The premise that multipolar decay should produce photons uniquely imprinted with a measurably corresponding angular momentum is shown in general to be untrue. To assume a one-to-one correlation between the transition multipoles involved in source decay and detector excitation is to impose a generally unsupportable one-to-one correlation between the multipolar form of emission transition and a multipolar character for the detected field. It is specifically proven impossible to determine without ambiguity, by use of any conventional detector, and for any photon emitted through the nondipolar decay of an atomic excited state, a unique multipolar character for the transition associated with its generation. Consistent with the angular quantum uncertainty principle, removal of a detector from the immediate vicinity of the source produces a decreasing angular uncertainty in photon propagation direction, reflected in an increasing range of integer values for the measured angular momentum. In such a context it follows that when the decay of an electronic excited state occurs by an electric quadrupolar transition, for example, any assumption that the radiation so produced is conveyed in the form of ``quadrupole photons'' is experimentally unverifiable. The results of the general proof based on irreducible tensor analysis invite experimental verification, and they signify certain limitations on quantum optical data transmission.The premise that multipolar decay should produce photons uniquely imprinted with a measurably corresponding angular momentum is shown in general to be untrue. To assume a one-to-one correlation between the transition multipoles involved in source decay and detector excitation is to impose a generally unsupportable one-to-one correlation between the multipolar form of emission transition and a multipolar character for the detected field. It is specifically proven impossible to determine without ambiguity, by use of any conventional detector, and for any photon emitted through the nondipolar decay of an atomic excited state, a unique multipolar character for the transition associated with its generation. Consistent with the angular quantum uncertainty principle, removal of a detector from the immediate vicinity of the source produces a decreasing angular uncertainty in photon propagation direction, reflected in an increasing range of integer values for the measured angular momentum. In such a context it follows that when the decay of an electronic excited state occurs by an electric quadrupolar transition, for example, any assumption that the radiation so produced is conveyed in the form of ``quadrupole photons'' is experimentally unverifiable. The results of the general proof based on irreducible tensor analysis invite experimental verification, and they signify certain limitations on quantum optical data transmission.

Physical Review AMar 15, 201036 citations

Single-Photon Transitions of Atomic Particles

В. П. Крайнов, Boris Michailovich Smirnov

Springer series on atomic, optical, and plasma physicsJan 1, 20190 citations

The conservation of orbital angular momentum and the two-photon detection amplitude in spontaneous parametric down-conversion

Sheng Feng, Chao-Hsiang Chen, Geraldo A. Barbosa +1 more

We study the two-photon detection amplitude of the down-converted beams in spontaneous parametric down-conversion when the physical variable of orbital angular momentum is involved, taking into account both conservation and non-conservation of angular momentum. Agreeing with experimental observations, our theoretical calculation shows that spatial structure of the two-photon detection amplitude of the down-converted beams carries important information about conservation or non-conservation of orbital angular momentum in spontaneous parametric down-conversion.We study the two-photon detection amplitude of the down-converted beams in spontaneous parametric down-conversion when the physical variable of orbital angular momentum is involved, taking into account both conservation and non-conservation of angular momentum. Agreeing with experimental observations, our theoretical calculation shows that spatial structure of the two-photon detection amplitude of the down-converted beams carries important information about conservation or non-conservation of orbital angular momentum in spontaneous parametric down-conversion.

arXiv:quant-ph/0703187Mar 20, 20070 citations

Transfer of angular momentum of guided light to an atom with an electric quadrupole transition near an optical nanofiber

Fam Le Kien, Síle Nic Chormaic, Thomas Busch

We study the transfer of angular momentum of guided photons to a two-level atom with an electric quadrupole transition near an optical nanofiber. We show that the generation of the axial orbital torque of the driving guided field on the atom is governed by the internal-state selection rules for the quadrupole transition and by the angular momentum conservation law with the photon angular momentum given in the Minkowski formulation. We find that the torque depends on the photon angular momentum, the change in the angular momentum of the atomic internal state, and the quadrupole-transition Rabi frequency. We calculate numerically the torques for the quadrupole transitions between the sublevel $M=2$ of the hyperfine-structure level $5{S}_{1/2}F=2$ and the sublevels ${M}^{\ensuremath{'}}=0$, 1, 2, 3, and 4 of the hyperfine-structure level $4{D}_{5/2}{F}^{\ensuremath{'}}=4$ of a $^{87}\mathrm{Rb}$ atom. We show that the absolute value of the torque for the higher-order mode ${\mathrm{HE}}_{21}$ is larger than that of the torque for the fundamental mode ${\mathrm{HE}}_{11}$ except for the case ${M}^{\ensuremath{'}}\ensuremath{-}M=2$, where the torque for the mode ${\mathrm{HE}}_{21}$ is vanishing.We study the transfer of angular momentum of guided photons to a two-level atom with an electric quadrupole transition near an optical nanofiber. We show that the generation of the axial orbital torque of the driving guided field on the atom is governed by the internal-state selection rules for the quadrupole transition and by the angular momentum conservation law with the photon angular momentum given in the Minkowski formulation. We find that the torque depends on the photon angular momentum, the change in the angular momentum of the atomic internal state, and the quadrupole-transition Rabi frequency. We calculate numerically the torques for the quadrupole transitions between the sublevel $M=2$ of the hyperfine-structure level $5{S}_{1/2}F=2$ and the sublevels ${M}^{\ensuremath{'}}=0$, 1, 2, 3, and 4 of the hyperfine-structure level $4{D}_{5/2}{F}^{\ensuremath{'}}=4$ of a $^{87}\mathrm{Rb}$ atom. We show that the absolute value of the torque for the higher-order mode ${\mathrm{HE}}_{21}$ is larger than that of the torque for the fundamental mode ${\mathrm{HE}}_{11}$ except for the case ${M}^{\ensuremath{'}}\ensuremath{-}M=2$, where the torque for the mode ${\mathrm{HE}}_{21}$ is vanishing.

arXiv:2205.12440Physical Review AJul 18, 202210 citations

Measuring the orbital angular momentum of a single photon

Jonathan Leach, Miles J. Padgett, Stephen Mark Barnett +2 more

Institute of Physics eBooksNov 26, 200413 citations

M=2

of the hyperfine-structure level

5{S}_{1/2}F=2

and the sublevels ${M}^{\ensuremath{'}}=0$, 1, 2, 3, and 4 of the hyperfine-structure level $4{D}_{5/2}{F}^{\ensuremath{'}}=4$ of a

^{87}\mathrm{Rb}

atom. We show that the absolute value of the torque for the higher-order mode

{\mathrm{HE}}_{21}

is larger than that of the torque for the fundamental mode

{\mathrm{HE}}_{11}

except for the case ${M}^{\ensuremath{'}}\ensuremath{-}M=2$, where the torque for the mode

{\mathrm{HE}}_{21}

is vanishing.