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arXiv:2308.13122 · Physical Review A

Protective measurements of photon polarization using a temporal pointer

Meng-Wei Chen, Owen Young, Maximilian Schlosshauer, M. Beck

Published Aug 24, 2023• 4 citations
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Abstract

We experimentally demonstrate protective measurements by weakly coupling the polarization of a single-photon-level field to a measurement pointer that corresponds to the arrival time of the photon. By using an optical loop, we implement a variable, controlled number (1--9) of protection and measurement stages. We demonstrate the measurement of expectation values of photon polarization by measuring arrival times while simultaneously protecting the polarization state. No knowledge of the initial photon state is required or available in our experiment, demonstrating that protective measurements provide a genuine information gain that cannot simply be reduced to a priori information about the protection procedure.

DOI
10.1103/physreva.108.022420

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We experimentally demonstrate protective measurements by weakly coupling the polarization of a single-photon-level field to a measurement pointer that corresponds to the arrival time of the photon. By using an optical loop, we implement a variable, controlled number (1--9) of protection and measurement stages. We demonstrate the measurement of expectation values of photon polarization by measuring arrival times while simultaneously protecting the polarization state. No knowledge of the initial photon state is required or available in our experiment, demonstrating that protective measurements provide a genuine information gain that cannot simply be reduced to a priori information about the protection procedure.
We have performed Zeno protective measurements of quantum polarization states by coupling the polarization to a temporal pointer (arrival time) in a birefringent optical fiber. It is necessary to actively stabilize the polarization, and we do this by using the signal photon counts themselves as the error signal in a feedback loop. We compare these measurements to a stabilization scheme using a classical reference beam as the error signal. The method using photon counts has higher signal levels and significantly reduced background. These improvements allow us to increase the number of Zeno stages in our measurements from 9 to 13, with a corresponding decrease in the measurement uncertainty.
This paper presents a proof-of-principle scheme for the protective measurement of a single photon. In this scheme, the photon is looped arbitrarily many times through an optical stage that implements a weak measurement of a polarization observable followed by a strong measurement protecting the state. The ability of this scheme to realize a large number of such interaction-protection steps means that the uncertainty in the measurement result can be drastically reduced while maintaining a sufficient probability for the photon to survive the measurement.
Weak measurements are used to amplify small signals, to address foundational questions, and to characterise quantum states without tomography. In direct state reconstruction each amplitude of the state vector is proportional to a single complex weak value, which for a temporal pointer is read from the mean arrival time and the mean frequency of the postselected pulse. Such an experiment requires three quantities to be fixed, the coupling, the angular resolution demanded of the reconstruction, and the set of states over which the method remains usable, and these are commonly set by the available apparatus rather than derived. We derive all three for a Gaussian temporal pointer and an arbitrary postselection state. The states that cannot be reconstructed form a spherical cap centred on the state orthogonal to the postselection, whose geodesic half-angle follows from the largest of three independent thresholds and involves no adjustable parameter. Two states are distinguishable only if they differ by more than a minimal step fixed by the coupling, by the number of incident photons and by the sensitivity of the weak value along the path followed. For an inversion at first order in the coupling the systematic and statistical errors are opposed and fix an optimal coupling that varies as the inverse sixth root of the number of incident photons, whereas an exact inversion at finite coupling removes the systematic error, the remaining bound being one on the two-centroid readout rather than on the inversion, since below an amplitude equal to a quarter of the coupling two states give the same pair of centroids while their profiles differ. These results allow a direct reconstruction experiment to be dimensioned before the apparatus is assembled.
Summary form only given. Measurements are the very basis of Physics, especially in Quantum Mechanics, where they assume even a more fundamental role because of wave function collapse after a “strong” (projective) measurement. Furthermore, measuring a quantum-mechanical observable completely erases the information on its conjugate one (e.g. measurement of position erases information on momentum, and vice-versa). Nevertheless, in Quantum Mechanics other kinds of measurement are possible. For example, wave function collapse can be overcome through Weak Measurements, i.e. measurements performed with an interaction sufficiently weak not to collapse the original state, featuring several interesting properties. An example of these are weak values [1-3], realised for the first time in [4-6], that have been used for addressing fundamental questions [7-12] as Contextuality and are also a tool for Quantum Metrology [13-19]. One of the most intriguing properties of Weak Measurements is that, since they are not affected by wave function collapse, they can allow gathering simultaneous information on non-commuting observables [20], impossible with the standard (projective) measurement protocols. A second example is offered by Protective Measurements [21], a new technique able to extract information on the expectation value of an observable even measuring a single particle. In this talk, after a general introduction to WMs, we present the first realisation of sequential weak value measurements [22], i.e. a joint measurement of the weak value of (incompatible) polarizations on a single photon. Then, we present an experiment addressed to explore the connection between anomalous weak values and Contextuality [23], showing a clear violation of the inequality proposed in [12] while satisfying all the additional theoretical requests, unequivocally demonstrating the contextual nature of weak values. Finally, we present and discuss the first implementation of Protective Measurements, showing unprecedented measurement capability and demonstrating how the expectation value of an observable can be obtained with a single measurement on a single particle.