
A quantum particle prepared as a superposition of positive momentum states can have a negative probability current during local instances of time [1]. The phenomenon of probability flow in the ‘wrong’ direction is referred to as ‘backflow’ and is a manifestation of wave interference. Superoscillations refer to situations where the local oscillation of a superposition is faster than its fastest Fourier component [2]. M.V. Berry’s work [3] highlighted the correspondence between backflow in quantum mechanics and superoscillations in waves. This correspondence has been used to demonstrate backflow in transverse linear momentum for optical waves [4,5]. In the present work, we examine the interference of classical light carrying only negative orbital angular momentum (OAM) and observe in the dark fringes of such an interference pattern, positive local OAM [6]. We refer to this as azimuthal backflow. Our finding may be useful where strong phase gradients over small spatial extents are needed, for instance, to enhance chiral lightmatter interactions [7], or for detecting photons in regions of low light intensity [8]. From the fundamental point of view, an interesting open question is to which extent a study of the transverse twodimensional spatial degree of freedom of a single photon can emulate the more robust twodimensional quantum backflow analyzed in [9]. The current work is a step towards observing quantum opticalbackflow [10].
References
[1] A. J. Bracken and G. F. Melloy, J. Phys. A: Math. Gen. 27, 2197 (1994).
[2] M. V. Berry and S. Popescu, J. Phys. A: Math. Gen. 39, 6965 (2006).
[3] M. V. Berry, J. Phys. A: Math. Theor. 43, 415302 (2010).
[4] Y. Eliezer, T. Zacharias, and A. Bahabad, Optica 7, 72 (2020).
[5] A. Daniel, B. Ghosh, B. Gorzkowski, and R. Lapkiewicz, New. J. Phys. 24, 123011 (2022).
[6] B. Ghosh, A. Daniel, B. Gorzkowski, and R. Lapkiewicz, arXiv:2304.13124 (2023).
[7] Y. Tang and A. E. Cohen, Science 332, 333 (2011).
[8] V. Klimov, D. Bloch, M. Ducloy, and J. R. R. Leite, Opt. Express 17, 9718 (2009).
[9] M. Barbier, A. Goussev and S. C. L. Srivastava, Phys. Rev. A 107, 032204 (2023).
[10] A realization of the experiment with single photons is underway.