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arXiv:1612.04920

How the Result of Counting One Photon Can Turn Out to Be a Value of 8

Matin Hallaji, Amir Feizpour, Greg Dmochowski, Josiah Sinclair, Aephraim M. Steinberg

Published Dec 15, 2016• 1 citation
arXivHTMLPDF

Abstract

In 1988, Aharonov, Albert, and Vaidman introduced a new paradigm of quantum measurement in a paper which had the unwieldy but provocative title "How the result of a measurement of a component of the spin of a spin-1=2 particle can turn out to be 100." This paradigm, so-called "weak measurement," has since been the subject of widespread theoretical and experimental attention, both for the perspective it offers on quantum reality and for possible applications to precision measurement. Yet almost all of the weak-measurement experiments carried out so far could be alternatively understood in terms of the classical (electro-magnetic wave) theory of optics. Here we present a truly quantum version, the first in which a measurement apparatus deterministically entangles two distinct optical beams, enabling us to experimentally ask a question directly analogous to that of the original proposal: "In a two-arm interferometer containing one photon in total, can the result of a measurement of the photon number in one arm turn out to be greater than 1?" Specifically, we show that a single photon, when properly post-selected, can have an effect equal to that of eight photons: that is, in a system where a single photon has been calibrated to write a nonlinear phase shift of ϕ_0 on a probe beam, we measure phase shifts as large as 8ϕ_0 for appropriately post-selected single photons. This is the first deterministic weak-value experiment in optics which defies classical explanation, and constitutes a realization of our proposal for weak-value amplification (WVA) of the small optical nonlinearity at the single-photon level. It opens up a new regime for the study of entanglement of optical beams, as well as further investigations of the power of WVA for the measurement of small quantities.

