We analyze bound modes of two-dimensional massless Dirac fermions confined within a hyperbolic secant potential, which provides a good fit for potential profiles of existing top-gated graphene structures. We show that bound states of both positive and negative energies exist in the energy spectrum and that there is a threshold value of the characteristic potential strength for which the first mode appears. Analytical solutions are presented in several limited cases and supercriticality is discussed.

We generalize measurement-device-independent quantum key distribution [Lo, Curty, and Qi, Phys. Rev. Lett. 108, 130503 (2012)] to the scenario where the Bell-state measurement station contains also heralded quantum memories. We find analytical formulas, in terms of device imperfections, for all quantities entering in the secret key rates, i.e., the quantum bit error rate and the repeater rate. We assume either single-photon sources or weak coherent pulse sources plus decoy states. We show that it is possible to significantly outperform the original proposal, even in presence of decoherence of the quantum memory. Our protocol may represent the first natural step for implementing a two-segment quantum repeater.

We introduce a general optical system for synthesis of partially coherent vector beams with a variety of correlation functions. In particular we employ it for generation of the family of beams, termed the specially correlated radially polarized (SCRP) beams and examine their free-space propagation both theoretically and experimentally. Our results clearly show that a SCRP beam exhibits unique features on propagation in comparison with those of beams with conventional correlation functions. The technique for modulation of the correlation functions and, hence, the coherence state of a SCRP beam in the source plane leads to efficient control of its intensity distribution and its degree of polarization on propagation, which is of importance in particle trapping and material thermal processing applications.

We study a class of three-waveguide axially varying structures whose dynamics are described by the su(3) algebra. Their analytic propagator can be found based on the corresponding Lie group generators. In particular, we show that the field propagator corresponding to three-waveguide structures that have arbitrarily varying coupling coefficients and identical refractive indices is associated with the orbital angular momentum algebra. The conditions necessary to achieve perfect transmission from the first to the last waveguide element are obtained and particular cases are elucidated analytically.

We present an interpretation for reduced density matrices of secondary variables in relativistic systems via an analysis of Wigner's method to construct the irreducible unitary representations of the Poincaré group. We argue that the usual partial trace method used to obtain spin-reduced matrices is not fully rigorous, however, employing our interpretation, similar effective reduced density matrices can be constructed. In addition, we show that our proposal is more useful than the usual one since we are not restricted only to the reduced density matrices that could be obtained by the ordinary partial trace method.

We describe the operation of a prototype polarized-electron source. Rubidium vapor, contained in a cell, is optically pumped in the presence of a buffer gas. Unpolarized electrons from a tungsten filament are injected into the cell and extracted after undergoing spin exchange with the Rb atoms. We compare the performance of the source when different buffer gases are used. We measure a decrease in electron polarization as their injection energy increases, but find an unexpected regime at higher injection energies yielding increased electron polarization accompanied by a 40-fold increase in current, suggesting the production of slow secondary electrons in the target cell. With ethylene, we have measured electron currents of 4 μA simultaneously with electron polarizations of 24%. This work offers the promise of a simple, benchtop, “turnkey” source of polarized electrons.

We present three protocols for directly measuring the concurrence of two-photon polarization-entangled states, including pure states and mixed states. Two signal photon pairs in the same polarization-entangled states are needed in each detection round, and the signal photons will pass through polarization-independent beam splitters simultaneously. The concurrence of the photon pairs will be encoded in the total probability of picking up the balanced states in the two output modes of the beam splitter, which can be directly measured by single-photon detectors. The photon detection efficiency can be further enhanced with the help of the weak cross-Kerr nonlinearity, and the signal photons will not be absorbed. The third scheme using the bilateral nondemolition measurements can measure the concurrence of both pure and mixed states with high efficiency and high fidelity and is robust against the copy error of the state to be measured. The sophisticated controlled-not operation of the previous schemes is not required here, so our protocols are more feasible within the current experimental technology.

