A series of quantum voting protocols of continuous variables is proposed. Three methods are employed to ensure that the quantum voting obeys some desirable rules. Entanglement is used to keep voters away from the voting results. We enable voters to operate identically to represent the same vote to prevent the tallyman from gaining information about individual voters. We also propose an effective scheme to prevent voters from voting more than once. In both two-valued and multivalued ballot protocols, several specific constraints are set to meet the rules.

We present a theoretical and experimental study of spin precession in the presence of both a static and an orthogonal oscillating magnetic field, which is nonresonant, not harmonically related to the Larmor precession, and of arbitrary strength. Due to the intrinsic nonlinearity of the system, previous models that account only for the simple sinusoidal case cannot be applied. We suggest an alternative approach and develop a model that closely agrees with experimental data produced by an optical-pumping atomic magnetometer. We demonstrate that an appropriately designed nonharmonic field makes it possible to extract a linear response to a weak dc transverse field, despite the scalar nature of the magnetometer, which normally causes a much weaker, second-order response.

Electron scattering from the ground state of cadmium atoms has been investigated theoretically using the convergent close-coupling, relativistic convergent close-coupling, relativistic optical potential, and relativistic distorted-wave methods. Elastic and inelastic differential cross sections, Stokes parameters, and spin-asymmetry parameters have been calculated and compared with available experimental and theoretical results. We find, in general, very good agreement between the theories and experiment.

Probability rates of electron-positron pair creation in collisions of a relativistic nucleus with a two-color laser field are calculated using the $S$-matrix approach. The case when both components of the laser field have commensurate frequencies and comparable strengths is considered. Pronounced interference effects are observed in angular distributions of created particles as well as in the total probability rates of pair production. These interference effects show a significant phase dependence of the pair-creation process.

The Auger decay channels of the Ar 2$p$ satellite states have been investigated using a multielectron coincidence technique, using a magnetic bottle time-of-flight electron spectrometer. For the Ar${}^{+}$(2$p^{-1}$3$p^{-1}np$) satellite states the 2$p$ hole is filled first, while for the Ar${}^{+}$(2$p^{-1}$3$s^{-1}$4$s$) satellite states the 3$s$ hole is filled first with leading to Ar${}^{2+}$(2$p^{-1}$3$p^{-1}$) states, which subsequently undergo an Auger decay leading to the filling of the 2$p$ hole.

We study the total cross section and angular distribution in Rayleigh scattering by hydrogen atom in the ground state, within the framework of Dirac relativistic equation and second-order perturbation theory. The relativistic states used for the calculations are obtained by making use of the finite basis-set method and expressed in terms of B splines and B polynomials. We pay particular attention to the effects that arise from higher (nondipole) terms in the expansion of the electron-photon interaction. It is shown that the angular distribution of scattered photons, while symmetric with respect to the scattering angle $\theta ={90}^{\circ }$ within the electric dipole approximation, becomes asymmetric when higher multipoles are taken into account. The analytical expression of the angular distribution is parametrized in terms of Legendre polynomials. Detailed calculations are performed for photons in the energy range 0.5 to 10 keV. When possible, results are compared with previous calculations.

A technique for complete population transfer between the two end states $|1\rangle$ and $|3\rangle$ of a three-state quantum system with a train of $N$ pairs of resonant and coincident pump and Stokes pulses is introduced. A simple analytic formula is derived for the ratios of the pulse amplitudes in each pair for which the maximum transient population $P_2\left(t\right)$ of the middle state $|2\rangle$ is minimized, $P_2^{\max }={\sin }^2(\pi /4N)$. It is remarkable that, even though the pulses are on exact resonance, $P_2\left(t\right)$ is damped to negligibly small values even for a small number of pulse pairs. The population dynamics resembles generalized $\pi$ pulses for small $N$ and stimulated Raman adiabatic passage for large $N$ and therefore this technique can be viewed as a bridge between these well-known techniques.

We explore the possibility of implementing a Heisenberg-limited Mach-Zehnder interferometer via an array of trapped ions, which obey a quantum Ising model within a transverse field. Based upon adiabatic processes of increasing the Ising interaction and then decreasing the transverse field, we demonstrate a perfect transition from paramagnetism to ferromagnetic states, which can be used as the beam splitter for the multi-ion Mach-Zehnder interferometer. The achieved NOON state of the ions enables the Heisenberg-limited interferometer. Using currently available techniques for ultracold ions, we discuss the experimental feasibility of our scheme with global operations.

