Conservation Of Orbital Angular Momentum Research Articles

Managing orbital angular momentum in second-harmonic generation

We propose a convenient approach for managing orbital angular momentum (OAM) of second-harmonic photons generated by a quadratic nonlinear interaction under noncolinear type-I phase matching condition. Since the OAMs of two fundamental photons can be flexibly controlled by using computer-generated holograms, we were able to realize arbitrary combination of both OAMs and experimentally confirm the OAM conservation selection rule ${\ensuremath{\ell}}_{2\ensuremath{\omega}}={\ensuremath{\ell}}_{\ensuremath{\omega}}^{\ensuremath{'}}+{\ensuremath{\ell}}_{\ensuremath{\omega}}^{\ensuremath{'}\ensuremath{'}}$ in general cases. In particular, our approach could be used to generate the second-harmonic photon states with fractional and odd-order OAMs.

Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam

We report orbital angular momentum (OAM) and angle correlations between signal and idler photons observed when the nonlinear crystal used in spontaneous parametric down-conversion is illuminated by a non-fundamental Gaussian pump beam. We introduce a π-phase step to the transverse profile of the pump, before it impinges on the crystal to create a phase-flipped Gaussian mode, which is a close approximation to an HG10 Hermite–Gaussian-like beam. The correlations in OAM and angular position are then measured holographically using two separate spatial light modulators in the signal and idler arms. We show the transfer of the OAM spectrum of the pump to the down-converted fields, manifested as a redistribution in the OAM correlations consistent with OAM conservation. This corresponds to a modulation of the angular position correlations consistent with the Fourier relationship between the OAM and angle.

Conservation and transfer of orbital angular momentum of light in optically induced photonic lattices

Using analytical and numerical methods, we elucidate the conservation and transfer of orbital angular momentum of light beams propagating in fully periodic and radially periodic photonic lattices, induced in photorefractive crystals. We consider paraxial beams propagating in both fixed and interacting lattices, in both copropagating and counterpropagating geometries, in photorefractive media with saturable nonlinearity. We also discuss the influence of beam intensity and the finite lattice size on the angular momentum transfer in such photonic lattices.

SUPER-ECCENTRIC MIGRATING JUPITERS

An important class of formation theories for hot Jupiters involves the excitation of extreme orbital eccentricity (e=0.99 or even larger) followed by tidal dissipation at periastron passage that eventually circularizes the planetary orbit at a period less than 10 days. In a steady state, this mechanism requires the existence of a significant population of super-eccentric (e>0.9) migrating Jupiters with long orbital periods and periastron distances of only a few stellar radii. For these super-eccentric planets, the periastron is fixed due to conservation of orbital angular momentum and the energy dissipated per orbit is constant, implying that the rate of change in semi-major axis a is \dot a \propto a^0.5 and consequently the number distribution satisfies dN/dlog a\propto a^0.5. If this formation process produces most hot Jupiters, Kepler should detect several super-eccentric migrating progenitors of hot Jupiters, allowing for a test of high-eccentricity migration scenarios.

The effect of scattering on single photon transmission of optical angular momentum

Schemes for the communication and registration of optical angular momentumdepend on the fidelity of transmission between optical system components. Itis known that electron spin can be faithfully relayed between exciton states inquantum dots; it has also been shown by several theoretical and experimental studiesthat the use of beams conveying orbital angular momentum can significantlyextend the density and efficiency of such information transfer. However, it remainsunclear to what extent the operation of such a concept at the single photon level ispracticable—especially where this involves optical propagation through a material system,in which forward scattering events can intervene. The possibility of transmitting anddecoding angular momentum over nanoscale distances itself raises other importantissues associated with near-field interrogation. This paper provides a framework toaddress these and related issues. A quantum electrodynamical representation isconstructed and used to pursue the consequences of individual photons, froma Laguerre–Gaussian beam, undergoing single and multiple scattering eventsin the course of propagation. In this context, issues concerning orbital angularmomentum conservation, and its possible compromise, are tackled by identifying therelevant components of the electromagnetic scattering and coupling tensors, using anirreducible Cartesian basis. The physical interpretation broadly supports the fidelity ofquantum information transmission, but it also identifies potential limitations ofprinciple.

