There are important differences between the nonrelativistic and relativistic description of electron beams. The orbital angular momentum quantum number cannot be used to specify the wave functions in the relativistic case. In this Letter we introduce analytic solutions of the Dirac equation in the form of exponential wave packets and we argue that they properly describe relativistic electron beams carrying angular momentum.
We investigate the decay properties of the quantumness including quantum entanglement, quantum discord and quantum coherence for two photonic qubits, which are partially entangled in their orbital angular momenta, through Kolmogorov turbulent atmosphere. It is found that the decay of quantum coherence and quantum discord may be qualitatively different from that of quantum entanglement when the initial state of two photons is not maximally entangled. We also derive two universal decay laws for quantum coherence and quantum discord, respectively, and show that the decay of quantum coherence is m…
Photons carrying a well-defined orbital angular momentum have been proven to modify spectroscopic selection rules in atomic matter. Excitation profiles of electric quadrupole transitions have been measured with single trapped $^{40}$Ca$^+$ ions for varying polarizations. We further develop the photo-absorption formalism to study the case of arbitrary alignment of the beam's optical axis with respect to the ion's quantization axis and mixed multipolarity. Thus, predictions for M1-dominated $^{40}Ar^{13+}$, E3-driven $^{171}Yb^+$ and $^{172}Yb^+$, and B-like $^{20}Ne^{5+}$ are presented. The lat…
We show how strongly correlated ultracold bosonic atoms loaded in specific orbital angular momentum states of arrays of cylindrically symmetric potentials can realize a variety of spin-1/2 models of quantum magnetism. We consider explicitly the dependence of the effective couplings on the geometry of the system and demonstrate that several models of interest related to a general $XYZ$ Heisenberg model with external field can be obtained. Furthermore, we discuss how the relative strength of the effective couplings can be tuned and which phases can be explored by doing so in realistic setups. Fi…
The quantum mechanical states of the neutral particle endowed with a magnetic moment in the combination of electromagnetic vortex field together with the constant magnetic field are dealt with. It is shown that this system of fields is capable to capture the particle in the perpendicular direction and guide it along the propagating wave. The quantum evolution is subject to tunneling processes, which can destroy the delicate trapping mechanism. The probability of these processes show that it should be in principle possible to catch and guide the particle for the time of several microseconds. Th…
The orbital angular momentum of light, unlike spin, is an infinite-dimensional discrete variable and may hence offer enhanced performances for encoding, transmitting, and processing information in the quantum regime. Hitherto, this degree of freedom of light has been studied mainly in the context of quantum states with definite number of photons. On the other hand, field-quadrature continuous-variable quantum states of light allow implementing many important quantum protocols not accessible with photon-number states. Here, we present the first generation and complete experimental characterizat…
We propose a procedure to achieve a complete energy conversion between laser pulses carrying orbital angular momentum (OAM) in a cloud of cold atoms characterized by a double-Λatom-light coupling scheme. A pair of resonant spatially dependent control fields prepare atoms in a position-dependent coherent population trapping state, while a pair of much weaker vortex probe beams propagate in the coherently driven atomic medium. Using the adiabatic approximation we derive the propagation equations for the probe beams. We consider a situation where the second control field is absent at the entrance…
We study two-dimensional quantum Gaussian packets with a fixed value of mean angular momentum. This value is the sum of two independent parts: the `external' momentum related to the motion of the packet center and the `internal' momentum due to quantum fluctuations. The packets minimizing the mean energy of an isotropic oscillator with the fixed mean angular momentum are found. They exist for `co-rotating' external and internal motions, and they have nonzero correlation coefficients between coordinates and momenta, together with some (moderate) amount of quadrature squeezing. Variances of angu…
The motion of a neutral atom endowed with a magnetic moment interacting with the magnetic field is determined from the Ehrenfest-like equations of motion. These equations for the average values of the translational and spin degrees of freedom are derived from the Schrödinger-Pauli wave equation and they form a set of nine coupled nonlinear evolution equations. The numerical and analytic solutions of these equations are obtained for the combination of the rotating magnetic field of a wave carrying orbital angular momentum and a static magnetic field. The running wave traps the atom only in the …
There is recent interest in the use of light beams carrying orbital angular momentum (OAM) for creating multiple channels within free-space optical communication systems. One limiting issue is that, for a given beam size at the transmitter, the beam divergence angle increases with increasing OAM, thus requiring a larger aperture at the receiving optical system if the efficiency of detection is to be maintained. Confusion exists as to whether this divergence scales linarly with, or with the square root of, the beam's OAM. We clarify how both these scaling laws are valid, depending upon whether …
