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arXiv:1801.00559 · Scientific Reports

Cooperative light scattering from helical-phase-imprinted atomic rings

H. H. Jen, M.-S. Chang, Ying-Cheng Chen

Published Jun 18, 2018• 19 citations
arXivHTMLPDF

Abstract

Abstract We theoretically investigate the light scattering of super- and subradiant states of an atomic ring prepared by single excitation with a photon which carries an orbital angular momentum (OAM). For excitations with linear polarizations, the helical phase imprinted (HPI) atomic ring presents a discrete C4 rotational symmetry when number of atoms N = 4n with integers n, while for circular polarizations with arbitrary N, the continuous and C N symmetries emerge for the super- and subradiant modes, respectively. The HPI superradiant modes predominantly scatter photons in the forward-backward direction, and the forward scattering can be further enhanced as atomic rings are stacked along the excitation direction. The HPI subradiant modes then preferentially scatter photons in the transversal directions, and when rings are stacked concentrically and on a plane, crossover from sub- to superradiance is observed which leads to splitting and localization of the far-field scattering patterns in the polar angle. The HPI super- and subradiant states are thus detectable through measuring the far-field radiation patterns, which further allow quantum storage and detection of a single photon with an OAM.

DOI
10.1038/s41598-018-27888-y

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Abstract We theoretically investigate the light scattering of super- and subradiant states of an atomic ring prepared by single excitation with a photon which carries an orbital angular momentum (OAM). For excitations with linear polarizations, the helical phase imprinted (HPI) atomic ring presents a discrete C4 rotational symmetry when number of atoms N = 4n with integers n, while for circular polarizations with arbitrary N, the continuous and C N symmetries emerge for the super- and subradiant modes, respectively. The HPI superradiant modes predominantly scatter photons in the forward-backward direction, and the forward scattering can be further enhanced as atomic rings are stacked along the excitation direction. The HPI subradiant modes then preferentially scatter photons in the transversal directions, and when rings are stacked concentrically and on a plane, crossover from sub- to superradiance is observed which leads to splitting and localization of the far-field scattering patterns in the polar angle. The HPI super- and subradiant states are thus detectable through measuring the far-field radiation patterns, which further allow quantum storage and detection of a single photon with an OAM.
We theoretically investigate the far-field scattering properties of multiphoton super- and subradiant states which can be prepared by multiphoton excitations with orbital angular momentum (OAM). Due to multiphoton interference, the far-field patterns of the subradiant modes show directional scattering along the excitation direction or transverse scattering with number of peaks equal to the number of atoms. When more atoms are involved, we consider structures of stacked and concentric rings, which respectively show enhanced directional scattering and smoothed emission patterns. Our scheme gives insights to prepare many-body subradiant states, and is potentially applicable to quantum storage of multiphoton with OAM. By designing atomic spatial distributions, these cooperative states can tailor the far-field emission properties, which is useful for light collections and quantum information manipulations.
Photons are an ideal candidate for encoding both classical and quantum information. Besides spin angular momentum associated with circular polarization, single photon can also carry other fundamentally new degree of freedom of orbital angular momentum related to the spiral phase structure of light. The key significance of orbital angular momentum lies in its potential in realizing a high-dimensional Hilbert space and in encoding a high-dimensional quantum information. Since Allen et al. [Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185] recognized the physical reality of photon orbital angular momentum in 1992, rapidly growing interest has been aroused in orbital angular momentum (OAM) from both classical and quantum points of view. Here we present an overall review on the high-order orbital angular momentum of photon, including its preparation and manipulation based on some specific techniques and also its applications. The spatial light modulator is a commercial device that has been widely employed to generate the OAM beams. We make and identify the optical OAM superposition with very high quantum numbers up to l=360. Recently, the metallic spiral phase mirrors were also developed to produce high-order OAM beams up to l=5050. In addition, the Q-plates made of anisotropic and inhomogeneous liquid crystals were invented to generate high-order OAM beams in a polarization-controllable manner, and the OAM superposition of l=± 50 were achieved. Owing to high rotational symmetry, these high OAM beams have been found to have more and more important applications in the fields of high-sensitivity sensing and high-precision measurements. Two fascinating examples are discussed in detail. The first example is that the research group led by Prof. Zeilinger has prepared and observed the quantum entanglement of high orbital angular momenta up to l=±300 by the technique of polarization-OAM entanglement swapping, and they demonstrated that the angular resolution could be significantly improved by a factor of l. Their result was the first step for entangling and twisting even macroscopic, spatially separated objects in two different directions. The second example is that the research group led by Prof. Padgett has demonstrated an elegant experiment of rotational Doppler effects for visible light with l=±20 OAM superposition. They showed that a spinning object with an optically rough surface might induce a Doppler effect in light reflected from the direction parallel to the rotation axis, and the frequency shift was proportional to both the disk's angular speed and the optical OAM. The potential applications in noncontact measurement of angular speed and in significant improvement of angular resolution for remote sensing will be particularly fascinating.
