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arXiv:2501.09952 · Optics Letters

Observation of single-photon azimuthal backflow with weak measurement

Zhen-Fei Zhang, Peng-Fei Huang, Shanchuan Dong, Yan-Xin Rong, Jin‐Shi Xu, Yongjian Gu, Ya Xiao

Published Dec 2, 2024• 9 citations
arXivHTMLPDF

Abstract

Quantum backflow (QB), a counterintuitive interference phenomenon where particles with positive momentum can propagate backward, is important in applications involving light-matter interactions. To date, experimental demonstrations of backflow have been restricted to classical optical systems using techniques such as slit scanning or Shack-Hartmann wavefront sensing, which suffer from low spatial resolution due to the inherent limitations in slit width and lenslet array density. Here, we report an observation of azimuthal backflow (AB) both theoretically and experimentally by employing the weak measurement technique, which enables the precise extraction of photon momentum at each pixel. Our results show that a heralded single photon, prepared in specific superposition states with solely negative orbital angular momentum (OAM), can exhibit positive OAM. The effects of mode ratio, propagation distance, and OAM index on the azimuthal backflow are systematically investigated. This work provides new techniques for observing and manipulating backflow in quantum systems.

DOI
10.1364/ol.540905

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Quantum backflow (QB), a counterintuitive interference phenomenon where particles with positive momentum can propagate backward, is important in applications involving light-matter interactions. To date, experimental demonstrations of backflow have been restricted to classical optical systems using techniques such as slit scanning or Shack-Hartmann wavefront sensing, which suffer from low spatial resolution due to the inherent limitations in slit width and lenslet array density. Here, we report an observation of azimuthal backflow (AB) both theoretically and experimentally by employing the weak measurement technique, which enables the precise extraction of photon momentum at each pixel. Our results show that a heralded single photon, prepared in specific superposition states with solely negative orbital angular momentum (OAM), can exhibit positive OAM. The effects of mode ratio, propagation distance, and OAM index on the azimuthal backflow are systematically investigated. This work provides new techniques for observing and manipulating backflow in quantum systems.
Quantum backflow is a counterintuitive phenomenon in which a forward-propagating quantum particle propagates locally backwards. The actual counter-propagation property associated with this delicate interference phenomenon has not been observed to date in any field of physics, to the best of our knowledge. Here, we report the observation of an analog optical effect, namely, transverse optical backflow where a beam of light propagating to a specific transverse direction is measured locally to propagate in the opposite direction. This observation is relevant to any physical system supporting coherent waves.
Optical orbital angular momentum (OAM) is a special property of photons and has evoked research onto the light–matter interaction in both classical and quantum regimes. In classical optics, OAM is related to an optical vortex with a helical phase structure. In quantum optics, photons with a twisted or helical phase structure will carry a quantized OAM. To our knowledge, however, so far, no experiment has demonstrated the fundamental property of the OAM at the single-photon level. In this Letter, we have demonstrated the average photon trajectories of twisted photons in a double-slit interference. We have experimentally captured the double-slit interference process of twisted photons by a time-gated intensified charge-coupled device camera, which is trigged by a heralded detection. Our work provides new perspectives for understanding the micro-behaviors of twisted particles and enables new applications in imaging and sensing.
Recently, Kocsis et al (2011 Science 332 1170) reported the observation of 'average trajectories of single photons' in a two-slit interference experiment. This was possible by using the quantum weak-measurement method, which implies averaging over many events, i.e. in fact, a multi-photon limit of classical linear optics. We give a classical-optics interpretation of this experiment and other related problems. It appears that weak measurements of the local momentum of photons made by Kocsis et al represent measurements of the Poynting vector in an optical field. We consider both the real and imaginary parts of the local momentum and show that their measurements have been realized in classical optics using small-probe particles. We also examine the appearance of 'anomalous' values of the local momentum: either negative (backflow) or exceeding the wavenumber (superluminal propagation). These features appear to be closely related to vortices and evanescent waves. Finally, we revisit a number of older works and find examples of photon trajectories and anomalous-momentum measurements in various optical experiments.
We present an introduction to the backflow effect in quantum mechanics – the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. We show that the effect is present even for simple states consisting of superpositions of gaussian wave packets, although the size of the effect is small. Inspired by the numerical results of Penz et al, we present a wave function whose current at any time may be computed analytically and which has periods of significant backflow, with a backwards flux equal to about 70 percent of the maximum possible backflow, a dimensionless number c bm ≈ 0.04, discovered by Bracken and Melloy. This number has the unusual property of being independent of ℏ (and also of all other parameters of the model), despite corresponding to a quantum-mechanical effect, and we shed some light on this surprising property by considering the classical limit of backflow. We conclude by discussing a specific measurement model in which backflow may be identified in certain measurable probabilities.
Bell states are the most fundamental resource in realizing quantum information tasks and have a very unique position in quantum mechanics. Utilizing orbital angular momentum (OAM) to encode single-photon Bell states enables the realization of high-dimensional Hilbert space, which is crucial for the field of quantum information. In this paper, we design a single-photon OAM Bell-state evolution device based on the Sagnac interferometer, which can make one-to-one correspondence between the input Bell states and the output states. Moreover, we also develop a single-photon single-pixel imaging (SPI) technique, which improves spatial resolution and decreases acquisition time in the meantime, to capture interference images of output states. The results show that single-photon OAM Bell states can be fully recognized by comparing the differences of interference images. We innovatively utilize the SPI technique for single-photon OAM Bell-state recognition. This indicates that the SPI technique effectively promotes the study of quantum information based on OAM, while the quantum information based on OAM provides a clear application scenario for the SPI technique.
Weak measurements are a unique tool for accessing information about weakly interacting quantum systems with minimal back action. Joint weak measurements of single-particle operators with pointer states characterized by a two-dimensional Gaussian distribution can provide, in turn, key information about quantum correlations that can be relevant for quantum information applications. Here we demonstrate that by employing two-dimensional pointer states endowed with orbital angular momentum (OAM), it is possible to extract weak values of the higher order moments of single-particle operators, an inaccessible quantity with Gaussian pointer states only. We provide a specific example that illustrates the advantages of our method both in terms of signal enhancement and information retrieval.