Spatial-state Stokes-operator squeezing and entanglement for optical beams

Abstract

The transverse spatial attributes of an optical beam can be decomposed into the position, momentum and orbital angular momentum observables. The position and momentum of a beam is directly related to the quadrature amplitudes, whilst the orbital angular momentum is related to the polarization and spin variables. In this paper, we study the quantum properties of these spatial variables, using a representation in the Stokes-operator basis. We propose a spatial detection scheme to measure all three spatial variables and consequently, propose a scheme for the generation of spatial Stokes operator squeezing and entanglement.

Quantum limited particle sensing in optical tweezers

“…The spatial homodyne scheme was also proven to perform at the Cramer-Rao bound [37], therefore extending the capabilities of the spatial homodyne scheme for the optimal measurement of any spatial parameter p (e.g. the measurement of the orbital angular momentum of light [40]). We now proceed to derive the photocurrent for the spatial homodyne detection scheme.…”

Experimental Generation of Continuous-Variable Hyperentanglement in an Optical Parametric Oscillator

“…The OAM of light is associated with the transverse spatial distribution of the optical beam, such as Laguerre-Gaussian (LG) modes [21]. A scheme for the generation of OAM CV entanglement has been proposed by Hsu et al [22], and CV entanglement between the two first-order LG modes and OAM squeezing on the orbital Poincare sphere has also been experimentally demonstrated with a spatially nondegenerate optical parametric oscillator (OPO) by Lassen et al [23].…”

“…The Stokes operators acting on a Poincaré sphere for the first-order OAM modes and SAM modes are denoted byÔ k [21,22] andŜ k [19,20] Ô 1 ,Ô 2 , andÔ 3 represent the differences of the photon number between the pairs of spatial modes HG 10 and HG 01 , HG 10ð45°Þ and HG 10ð135°Þ , and LG 1 0 and LG −1 0 , respectively.Ŝ 1 , S 2 , andŜ 3 represent the differences of the photon number between horizontally (H) and vertically (V) polarized modes, 45°and 135°linearly polarized modes, and right-circularly (R) and left-circularly (L) polarized modes, respectively.…”

“…Additionally, according to another stricter sufficient but not necessary criterion of entanglement for OAM [22] and SAM [20], there is OAM entanglement (IðÔ 2 ;Ô 3 Þ ¼ 0.84AE 0.06 < 1) but no SAM entanglement because our experimental setup does not include a bright coherent beam [20].…”

Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes

“…whereŜ i are the quantum Stokes operators corresponding to the classical Stokes parameters[22][23][24]. Moreover, (σ, ρ) = (1, 2), (1, 3), or (2, 3) are the three combinations of the Stokes operators and (DOF 1, DOF 2) = (pol, pol), (spa, spa), (pol, spa) and (spa, pol) being the possible combinations of the spatial (spa) or polarization (pol) Stokes measurements on the two orthogonally polarized Hermite-Gaussian basis modes, one of which is in subsystem a the other in subsystem b.…”