Twisted light has received a lot of attention in recent years. And there are justified reasons for this. The properties of twisted light are unusual and differ fundamentally from the plane-wave properties. The phase fronts of these light beams have a helical structure, giving them the name twisted. This helical phase structure originates from the well-defined orbital angular momentum (OAM) that they carry along their propagation direction and in addition to the spin angular momentum (SAM). Moreover, they have a characteristic intensity profile, which consists of concentric rings with a central minimum, and a phase singularity in the beam center. This thesis is based on two main parts, each dealing with a different aspect of twisted light. These investigations are carried out using Bessel beams, one type of twisted light. Twisted light beams are cylindrically symmetrical. Therefore, they are defined on the basis of circularly polarized light. This fact leads to the first question: Is it possible to generate twisted light in other polarization states? In this work, we derive how this can be achieved by using the superposition principle and how this can be used to construct linearly, radially, or azimuthally polarized Bessel beams. The focus in the second part is on excitations of atoms by twisted Bessel beams. In particular, we analyze how the use of twisted light can modify individual atomic multipole transitions. The obtained results show that for an efficient modification a precise localization of the target atom is required. In the last chapter, both aspects are combined. We analyze transitions between magnetic hyperfine states in a single trapped atom (or ion), which is exposed to an additional external magnetic field. The presented calculations for these multipole excitations are based on a formalism that accounts for the alignment of the applied external magnetic field with respect to the light propagation direction, and additionally different polarization states of the radiation field are considered. The obtained results indicate that twisted light could be of particular interest for precision experiments. One possible application is the use in single-ion clocks. The work shows that high multipole orders of the vortex beams allow excitations in the intensity minimum in the center of these beams without causing large disturbances, and thus may enable a significant reduction of the light shift in atomic transitions.
Orbital angular momentum (OAM) of single photons represents a new optical degree of freedom for the entanglement of photons [1,2]. One physical realization of OAM carrying light beams are the so called Laguerre-Gaussian modes of light with the required helical phase structure. One big advantage over the well known polarization degree of freedom is the possibility of realizing entanglement between two photons with very high quantum numbers. However, the creation of photonic OAM entanglement using the widely used spontaneous parametric downconversion process is limited by the strongly reduced efficiency for higher momenta [3]. We have realized a novel method to create entanglement between two photons with a very high difference in their OAM quantum number and momentum respectively. Furthermore we have explored hybrid entanglement of photons in the OAM and polarization degree of freedom.
Collective excitations in ordered subwavelength atomic arrays can exhibit strongly suppressed radiative decay due to interference between light scattered by neighboring emitters. These so-called subradiant states make these systems a promising platform for storing and manipulating photonic excitations. The external geometry of the array, combined with dynamical control of the atomic dipole orientation, enables localized trapping and coherent transport of these subradiant excitations. Here, we theoretically demonstrate these capabilities in ring-shaped atomic arrays. Specifically, we show adiabatic transport of a localized excitation around a single ring, coherent transfer of a single excitation between two neighboring rings with geometry-controlled selectivity, and interaction-induced conditional phase shifts between two simultaneously trapped excitations in neighboring rings. The latter can be interpreted as effective controlled-phase operations between stored excitations. Together, these results demonstrate the potential of ordered atomic arrays as a platform for coherent photonic quantum information processing with dissipation-protected collective excitations.
We propose a set of subradiant states which can be prepared and detected in a one-dimensional optical lattice. We find that the decay rates are highly dependent on the spatial phases imprinted on the atomic chain, which allows systematic investigations of the subradiance in fluorescence experiments. The time evolution of these states can have a long decay time where up to 100 ms of lifetime is predicted for 100 atoms. They can also show decayed Rabi-like oscillations with a beating frequency determined by the difference of the cooperative Lamb shift in the subspace. Experimental requirements are also discussed for practical implementation of the subradiant states. Our proposal provides a scheme for quantum storage of photons in arrays of two-level atoms through the preparation and detection of subradiant states, which offers opportunities for quantum many-body state preparation and quantum information processing in optical lattices.