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Journal of Physics Conference Series

Quantum noise in optical tweezers

Michael A. Taylor, Warwick P. Bowen

Published Dec 6, 2013• 3 citations
Publisher

Abstract

Quantum enhanced sensitivity in optical tweezers based particle tracking was recently demonstrated. This has provided the necessary tool for quantum metrology to play an important role in biological measurements. Here we introduce the basic theory relevant to such optical tweezers experiments, and overview the significance of sub-shot noise limited sensitivity to practical experiments. In particular, biophysical experiments are subject to optical power constraints, which therefore limits the absolute sensitivity which is classically achievable. Quantum enhanced particle tracking can overcome this limit, and is therefore likely to play an important role in such biophysical experiments in the near future.

DOI
10.1088/1742-6596/467/1/012007

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Quantum enhanced sensitivity in optical tweezers based particle tracking was recently demonstrated. This has provided the necessary tool for quantum metrology to play an important role in biological measurements. Here we introduce the basic theory relevant to such optical tweezers experiments, and overview the significance of sub-shot noise limited sensitivity to practical experiments. In particular, biophysical experiments are subject to optical power constraints, which therefore limits the absolute sensitivity which is classically achievable. Quantum enhanced particle tracking can overcome this limit, and is therefore likely to play an important role in such biophysical experiments in the near future.
A general quantum limit to the sensitivity of particle position measurements is derived following the simple principle of the Heisenberg microscope. The value of this limit is calculated for particles in the Rayleigh and Mie scattering regimes, and with parameters which are relevant to optical tweezers experiments. The minimum power required to observe the zero-point motion of a levitating bead is also calculated, with the optimal particle diameter always smaller than the wavelength. We show that recent optical tweezers experiments are within two orders of magnitude of quantum limited sensitivity, suggesting that quantum optical resources may soon play an important role in high sensitivity tracking applications.
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
Advancements in physics are often motivated/accompanied by advancements in our precision measurements abilities. The current generation of atomic and optical interferometers is limited by shot noise, a fundamental limit when estimating a phase shift with classical light or uncorrelated atoms. In the last years, it has been clarified that the creation of special quantum correlations among particles, which will be called here useful entanglement, can strongly enhance the interferometric sensitivity. Pioneer experiments have already demonstrated the basic principles. We are probably at the verge of a second quantum revolution where quantum mechanics of many-body systems is exploited to overcome the limitations of classical technologies. This review illustrates the deep connection between entanglement and sub shot noise sensitivity.
Advancements in physics are often motivated/accompanied by advancements in our precision measurements abilities. The current generation of atomic and optical interferometers is limited by shot noise, a fundamental limit when estimating a phase shift with classical light or uncorrelated atoms. In the last years, it has been clarified that the creation of special quantum correlations among particles, which will be called here useful entanglement, can strongly enhance the interferometric sensitivity. Pioneer experiments have already demonstrated the basic principles. We are probably at the verge of a second quantum revolution where quantum mechanics of many-body systems is exploited to overcome the limitations of classical technologies. This review illustrates the deep connection between entanglement and sub shot noise sensitivity.
Quantum metrology allows high sensitivity measurements to proceed with a lower light intensity than classically possible [1]. An important frontier for this technology is in biological measurements, where photochemical interactions often disturb biological processes and can damage the specimen [2]. Here we report the first demonstration of biological measurement with precision surpassing the quantum noise limit [3]. This was enabled through the development of a new microscopy system which extended previous methods used to track the motion of highly reflective mirrors with non-classical light to measurements of microscopic particles with non-paraxial fields (see Fig. 1). Biological dynamics in the critical Hz-kHz frequency range were made accessible by applying a quantum optical lock-in technique for the first time. This straightforward technique allowed quantum enhancement over a frequency range which reached as low as the range reported for squeezed light sources developed for gravity wave interferometers [4].