Effect of Interactions on Vortices in a Nonequilibrium Polariton Condensate

We demonstrate the creation of vortices in a macroscopically occupied polariton state formed in a semiconductor microcavity. A weak external laser beam carrying orbital angular momentum (OAM) is used to imprint a vortex on the condensate arising from the polariton optical parametric oscillator (OPO). The vortex core radius is found to decrease with increasing pump power, and is determined by polariton-polariton interactions. As a result of OAM conservation in the parametric scattering process, the excitation consists of a vortex in the signal and a corresponding antivortex in the idler of the OPO. The experimental results are in good agreement with a theoretical model of a vortex in the polariton OPO.

Comment on “Spatial Symmetry and Conservation of Orbital Angular Momentum in Spontaneous Parametric Down-Conversion”

A Comment on the Letter by Sheng Feng and Prem Kumar, [Phys. Rev. Lett. 101, 163602 (2008)]. The authors of the Letter offer a Reply.

Spatial Symmetry and Conservation of Orbital Angular Momentum in Spontaneous Parametric Down-Conversion

Directly contradictory arguments coexist regarding the conservation rule of orbital angular momentum in spontaneous parametric down-conversion. We analytically show how this rule is decided by spatial symmetry. We discover that the down-converted photon pairs can carry non-negligible extrinsic orbital angular momentum in the degrees of relative-movement freedom due to spatial symmetry breaking, leading to nonconservation of total orbital angular momentum in type-II down-conversion. Also, we demonstrate that the traditional technique does not measure the extrinsic orbital angular momentum.

Delocalized Correlations in Twin Light Beams with Orbital Angular Momentum

We generate intensity-difference-squeezed Laguerre-Gauss twin beams of light carrying orbital angular momentum by using four-wave mixing in a hot atomic vapor. The conservation of orbital angular momentum in the four-wave mixing process is studied as well as the spatial distribution of the quantum correlations obtained with different configurations of orbital angular momentum. Intensity-difference squeezing of up to -6.7 dB is demonstrated with beams carrying orbital angular momentum. Delocalized spatial correlations between the twin beams are observed.

Observation of Orbital Angular Momentum Transfer between Acoustic and Optical Vortices in Optical Fiber

Acousto-optic interaction in optical fiber is examined from the perspective of copropagating optical and acoustic vortex modes. Calculation of the acousto-optic coupling coefficient between different optical modes leads to independent conservation of spin and orbital angular momentum of the interacting photons and phonons. We show that the orbital angular momentum of the acoustic vortex can be transferred to a circularly polarized fundamental optical mode to form a stable optical vortex in the fiber carrying orbital angular momentum. The technique provides a useful way of generating stable optical vortices in the fiber medium.

Observation of Orbital Angular Momentum Transfer between Acoustic and Optical Vortices in Optical Fiber

Acousto-optic interaction in optical fiber is examined from the perspective of copropagating optical and acoustic vortex modes. Calculation of the acousto-optic coupling coefficient between different optical modes leads to independent conservation of spin and orbital angular momentum of the interacting photons and phonons. We show that the orbital angular momentum of the acoustic vortex can be transferred to a circularly polarized fundamental optical mode to form a stable optical vortex in the fiber carrying orbital angular momentum. The technique provides a useful way of generating stable optical vortices in the fiber medium.

Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion

We show that the transfer of the plane-wave spectrum of the pump beam to the fourth-order transverse spatial correlation function of the two-photon field generated by spontaneous parametric down-conversion leads to the conservation and entanglement of orbital angular momentum of light. By means of a simple experimental setup based on fourth-order (or two-photon) interferometry, we show that our theoretical model provides a good description for down-converted fields carrying orbital angular momentum.

Orbital angular momentum of photons in noncollinear parametric downconversion

Conservation of the orbital angular momentum (OAM) of light in photon downconversion has been observed experimentally in nearly collinear phase-matching geometries, where the pump, signal and idler photons propagate along almost the same direction [Nature 412 (2001) 313]. However, here we predict that such paraxial measurements conducted with entangled photons in noncollinear geometries are not expected to comply with OAM conservation in the above sense. Under proper conditions, the strength of such apparent anomaly approaches 100%. We discuss the physical origin of the effect and suggest experimental schemes where it can be verified.

