Cody C. Leary

Remote preparation of complex spatial states of single photons and verification by two-photon coincidence experiment

We propose and provide experimental evidence in support of a theory for the remote preparation of a complex spatial state of a single photon. An entangled two-photon source was obtained by spontaneous parametric down-conversion, and a double slit was placed in the path of the signal photon as a scattering object. The signal photon was detected after proper spatial filtering so that the idler photon was prepared in the corresponding single-photon state. By using a two-photon coincidence measurement, we obtained the Radon transform, at several longitudinal distances, of the single-photon Wigner distribution function modified by the double slit. The experimental results are consistent with the idler photon being in a pure state. An inverse Radon transformation can, in principle, be applied to the measured data to reconstruct the modified single-photon Wigner function, which is a complete representation of the amplitude and phase structure of the scattering object.

Stable mode sorting by two-dimensional parity of photonic transverse spatial states

We describe a mode sorter for two-dimensional parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. Both Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two output ports according to the two-dimensional parity of the mode in question. Our interferometer sorts HG(nm) input modes depending upon whether they have even or odd order n+m; it equivalently sorts LG(l)(p) modes depending upon whether they have an even or odd value of their orbital angular momentum l. It functions efficiently at the single-photon level, and therefore can be used to sort single-photon states. Due to the inherent phase stability of this type of interferometer as compared to those of the Mach-Zehnder type, it provides a promising tool for the manipulation and filtering of higher order transverse spatial modes for the purposes of quantum information processing. For example, several similar Sagnacs cascaded together may allow, for the first time, a stable measurement of the orbital angular momentum of a true single-photon state. Furthermore, as an alternative to well-known holographic techniques, one can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode filter, which can be used to produce spatial-mode entangled Bell states and heralded single photons in arbitrary first-order (n+m = 1) spatial states, covering the entire Poincar e sphere of first-order transverse modes.

Observation of Interaction of Spin and Intrinsic Orbital Angular Momentum of Light

The interaction of spin and intrinsic orbital angular momentum of light is observed, as evidenced by length-dependent rotations of both spatial patterns and optical polarization in a cylindrically symmetric isotropic optical fiber. Such rotations occur in a straight few-mode fiber when superpositions of two modes with parallel and antiparallel orientation of spin and intrinsic orbital angular momentum (IOAM=2ℏ) are excited, resulting from a degeneracy splitting of the propagation constants of the modes.

Spin and orbital rotation of electrons and photons via spin-orbit interaction

S interacts with the orbital angular momentum (OAM) ^ L associated with its own curvilinear motion. It is also known that when light propagates in a trans- parent medium with an inhomogeneous refractive index, an analogous eect can take place: its polarization and OAM can interact and alter the propagation character- istics of the light. Several instances of this have been predicted (cf. (1, 2, 3)), and a few experiments have been done (4, 5, 6). What has not yet been made clear is the extent to which a unied wave-picture description of this spin-orbit interaction (SOI) for both photons (elec- tromagneticelds) and electrons (matter waves) can be reached. In this work we study the dynamics of the SOI from within such a unied framework. Remarkably, wend that the SOI is quantitatively described by a single ex- pression applying to either an electron or a photon prop- agating in a straight, cylindrically symmetric waveguide geometry. This leads to the prediction of several novel rotational eects for both particle types, in which the particles spin and orbital degrees of freedom inuence one another as it propagates down the waveguide. These phenomena allow for the reversible transfer of entangle- ment between the SAM and OAM degrees of freedom of two-particle states. To provide deeper insight, we show that the common origin of these eects in electrons and photons is a universal geometric (Berry) phase associ- ated with the interplay between either particles spin and OAM. This implies that the SOI occurs for any particle with spin, and thereby exists independently of whether or not the particle has mass, charge, or magnetic moment. Previous authors have examined the connection be- tween the geometric phase and the SOI for both particle types (cf. (6, 7) and Refs. therein). However, the cylindri- cal geometry we treat here, which supports transversely stationary waves with well-dened OAM that propagate down a straight waveguide axis, contrasts with the ge-

Self-spin-controlled rotation of spatial states of a Dirac electron in a cylindrical potential via spin–orbit interaction

Solution of the Dirac equation predicts that when an electron with nonzero orbital angular momentum (OAM) propagates in a cylindrically symmetric potential, its spin and orbital degrees of freedom interact, causing the electrons phase velocity to depend on whether its spin angular momentum (SAM) and OAM vectors are oriented parallel or anti-parallel with respect to each other. This spin–orbit splitting of the electronic dispersion curves can result in a rotation of the electrons spatial state in a manner controlled by the electrons own spin z-component value. These effects persist at non-relativistic velocities. To clarify the physical origin of this effect, we compare solutions of the Dirac equation to perturbative predictions of the Schrodinger–Pauli equation with a spin–orbit term, using the standard Foldy–Wouthuysen Hamiltonian. This clearly shows that the origin of the effect is the familiar relativistic spin–orbit interaction.

Cluster State LOQC with Entangled Spatial Modes

We present a scheme for cluster state linear optical quantum computation using Hermite-Gauss (HG) transverse spatial modes. We describe HG fusion gate elements, an HG-entangled biphoton source, and multi-photon spatial cluster state characterization.

Polarization-based control of spin-orbit vector modes of light in biphoton interference.

We report the experimental generation of a class of spin-orbit vector modes of light via an asymmetric Mach-Zehnder interferometer, obtained from an input beam prepared in a product state of its spin and orbital degrees of freedom. These modes contain a spatially varying polarization structure which may be controllably propagated about the beam axis by varying the retardance between the vertical and horizontal polarization components of the light. Additionally, their transverse spatial intensity distributions may be continuously manipulated by tuning the input polarization parameters. In the case of an analogous biphoton input, we predict that this device will exhibit biphoton (Hong-Ou-Mandel) interference in conjunction with the aforementioned tunable mode transformations.

Coupling of spin and orbital degrees of freedom in tunable Hong-Ou-Mandel interference involving photons in hybrid spin-orbit modes

We investigate the connection between biphoton states involving photons in product modes of their spin and orbital degrees of freedom and those involving photons in hybrid spin-orbit modes, as mediated by Hong-Ou-Mandel interference (HOMI) in an asymmetric Mach-Zehnder interferometer. We predict that two input photons in balanced superposition states of both their spin and orbital degrees of freedom will exhibit HOMI while undergoing a simultaneous mode conversion from product spin-orbit input modes to hybrid output modes bearing orbital angular momentum. These hybrid outputs contain a spatially varying polarization structure which may be controllably rotated about the photonic beam axis by varying the relative phase between the vertical and horizontal components of each input photons polarization. Additionally, a type of coupling of the spin and orbital degrees of freedom is exhibited in this system: the transverse spatial profile of the output photons may be continuously manipulated by tuning the polarization parameters of the input photons, in such a way that the HOMI between the photons remains stable. An interesting corollary to this work is the possibility of demonstrating in a simple experimental system that HOMI may occur between distinguishable input modes.

Bimodal Hong-Ou-Mandel Interference in Symmetric and Asymmetric Optical Systems

We investigate Hong-Ou-Mandel interference in symmetric and asymmetric interferometers, with the input photons prepared in arbitrary first-order spatial modes. We find that Hong-Ou-Mandel interference may occur in conjunction with mode transformation, and between distinguishable inputs.

Photonic Spin-Orbit Interaction in Few-Mode Optical Fiber

We demonstrate interaction between spin and orbital angular momentum of light in a straight few-mode fiber, evidenced by rotation of output intensity patterns controlled by input spin handedness.