Observation of the Spin Hall Effect of Light via Weak Measurements

Abstract

We have detected a spin-dependent displacement perpendicular to the refractive index gradient for photons passing through an air-glass interface. The effect is the photonic version of the spin Hall effect in electronic systems, indicating the universality of the effect for particles of different nature. Treating the effect as a weak measurement of the spin projection of the photons, we used a preselection and postselection technique on the spin state to enhance the original displacement by nearly four orders of magnitude, attaining sensitivity to displacements of approximately 1 angstrom. The spin Hall effect can be used for manipulating photonic angular momentum states, and the measurement technique holds promise for precision metrology.

Heisenberg scaling with weak measurement: a quantum state discrimination point of view

“…Given this insight, could this scheme could be implemented in the optical experiments demonstrating weak value amplification by simply monitoring the post-selection probability? A von Neumann-type interaction has been shown using both polarization [18] or which-path [19] degrees of freedom. The answer is that those experiments use a single photon as both the meter (transverse deflection) and system (polarization or which-path), so the number of meter photons per system projection is 1.…”

“…We can explore this effect from another point of view by calculating the quantum Fisher information F in the state (18). This sets the minimum uncertainty on the parameter g min ≥ 1/ √ F, the quantum Cramér-Rao bound.…”

What Is a Quantum-Mechanical “Weak Value” the Value of?

“…These include determining (even if only statistically) the trajectories in a double slit experiment without destroying the interference pattern [5], and directly measuring the wave function [6]. The use of the technique for amplification purposes has been spectacular [7][8][9]. Weak measurements have also been employed to illuminate the fundamental difference between classical and quantum mechanics exhibited by violation of Leggett-Garg inequalities [3,[10][11][12][13][14], also called "Bell inequalities in time".…”

“…Note that I do not here question the weak value as a measureable entity pertaining to the system under study, nor the many ingenious ways experimentalist have exploited the weak measurement + post-selection idea ( [5][6][7][8][9][11][12][13][14]; see also [3] for a brief review). What I do question is whether a weak value can be given an 'ordinary' meaning.…”

Weak Values and Quantum Nonlocality

“…Weak measurements were shown to be very useful in analyzing a variety of problems [11,12,13,14]. We will focus henceforth on entanglement and nonlocality.…”