Useful Integrals for Ab-Initio Molecular Quantum Similarity Measurements Using Slater Type Atomic Orbitals

Molecular quantum similarity measurements are based on a quantitative comparison of the one-electron densities of two molecules superposed and aligned to optimize a well-defined similarity function. In most previous work the densities have been related using a Dirac delta leading to the overlap-like quantum similarity function. The densities for the two molecules compared have generally been approximated often with a simple LCAO of s-gaussian functions. In this work, we present a one center two range expansion method for the evaluation of the overlap integrals involved in the overlap-like quantum similarity function over Slater type orbitals (STO). The single center and three types of two-center overlap integrals (involving four atomic orbitals; two in each molecule) have led to finite sums using a single center approach combined with selection rules obtained by analysis of orbital angular momentum (conservation). The three- and four-center integrals are also obtained analytically but involve infinite sums which require further study before leading to a complete set of integral codes for ab-initio quantum similarity.

Renormalizing the Lippmann-Schwinger equation for the one-pion exchange potential

We address the question whether the cut-off dependence, which has to be introduced in order to properly define the Lippmann-Schwinger equation for the one pion exchange potential plus local (delta-function) potentials, can be removed (up to inverse powers of it) by a suitable tuning of the various (bare) coupling constants. We prove that this is indeed so both for the spin singlet and for the spin triplet channels. However, the latter requires such a strong cut-off dependence of the coupling constant associated to the non-local term which breaks orbital angular momentum conservation, that the renormalized amplitude lacks from partial wave mixing. We argue that this is an indication that this term must be treated perturbatively.

Conservation of orbital angular momentum in stimulated down-conversion

We report on an experiment demonstrating the conservation of orbital angular momentum in stimulated down-conversion. The orbital angular momentum is not transferred to the individual beams of the spontaneous down-conversion, but it is conserved when twin photons are taken individually. We observe the conservation law for an individual beam of the down-conversion through cavity-free stimulated emission.

Collisional dynamics of Ca1D + HBr reactions: evidence for transition-state motions

The total cross-sections σA (E) and σB(E) for the exoergic Ca1D + HBr → CaBr A2Π, B2Σ+ + H reactions have been measured as a function of reagent relative translational energy in a crossed atomic and molecular beam experiment. For CaBr A 2Π production, σA(E) proceeds to a maximum after exceeding a threshold energy, and then decreases with further translational excitation of reagents. The energy dependence of σB(E), though similar in overall form, appears to be characterized by a series of maxima in the post-threshold region. These may be attributed to the opening of successive bending vibrational channels through an excited, bent van de Waals transition state [Ca…HBr]*‡ the widths of the resonance features in the excitation function give lifetimes of 435 fs and 610 fs for the two lowest vibrational levels of [Ca…HBr]*‡. An heuristic model of the dynamics of CaBr B2Σ+ formation is developed in terms of Landau-Zener transition probabilities for neutral—ionic curve crossing at two locations in the entrance channel coupled with a dynamic preference for utilization of vibrational energy in the transition state, which enables trajectories to surmount the energy barrier for electron transfer into the ionic exit channel with conservation of electronic orbital angular momentum. It is argued that this mechanism is consistent with theoretical calculations of the entrance channel and transition state potentials, and with information from laser spectroscopy of [Ca-HBr]*.

Parametric down-conversion for light beams possessing orbital angular momentum

We investigate the spontaneous parametric down-conversion for light beams possessing orbital angular momentum. The experimental results indicate that the orbital angular momentum is not conserved within the classical light fields. This is in contrast to second harmonic generation where the conservation of orbital angular momentum leads to a well-defined mode transformation. We attribute this difference in behavior to the loss of spatial coherence within each of the down-converted fields. [S1050-2947(99)01205-6].

Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes

Laguerre-Gaussian modes of various order are frequency doubled. The azimuthal phase structure of the second-harmonic light is measured directly by interfering the beam with its mirror image. We show that the orbital angular momentum per photon is doubled, so conserving the orbital angular momentum in the light beam. The frequency-doubled output beam is shown to have a Gegenbauer-Gaussian amplitude distribution at the beam waist. The beam can be described as a summation of Laguerre-Gaussian modes that interfere so that it changes form with propagation, but the distribution at the beam waist is reproduced in the far field.

Optical Solitons Carrying Orbital Angular Momentum

We predict a new kind of ring-profile solitary wave in nonlinear optical media, with finite orbital angular momentum. During propagation these fragment into fundamental solitons. Like free Newtonian particles, these fly off tangential to the ring, vividly demonstrating conservation of orbital angular momentum in soliton motion.