TY - JOUR

T1 - Fate of the Landau-Yang theorem for twisted photons

AU - Ivanov, Igor P.

AU - Serbo, Valeriy G.

AU - Zhang, Pengming

PY - 2019/10/16

Y1 - 2019/10/16

N2 - The Landau-Yang theorem is sometimes formulated as a selection rule forbidding two real (that is, non-virtual) photons with zero total momentum to be in the state of the total angular momentum J = 1. In this paper, we discuss whether the theorem itself and this particular formulation can be extended to a pair of two twisted photons, which carry orbital angular momentum with respect to their propagation direction. We point out possible sources of confusion, which may arise both from the unusual features of twisted photons and from the fact that usual proofs of the Landau-Yang theorem operate in the center of motion reference frame, which, strictly speaking, exists only for plane waves. We show with an explicit calculation that a pair of twisted photons does have a non-zero overlap with the J = 1 state. What is actually forbidden is production of a spin-1 particle by such a photon pair, and in this formulation the Landau-Yang theorem is rock-solid. Although both the twisted photon pair and the spin-1 particle can exist in the J = 1 state, these two systems just cannot be coupled in a gauge-invariant and Lorentz invariant manner respecting Bose symmetry.

AB - The Landau-Yang theorem is sometimes formulated as a selection rule forbidding two real (that is, non-virtual) photons with zero total momentum to be in the state of the total angular momentum J = 1. In this paper, we discuss whether the theorem itself and this particular formulation can be extended to a pair of two twisted photons, which carry orbital angular momentum with respect to their propagation direction. We point out possible sources of confusion, which may arise both from the unusual features of twisted photons and from the fact that usual proofs of the Landau-Yang theorem operate in the center of motion reference frame, which, strictly speaking, exists only for plane waves. We show with an explicit calculation that a pair of twisted photons does have a non-zero overlap with the J = 1 state. What is actually forbidden is production of a spin-1 particle by such a photon pair, and in this formulation the Landau-Yang theorem is rock-solid. Although both the twisted photon pair and the spin-1 particle can exist in the J = 1 state, these two systems just cannot be coupled in a gauge-invariant and Lorentz invariant manner respecting Bose symmetry.

KW - Landau-Yang theorem

KW - twisted photons

KW - optical angular momentum

KW - ORBITAL ANGULAR-MOMENTUM

KW - BEAMS

UR - http://www.scopus.com/inward/record.url?scp=85080936302&partnerID=8YFLogxK

U2 - 10.1088/2040-8986/ab491a

DO - 10.1088/2040-8986/ab491a

M3 - Article

VL - 21

JO - Journal of optics

JF - Journal of optics

SN - 2040-8978

IS - 11

M1 - 114001

ER -