The (elastic) Rayleigh scattering of hard x rays by hydrogenlike ions has been investigated within the framework of second-order perturbation theory and Dirac's relativistic equation. The focus of this study was, in particular, on two questions: (i) How is the polarization of scattered photons affected if the incident light is itself (linearly) polarized, and (ii) how do the nondipole contributions to the electron-photon interaction and the relativistic contraction of the wave functions influence such a polarization transfer? Detailed calculations were performed for Ne${}^{9+}$, Xe${}^{53+}$, and U${}^{91+}$ targets and for photon energies up to ten times the $1s$ ionization threshold of the ions. From the comparison of these fully relativistic computations with the (nonrelativistic) dipole approximation we conclude that relativistic and higher-multipole effects often lead to a significant or even complete depolarization for heavy targets and at high photon energies.

The electron dynamics in the classically forbidden region during relativistic tunnel ionization is investigated. The classical forbidden region in the relativistic regime is identified by defining a gauge-invariant total-energy operator. Introducing position-dependent energy levels inside the tunneling barrier, we demonstrate that the relativistic tunnel ionization can be well described by a one-dimensional intuitive picture. This picture predicts that, in contrast to the well-known nonrelativistic regime, the ionized electron wave packet arises with a momentum shift along the laser's propagation direction. This is compatible with results from a strong-field approximation calculation where the binding potential is assumed to be zero ranged. Further, the tunneling time delay, stemming from Wigner's definition, is investigated for model configurations of tunneling and compared with results obtained from the exact propagator. By adapting Wigner's time delay definition to the ionization process, the tunneling time is investigated in the deep-tunneling and in the near-threshold-tunneling regimes. It is shown that while in the deep-tunneling regime signatures of the tunneling time delay are not measurable at remote distance, they are detectable, however, in the latter regime.

Single-shot photoelectron spectroscopy of nonresonant two-color two-photon ionization of He has been carried out using an intense free-electron laser (FEL) at 59.7 nm and a femtosecond UV laser at 268 nm. By shot-by-shot analysis of photoelectron spectra, the cross section for nonresonant two-color ionization of He is determined to be ${\sigma }^{\left(2\right)}=4.1\left(6\right)\times {10}^{-52}$ cm${}^4$ s. The cross-correlation trace derived from the nonresonant signals shows that the temporal resolution of the system is 0.36(3) ps, which is mainly governed by the timing jitter between the FEL and UV laser pulses.

We study the competition between one-body and two-body couplings in weakly interacting two-component Bose gases, in particular as regards field correlations. We derive the mean-field theory for both ground-state and low-energy pair excitations in the general case where both one-body and two-body couplings are position dependent and the fluid is subjected to a state-dependent trapping potential. General formulas for phase and density correlations are also derived. Focusing on the case of homogeneous systems, we discuss the pair-excitation spectrum and the corresponding excitation modes, and use them to calculate correlation functions, including both quantum and thermal fluctuation terms. We show that the relative phase of the two components is imposed by that of the one-body coupling, while its fluctuations are determined by the modulus of the one-body coupling and by the two-body coupling. One-body coupling and repulsive two-body coupling cooperate to suppress relative-phase fluctuations, while attractive two-body coupling tends to enhance them. Further applications of the formalism presented here and extensions of our work are also discussed.

The nonlinearity is an important feature in the field of optomechanics. Employing atomic coherence, we put forward a scheme to enhance the nonlinearity of the cavity optomechanical system. The effective Hamiltonian is derived, which shows that the nonlinear strength can be enhanced by increasing the number of atoms at a certain range of parameters. We also numerically study the nonlinearity enhancement beyond the effective Hamiltonian. Furthermore, we investigate the potential usage of the nonlinearity in performing a quantum nondemolition (QND) measurement of the bosonic modes. Our results show that the present system exhibits synchronization, and the nonlinear effects provide us an effective method in performing QND.

Based on the idea that the vacuum fluctuations of electromagnetic fields can induce instantaneous correlated dipoles, we study the far-zone Casimir-Polder potential between two atoms in the Boulware, Unruh, and Hartle-Hawking vacua outside a Schwarzschild black hole. We show that at spatial infinity, the Casimir-Polder potential in the Boulware vacuum is similar to that in the Minkowski vacuum in flat space-time with a behavior of $R^{-7}$, so it is in the Unruh vacuum as a result of the backscattering of the Hawking radiation from the black hole off the space-time curvature. However, the interatomic Casimir-Polder potential in the Hartle-Hawking vacuum behaves like that in a thermal bath at the Hawking temperature. In the region near the event horizon of the black hole, the modifications caused by the space-time curvature make the interatomic Casimir-Polder potential smaller in all three vacuum states.