Light with orbital angular momentum (OAM) has great potentials in both classical and quantum optical communications such as enhancing the transmission capacity of a single communication channel because of its unlimited dimensions. Based on OAM conservation in second order nonlinear interaction processes, we create a classical to quantum optical network link in OAM degree of freedoms of light via sum frequency generation (SFG) following by a spontaneous parametric down conversion (SPDC). A coherent OAM-carrying beams at telecom wavelength 1550nm is up-converted to 525.5nm OAM-carrying beams in …
We report on the amplification of an optical vortex beam carrying orbital angular momentum via induced narrow Raman gain in an ensemble of cold cesium atoms. A 20\% single-pass Raman gain of a weak vortex signal field is observed with a spectral width of order of 1 MHz, much smaller than the natural width, demonstrating that the amplification process preserves the phase structure of the vortex beam. The gain is observed in the degenerated two-level system associated with the hyperfine transition $6S_{1/2}(F=3)\leftrightarrow 6P_{3/2}(F^{\prime}=2)$ of cesium. Our experimental observations are …
A chain of cofacial molecules with CN or CNh symmetry supports excitonic states with a screw-like structure. These can be quantified with the combination of an axial wavenumber and an azimuthal winding number. Combinations of these states can be used to construct excitonic wave packets that spiral down the chain with well-determined linear and angular momenta. These twisted exciton wave packets can be created and annihilated using laser pulses, and their angular momentum can be optically modified during transit. This allows for the creation of opto-excitonic circuits in which information, enco…
In this paper, we introduce an extension of the Dirac equation, very similar to Dirac oscillator, that gives stationary localized wave packets as eigenstates of the equation. The extension to the Dirac equation is achieved through the replacement of the momentum operator by a PT-symmetric generalized momentum operator. In the 1D case, the solutions represent bound particles carrying spin having continuous energy spectrum, where the envelope parameter defines the width of the packet without affecting the dispersion relation of the original Dirac equation. In the 2D case, the solutions are local…
Nondegenerate four-wave mixing (FWM) process based on a double-$Λ$ scheme in hot alkali metal vapor is a versatile tool in quantum state engineering, quantum imaging, and quantum precision measurements. In this Letter, we investigate the generation of quantum correlated twin beams which carry nonzero orbital angular momentums (OAMs) based on the FWM process in hot cesium vapor. The amplified probe beam and the newly generated conjugate beam in the FWM process have the same and opposite topological charge as the seed beam, respectively. We also explore the FWM process operated in a nonamplifyin…
Orbital angular momentum (OAM) multiplexing provides an efficient method to improve data-carrying capacity in various quantum communication protocols. It is a precondition to distribute OAM multiplexed quantum resources in quantum channels for implementing quantum communication. However, quantum steering of OAM multiplexed optical fields and the effect of channel noise on OAM multiplexed quantum resources remain unclear. Here, we generate OAM multiplexed continuous-variable (CV) entangled states and distribute them in lossy or noisy channels. We show that the decoherence property of entangleme…
Orbital angular momentum (OAM) of light is a fundamental optical degree of freedom that has recently motivated much exciting research in diverse fields ranging from optical communication to quantum information. We show for the first time that it is also a unique and valuable resource for quantum simulation, by demonstrating theoretically how \emph{2d} topological physics can be simulated in a \emph{1d} array of optical cavities using OAM-carrying photons. Remarkably, this newly discovered application of OAM states not only reduces required physical resources but also increases feasible scale o…
We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noether's theorem. We consider two slightly different formulations of Gaussian wave packet dynamics; one is based on earlier works of Heller and Hagedorn, and the other based on the symplectic-geometric approach by Lubich and others. In either case, we reveal the symplectic and Hamiltonian nature of the dynamics and formulate natural symmetry group actions in the setting to derive the corresponding conserved quantities (mom…
Laser photons carrying non-zero orbital angular momentum are known and exploited during the last twenty years. Recently it has been demonstrated experimentally that such (twisted) electrons can be produced and even focused to a subnanometer scale. Thus, twisted electrons emerge as a new tool in atomic physics. The state of a twisted electron can be considered as a specific wave packet of plane waves. In the present paper-I we consider elastic scattering of the wave packets of fast non-relativistic particles on a potential field. We obtain simple and convenient formulae for a number of events i…
