Optics

Practical Implications of Quantum Noise

Hans‐A. Bachor, P. J. Manson

Published Nov 1, 1990• 14 citations
Publisher

Abstract

This paper gives an introduction to quantum noise and the limits it places on optical measurements. Squeezed states of light, and their representation on phasor diagrams, are then introduced. The use of squeezed states to improve interferometric measurements is described. Quantum non-demolition measurements are discussed, with particular reference to their use in high sensitivity absorption experiments. Finally, sources of some other types of non-classical light and possible experiments making use of these sources are considered.

DOI
10.1080/09500349014551951

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This paper gives an introduction to quantum noise and the limits it places on optical measurements. Squeezed states of light, and their representation on phasor diagrams, are then introduced. The use of squeezed states to improve interferometric measurements is described. Quantum non-demolition measurements are discussed, with particular reference to their use in high sensitivity absorption experiments. Finally, sources of some other types of non-classical light and possible experiments making use of these sources are considered.
In ref [Phys. Rev. A 106, 013720], the scheme of quantum non-demolition measurement of optical quanta that uses a resonantly enhanced Kerr nonlinearity in optical microresonators was analyzed theoretically. It was shown that using the modern high-Q microresonators, it is possible to achieve the sensitivity several times better than the standard quantum limit. Here we propose and analyze in detail a significantly improved version of that scheme. We show, that by using a squeezed quantum state of the probe beam and the anti-squeezing (parametric amplification) of this beam at the output of the microresonator, it is possible to reduce the measurement imprecision by about one order of magnitude. The resulting sensitivity allows to generate and verify multi-photon non-Gaussian quantum states of light, making the scheme considered here interesting for the quantum information processing tasks.
Squeezed states of light are minimum uncertainty states for which the mean square fluctuations in phase and in quadrature with respect to a reference signal are unequal. Among other interesting properties, they provide improved sensitivity of optical interferometric phase measurements. To understand this potential, one must note that quantum theory imposes measurement uncertainty only on a pair of noncommuting variables; the measurement of any one quantum observable could be done with no uncertainty.>
This thesis reports the development of a quantum enhanced microparticle tracking technique, which applied to measurements within living cells, allowed the first demonstrations of both biological measurements beyond the quantum noise limit and quantum enhanced spatial resolution within biology. The sensitivity of any optical measurement is limited by noise which follows from quantization of the electromagnetic field. This thesis theoretically characterizes the resulting quantum limit on particle tracking precision; both in the limit of perfect measurements and for the measurements used in real experiments, and theoretically establishes an experimental strategy which could allow the quantum limit to be surpassed via the application of non-classical light. Further, a computational tool is developed which allows rapid characterization of particle tracking experiments, thus providing researchers the benefit of rigorous theoretical predictions without requiring detailed calculations. Following this, classical technologies are developed which can improve microparticle tracking sensitivity and which are enabling steps toward integration of non-classical light. An interferometric strategy is described whereby signal-to-noise is improved by removing unwanted light from the detector. An optical lock-in technique is developed which eliminates low-frequency noise, thus allowing quantum noise limited performance at low frequencies. This is a crucial requirement for quantum enhanced measurements, and can also improve precision in classical experiments. Dark-field illumination is also explored as a method to remove unwanted background light, and the optimal illumination angle is calculated for our intended experiments. These advances are then applied in the development of the first quantum enhanced particle tracking apparatus. Squeezed states of light are used to improve particle tracking precision by 2.7 dB, demonstrating quantum enhanced microscopy for the first time. This was applied to perform the first measurements of living systems with quantum enhanced precision. Naturally occurring lipid particles were tracked within the cytoplasm of Saccharomyces cerevisiae yeast cells, with squeezed light enhancing precision by 2.4 dB. The thermal motion of these particles could then be analyzed to infer the viscosity and elasticity of the local environment, with squeezed light allowing 64% faster observations, thus improving the sensitivity to dynamic biological changes. This experiment was then extended to spatially resolved quantum imaging, with lipid particles used as scanning probes in a technique called photonic force microscopy. The particles sample variations in the local environment with resolution limited by measurement precision rather than the diffraction limit. The use of squeezed light was found to enhance spatial resolution by 14% at an absolute resolution level of 10 nm, comparable to leading classical experiments. This was the first demonstration of both sub-diffraction limited resolution and quantum enhanced resolution in biology, and places practical applications of quantum imaging within reach. Finally, the future challenges and prospects of quantum enhanced particle tracking are outlined.n
Squeezed state light is a nonclassical optical field which has extensive potential applications in optical measurement with high sensitivity exceeding the standard quantum limit as well as in optical communications and quantum information with extremely low noise. This has given birth to cross-disciplines of physics and information science. An overview is presented of the generation of squeezed state light fields and their important applications in sub-shot-noise-limit optical measurement and quantum information research.