Hardy's proof is considered the simplest proof of nonlocality. Here we introduce an equally simple proof that (i) has Hardy's as a particular case, (ii) shows that the probability of nonlocal events grows with the dimension of the local systems, and (iii) is always equivalent to the violation of a tight Bell inequality. Our proof has all the features of Hardy's and adds the only ingredient of the Einstein-Podolsky-Rosen scenario missing in Hardy's proof: It applies to measurements with an arbitrarily large number of outcomes.

We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The resulting Wigner function displays the axioms of a quasiprobability distribution, and any Weyl-ordered operator gets associated with the corresponding phase-space function, even in the absence of continuous symmetries. The corresponding quantum Liouville equation reduces to the classical curved space Liouville equation in the semiclassical limit. We demonstrate the formalism for a point particle moving on two-dimensional manifolds, such as a paraboloid or the surface of a sphere. The latter clarifies the treatment of compact coordinate spaces, as well as the relation of the presented phase-space representation to symmetry groups of the configuration space.

We propose and analyze the implementation of a two-qubit quantum gate using circular Rydberg states with maximum orbital angular momentum. The intrinsic quantum gate error is limited by the finite Rydberg lifetime and finite Rydberg blockade shift. Circular states have much longer radiative lifetimes than low orbital angular momentum states and are therefore candidates for high-fidelity gate operations. We analyze the dipole-dipole interaction of two circular state Rydberg atoms and present numerical simulations of quantum process tomography to find the intrinsic fidelity of a Rydberg blockade-controlled phase gate. Our analysis shows that the intrinsic gate error can be less than $9\times {10}^{-6}$ for circular Cs atoms in a cryogenic environment.

The demonstration of quantum teleportation of a photonic qubit from Alice to Bob usually relies on data conditioned on detection at Bob's location. I show that Bohm's Einstein-Podolsky-Rosen (EPR) paradox can be used to verify that the quantum benchmark for qubit teleportation has been reached, without postselection. This is possible for scenarios insensitive to losses at the generation station, and with efficiencies of ${\eta }_B>1/3$ for the teleportation process. The benchmark is obtained if it is shown that Bob can “steer” Alice's record of the qubit as stored by Charlie. EPR steering inequalities involving $m$ measurement settings can also be used to confirm quantum teleportation, for efficiencies ${\eta }_B>1/m$, if one assumes trusted detectors for Charlie and Alice. Using proofs of monogamy, I show that two-setting EPR steering inequalities can signify secure teleportation of the qubit state.

We study the measurement-device-independent quantum key distribution (MDI-QKD) in practice with limited resources, when there are only three different states in implementing the decoy-state method. We present a tighter explicit formula to estimate the lower bound of the yield of two-single-photon pulses sent by Alice and Bob. Moreover, we show that the bounding of this yield and phase flip error of single-photon pulse pairs can be further improved by using other constraints which can be solved by a simple and explicit program. Our methods here can significantly improve the key rate and the secure distance of MDI-QKD with only three intensities.

Open quantum random walks (OQRWs) deal with quantum random motions on a line for systems with internal and orbital degrees of freedom. The internal system behaves as a quantum random gyroscope coding for the direction of the orbital moves. We reveal the existence of a transition, depending on OQRW moduli, in the internal system behaviors from simple oscillations to random flips between two unstable pure states. This induces a transition in the orbital motions from the usual diffusion to ballistically induced diffusion with a large mean free path and large effective diffusion constant at large times. We also show that mixed states of the internal system are converted into random pure states during the process. We touch upon possible experimental realizations.

A pulsed scheme for generating robust optical entanglement via the coupling of two optical modes to a mechanical oscillator is proposed. This scheme is inspired by the Sørensen-Mølmer approach for entangling trapped ions in a thermal environment and is based on the use of optical driving pulses that are slightly detuned from the respective sideband resonance. We show that for certain pulse durations, the optomechanical interaction can return the mechanical oscillator to its initial state, disentangling the mechanical and optical systems. The corresponding optical entanglement generation is robust against thermal mechanical noise in the weak as well as the strong-coupling regimes. Significant optical entanglement can be generated in the weak-coupling regime, even in the presence of a large thermal phonon occupation.