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Mode Invisibility Technique - A Quantum Non-Demolition Measurement for Light

Marvellous Onuma-Kalu

Published Jul 14, 2014• 0 citations
OpenAlex

Abstract

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii The act of measuring an observable of a quantum system introduces backaction noise to the measured system. In the most extreme case, the system gets destroyed with its state left unavailable for future measurement. An example is the photodetection process where photons are destroyed upon detection. It is desirable to consider schemes that avoid the back action effect induced on detected observable due to the measurement. Such measurement scheme in which one is able to repeat a measurement on a physical observable, with the result of each measurement being the same for all measurement times is known as quantum non-demolition (QND) measurement. With the QND measurement idea, it has become possible to detect photons without destroying its state. In this thesis, we present an optical QND measurement scheme known as the Mode invisibility technique to measure

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I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii The act of measuring an observable of a quantum system introduces backaction noise to the measured system. In the most extreme case, the system gets destroyed with its state left unavailable for future measurement. An example is the photodetection process where photons are destroyed upon detection. It is desirable to consider schemes that avoid the back action effect induced on detected observable due to the measurement. Such measurement scheme in which one is able to repeat a measurement on a physical observable, with the result of each measurement being the same for all measurement times is known as quantum non-demolition (QND) measurement. With the QND measurement idea, it has become possible to detect photons without destroying its state. In this thesis, we present an optical QND measurement scheme known as the Mode invisibility technique to measure
This is a limited overview of quantum non-demolition (QND) measurements, with brief discussions of illustrative examples meant to clarify the essential features. In a QND measurement, the predictability of a subsequent value of a precisely measured observable is maintained and any random back-action from uncertainty introduced into a noncommuting observable is avoided. The fundamental ideas, relevant theory and the conditions and scope for applicability are discussed with some examples. Precision measurements have indeed gained from developing QND measurements. Some implementations in quantum optics, gravitational wave detectors and spin-magnetometry are discussed.
Unlike classical systems, the very act of observing quantum systems perturbs their behaviour. This introduces noise, which imposes limits on the knowledge that can be obtained through measurement. Certain measurement techniques, known generally as quantum non-demolition (QND) measurements, exist to circumvent this noise. An alternative method to evade backaction noise is to amplify the observable of interest above the noise. However, this generally leaves the system in a different state, and is therefore not considered a QND measurement. In this thesis, I examine the benefits of amplification for various kinds of measurement of mechanical harmonic oscillators which, at the micrometre and nanometre scale, comprise an emerging quantum technology. For this prototypical case, modulation of the spring constant, also known as parametric amplification, is a well-studied noiseless amplification technique. Using the theory of trajectories developed in the field of quantum optics, I show that a weak measurement combined with a detuned parametric drive achieves the same ends as strong QND measurement. Namely, it allows backaction-free observation of one quadrature of mechanical motion, and through this, quantum squeezing below the quantum zero-point motion. This equivalence is experimentally confirmed in the classical limit using an optically detected, electrically modulated cantilever. In addition, I analyse similar amplification enhanced techniques for quantum entanglement and quantum tomography. These results are applicable to research in quantum optomechanics and electromechanics, and can be translated to other kinds of quantum harmonic oscillators, such as microwave cavities.
According to Heisenberg’s uncertainty principle, measurement of a quantum observable introduces noise to this observable and thus limits the available precision of measurement. Quantum non-demolition measurements are designed to circumvent this limitation and have been demonstrated in detecting the photon flux of classical light beam. Quantum non-demolition measurement of a single photon is the ultimate goal because it is of great interest in fundamental physics and also a powerful tool for applications in quantum information processing. This chapter presents a brief introduction of the history and a review of the progress in quantum non-demolition measurement of light. In particular, a detailed description is presented for two works toward cavity-free schemes of quantum non-demolition measurement of single photons. Afterward, an outlook of the future in this direction is given.
According to the Heisenberg uncertainty principle, if we measure one variable describing a physical system, we inevitably introduce noise into some other variable describing the same system. In practice, the situation is worse than that: measuring one variable usually introduces random noise into the very quantity we are measuring. It is possible in principle to make measurements, known as quantum non-demolition (or QND) measurements, which do not have this latter effect. A QND measurement may approach the ideal quantum measurement commonly encountered in quantum mechanics textbooks. Philippe Grangier and his co-workers at the Université Paris-Sud, at Orsay in France, have recently attempted to measure the intensity of a beam of light in this way (Phys. Rev. Len. (1991) 66 1418). Their experiment has shown that it is indeed possible to make a measurement which at least partially preserves the quantum mechanical state of the detected beam.
An extensive debate on quantum non-demolition (QND) measurement, reviewed in Grangier et al (1998 Nature 396 537), finds that true QND measurements must have both non-classical state-preparation capability and non-classical information-damage tradeoff. Existing figures of merit for these non-classicality criteria require direct measurement of the signal variable and are thus difficult to apply to optically-probed material systems. Here we describe a method to demonstrate both criteria without need for to direct signal measurements. Using a covariance matrix formalism and a general noise model, we compute meter observables for QND measurement triples, which suffice to compute all QND figures of merit. The result will allow certified QND measurement of atomic spin ensembles using existing techniques.
According to quantum mechanics, there exists a class of observables for which is possible to confine the perturbation produced by a continuous measurement to the conjugate variable. Therefore, it is possible to devise experimental schemes that allow estimating the observed variable with arbitrary accuracy, or preparing it in a well-known state. Such schemes are referred to as quantum non-demolition measurements (QND). Among these observables there is the amplitude of the light field. Indeed, it is possible to exploit a movable mirror to implement a QND scheme [1]. Intensity fluctuations of an optical field impinging on it are not affected by the interaction. However, the movable mirror is excited by the associated radiation pressure. This, in turn, affects the phase of the field.