DOI
10.48550/arxiv.1612.04920

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In 1988, Aharonov, Albert, and Vaidman introduced a new paradigm of quantum measurement in a paper which had the unwieldy but provocative title "How the result of a measurement of a component of the spin of a spin-1=2 particle can turn out to be 100." This paradigm, so-called "weak measurement," has since been the subject of widespread theoretical and experimental attention, both for the perspective it offers on quantum reality and for possible applications to precision measurement. Yet almost all of the weak-measurement experiments carried out so far could be alternatively understood in terms of the classical (electro-magnetic wave) theory of optics. Here we present a truly quantum version, the first in which a measurement apparatus deterministically entangles two distinct optical beams, enabling us to experimentally ask a question directly analogous to that of the original proposal: "In a two-arm interferometer containing one photon in total, can the result of a measurement of the photon number in one arm turn out to be greater than 1?" Specifically, we show that a single photon, when properly post-selected, can have an effect equal to that of eight photons: that is, in a system where a single photon has been calibrated to write a nonlinear phase shift of ϕ_0 on a probe beam, we measure phase shifts as large as 8ϕ_0 for appropriately post-selected single photons. This is the first deterministic weak-value experiment in optics which defies classical explanation, and constitutes a realization of our proposal for weak-value amplification (WVA) of the small optical nonlinearity at the single-photon level. It opens up a new regime for the study of entanglement of optical beams, as well as further investigations of the power of WVA for the measurement of small quantities.
Weak value amplification (WVA) is a measurement technique in which the effect of a pre- and post-selected system on a weakly interacting probe is magnified. In this thesis, I present the first experimental observation of WVA of a single photon. We observed that a signal photon - sent through a polarization interferometer and post-selected by photodetection in the almost-dark port - can act like eight photons. The effect of this single photon is measured as a nonlinear phase shift on a separate laser beam. The interaction between the two is mediated by a sample of laser- cooled 85Rb atoms. Electromagnetically induced transparency (EIT) is used to enhance the nonlinearity and overcome resonant absorption. I believe this work to be the first demonstration of WVA where a deterministic interaction is used to entangle two distinct optical systems. In WVA, the amplification is contingent on discarding a large portion of the original data set. While amplification increases measurement sensitivity, discarding data worsens it. Questioning whether these competing effects conspire to improve or diminish measurement accuracy has resulted recently in controversy. I address this question by calculating the maximum amount of information achievable with the WVA technique. By comparing this information to that achievable by the standard technique, where no post-selection is employed, I show that the WVA technique can be advantageous under a certain class of noise models. Finally, I propose a way to optimally apply the WVA technique.
Abstract Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror’s position displacement of one photon. In the weak value amplification (WVA) regime, the weak value of one photon can lie outside the eigenvalue spectrum, proportional to the difference of the mirror’s position displacement between the successful and failed postselection and its successful postselection probability is dependent of the mean photon number of the coherent light and improved by adjusting it accordingly. Outside the WVA regime, the amplification limit can reach the level of the vacuum fluctuations, and when the mean photon number and the optomechanical coupling parameter are selected appropriately, its successful postselection probability becomes higher, which is beneficial to observe the maximum amplification value under the current experimental conditions. This result breaks the constraint that it is difficult to detect outside the WVA regime. This opens up a new regime for the study of a single photon nonlinearity in optomechanical system.
Abstract Is it possible that a measurement of a spin component of a spin-1/2 particle yields the value 100? In 1988 Aharonov, Albert and Vaidman argued that upon pre- and postselection of particular spin states, weakening the coupling of a standard measurement procedure ensures this paradoxical result1. This theoretical prediction, called weak value, was realised in numerous experiments2–9, but its meaning remains very controversial10–19, since its “anomalous” nature, i.e., the possibility to exceed the eigenvalue spectrum, as well as its “quantumness” are debated20–22. We address these questions by presenting the first experiment measuring anomalous weak values with just a single click, without the need for statistical averaging. The measurement uncertainty is significantly smaller than the gap between the measured weak value and the nearest eigenvalue. Beyond clarifying the meaning of weak values, demonstrating their non-statistical, single-particle nature, this result represents a breakthrough in understanding the foundations of quantum measurement, showing unprecedented measurement capability for further applications of weak values to quantum photonics.
Abstract Even though weak measurements and weak value amplification (WVA) are founded on the principles of quantum mechanics and quantum measurements, these have found widespread applications in optics due to their inherent origin in wave interference. Besides their use in addressing foundational questions of quantum mechanics or for resolving quantum paradoxes, weak measurements and WVA have thus been used for numerous metrological applications, e.g., quantification of small optical beam displacement, tiny angular rotation, determination of extremely small phase shifts, spectral shifts, unraveling weak fundamental optical effects, improved optical imaging, amplifying weak signal and extracting small physical parameters and so forth. In this review, after providing the mathematical foundation of weak measurement and WVA, some of the metrological applications of weak measurements in the classical optics domain are briefly summarized, and the controversies and debates on the potential advantages of WVA in the estimation and detection of weak signal are discussed, and the interferometric philosophy of WVA is elucidated. The experimental weak measurement and WVA schemes in the domain of quantum optics are also discussed and highlighted the new perspectives and emerging trends of weak measurements in both the classical and quantum optics domain and their prospects in the development of next‐generation ultra‐sensitive optical devices.
We show that weak measurement can be used to "amplify" optical nonlinearities at the single-photon level, such that the effect of one properly postselected photon on a classical beam may be as large as that of many unpostselected photons. We find that "weak-value amplification" offers a marked improvement in the signal-to-noise ratio in the presence of technical noise with long correlation times. Unlike previous weak-measurement experiments, our proposed scheme has no classical equivalent.
Quantum weak measurements became extremely popular in classical optics to amplify small optical signals for fundamental interests and potential applications. Later, a more general extension, joint weak measurement has been proposed to extract weak value from a joint quantum measurement. However, the detection of joint weak value in the realm of classical optics remains less explored. Here, using the polarization-dependent longitudinal and transverse optical beam shift as a platform, we experimentally realize the quantum joint weak measurement in a classical optical setting. Polarization states are cleverly pre and post-selected, and different single and joint canonical position-momentum observables of the beam are experimentally extracted and subsequently analyzed for successful detection of complex joint weak value. We envision that this work will find usefulness for gaining fundamental insights on quantum measurements and to tackle analogous problems in optics.