We address the time evolution of two- and three-dimensional nonrelativistic Gaussian wave packets in the presence of a weak external potential of arbitrary functional form. The focus of our study is the phenomenon of rotation of a Gaussian wave packet around its center of mass, as quantified by mean angular momentum computed relative to the wave packet center. Using a semiclassical approximation of the eikonal type, we derive an explicit formula for a time-dependent change of mean angular momentum of a wave packet induced by its interaction with a weak external potential. As an example, we app…
One of the reasons for the tremendous success of a plane-wave approximation in particle physics is that the non-paraxial corrections to such observables as energy, magnetic moment, scattering cross section, and so on are attenuated as $λ_c^2/σ_{\perp}^2 \ll 1$ where $σ_{\perp}$ is a beam width and $λ_c = \hbar/mc$ is a Compton wavelength. This amounts to less than $10^{-14}$ for modern electron accelerators and less than $10^{-6}$ for electron microscopes. Here we show that these corrections are $|\ell|$ times enhanced for vortex particles with high orbital angular momenta $|\ell|\hbar$, which…
While wave-packet solutions for relativistic wave equations are oftentimes thought to be approximate (paraxial), we demonstrate that there is a family of such solutions, which are exact, by employing a null-plane (light-cone) variables formalism. A scalar Gaussian wave-packet in transverse plane is generalized so that it acquires a well-defined z-component of the orbital angular momentum (OAM), while may not acquire a typical "doughnut" spatial profile. Such quantum states and beams, in contrast to the Bessel ones, may have an azimuthal-angle-dependent probability density and finite quantum un…
We present a comprehensive theoretical investigation of the photo-generated excitons in transition-metal dichalcogenide monolayers (TMD-ML's) by Laguerre-Gaussian beams, a celebrated kind of twisted lights (TL's) carrying quantized orbital angular momenta (OAM). We show that the photo-excitation of TL incident to a TMD-ML leads to the formation of spatially localized exciton wave packets, constituted by the superposition of finite-momentum exciton states determined by the intriguing interplay between the multiple degrees of freedom of the optical and excitonic subsystems. Consequently, the TL-…
We employ a cascaded system approach to numerically simulate the interaction of photon pulses with a two-level scatterer in a chiral waveguide QED setup. It is possible to expand any pure state of two photons as a superposition of orthogonal two-photon pulses. We show that the scattering of a two-photon pulse of suitable duration may lead to an entangled output state between predominately two equally populated two-photon states. In a complementary wave packet basis, this state is a product state of two orthogonal single photon wave packets. The time reversal of the above scattering process all…
Light carrying orbital angular momentum (OAM) has attractive applications in the fields of precise optical measurements and high capacity optical communications. We study the rotation of a light beam propagating in warm 87Rb atomic vapor using a method based on magnetic-field-induced circular birefringence. The dependence of the rotation angle on the magnetic field makes it appropriate for weak magnetic field measurements. We quote a detailed theoretical description that agrees well with the experimental observations. The experiment shown here provides a method to measure the magnetic field in…
Light carrying orbital angular momentum (OAM) has great potential in enhancing the information channel capacity in both classical and quantum optical communications. Long distance optical communication requires the wavelengths of light are situated in the low-loss communication windows, but most quantum memories currently being developed for use in a quantum repeater work at different wavelengths, so a quantum interface to bridge the wavelength gap is necessary. So far, such an interface for OAM-carried light has not been realized yet. Here, we report the first experimental realization of a qu…
On-chip photon sources carrying orbital angular momentum (OAM) are in demand for high-capacity optical information processing in both classical and quantum regimes. However, currently-exploited integrated OAM sources have been primarily limited to the classical regime. Herein, we demonstrate a room-temperature on-chip integrated OAM source that emits well-collimated single photons, with a single-photon purity of g(2)(0) = 0.22, carrying entangled spin and orbital angular momentum states and forming two spatially separated entangled radiation channels with different polarization properties. The…
The potential scattering of electrons carrying non--zero quanta of the orbital angular momentum (OAM) is studied in a framework of the generalized Born approximation, developed in our recent paper by Karlovets \textit{et al.}, Phys. Rev. A. {\textbf 92}, 052703 (2015). We treat these so--called \textit{twisted} electrons as spatially localized wave--packets. The simple and convenient expressions are derived for a number of scattering events in collision of such a vortex electron with a single potential, located at a given impact parameter with respect to the wave-packet's axis. The more realis…
The variance of the position operator is associated with how wide or narrow a wave-packet is, the momentum variance is similarly correlated with the size of a wave-packet in momentum space, and the angular-momentum variance quantifies to what extent a wave-packet is non-spherically symmetric. We examine an interacting three-dimensional trapped Bose-Einstein condensate at the limit of an infinite number of particles, and investigate its position, momentum, and angular-momentum anisotropies. Computing the variances of the three Cartesian components of the position, momentum, and angular-momentum…