Spin-orbit coupling (SOC) can give rise to interesting physics, from spin Hall to topological insulators, in condensed matter systems. Recently, this topical area has extended into atomic quantum gases in searching for artificial or synthetic gauge potentials. The prospects of tunable interaction and quantum state control promote neutral atoms as nature's quantum emulators for SOC. Lin et al. recently demonstrated a special form of the SOC $k_x{\sigma }_y$, which they interpret as an equal superposition of Rashba and Dresselhaus couplings in Bose-condensed atoms [Lin, Jiménez-García, and Spielman, Nature (London) 471, 83 (2011)]. This work reports a method of implementing arbitrary forms of SOC by switching between two pairs of Raman laser pulses like the method used by Lin et al. While one pair affects $k_x{\sigma }_y$ for some time, a second pair creates $k_y{\sigma }_y$ at other times with Raman pulses from different directions and a subsequent spin rotation into $\pm k_y{\sigma }_x$. With a sufficient number of pulses, the effective actions from different durations are small and accumulate in the same exponent despite the fact that $k_x{\sigma }_y$ and $\pm k_y{\sigma }_x$ do not commute. Our scheme involves no added complication and can be demonstrated within current experiments. It applies equally to bosonic or fermionic atoms.

Using the thermodynamic Bethe ansatz equations we study the quantum phase diagram, thermodynamics, and criticality of one-dimensional (1D) spin-1 bosons with strongly repulsive density-density and antiferromagnetic spin-exchange interactions. We analytically derive a high-precision equation of state from which the Tomonaga-Luttinger-liquid physics and quantum critical behavior of the system are computed. We obtain explicit forms for the scaling functions near the critical points yielding the dynamical exponent $z=2$ and correlation length exponent $\nu =1/2$ for the quantum phase transitions driven by either the chemical potential or the magnetic field. Consequently, we further demonstrate that quantum criticality of the system can be mapped out from the finite temperature density and magnetization profiles of the 1D trapped gas. Our results provide the physical origin of quantum criticality in a 1D many-body system beyond the Tomonaga-Luttinger-liquid description.

We theorize the spin Hall effect of light (SHEL) on a nanometal film and demonstrate it experimentally via weak measurements. A general propagation model to describe the relationship between the spin-orbit coupling and the thickness of the metal film is established. It is revealed that the spin-orbit coupling in the SHEL can be effectively modulated by adjusting the thickness of the metal film, and the transverse displacement is sensitive to the thickness of metal film in a certain range for horizontal polarization light. Importantly, a large negative transverse shift can be observed as a consequence of the combined contribution of the ratio and the phase difference of Fresnel coefficients.

A transmission electron microscope that takes advantage of superconducting quantum circuitry is proposed. The microscope is designed to improve the image contrast of radiation-sensitive weak-phase objects, in particular, biological specimens. The objective in this setting is to measure the phase shift of the probe electron wave to a precision Δθ within the number of electrons $N$ that does not destroy the specimen. In conventional electron microscopy Δθ scales as ∼1/$N^{1/2}$, which falls short of the Heisenberg limit ∼1/$N$. To approach the latter by using quantum entanglement, we propose a design that involves a Cooper-pair box placed on the surface of an electrostatic electron mirror in the microscope. Significant improvement could be attained if inelastic scattering processes are sufficiently delocalized.

Using a fiber laser system as a specific illustrative example, we introduce the concept of intermediate asymptotic states in finite nonlinear optical systems. We show that intermediate asymptotics of nonlinear equations (e.g., coherent structures with a finite lifetime or distance) can be used in applications similar to those of truly stable asymptotic solutions, such as, e.g., solitons and dissipative nonlinear waves. Applying this general idea to a particular, albeit practically important, physical system, we demonstrate a novel type of nonlinear pulse-shaping regime in a mode-locked fiber laser leading to the generation of linearly chirped pulses with a triangular distribution of the intensity.

We study inelastic collisions of counterpropagating self-induced transparency solitons in a homogeneously broadened two-level medium. The energy of the pulse can be almost totally absorbed in the medium due to asymmetric collision with a properly chosen control pulse. The medium state thus prepared demonstrates the property of an all-optical diode which transmits pulses from one direction and blocks from another. The saturation process of a controlled absorption effect, local-field correction influence, and the parameter ranges for the diode action are studied as well.

We present a scheme to achieve efficient single-photon frequency conversion by exploiting quantum interference between different transition pathways for single-photon states. As an example, we discuss the single-photon frequency-conversion process in the configuration wherein a $\Lambda$-type (Lambda-type) three-level quantum emitter is coupled to a Sagnac interferometer. It is shown that the efficiency of the frequency conversion approaches unity in the ideal case. A real-space theoretical approach and a pseudospectral numerical method are developed, which facilitate the computation for the full spatiotemporal dynamics of the scattering process.

It is demonstrated that the Hamiltonian for the internal motion of a nonrelativistic quantum mechanical system can be obtained just from the requirement of its overall translational momentum to be zero. Some particular cases relevant to an atomic system are also considered in some detail.

We study production of entanglement with highly mixed states. We find that entanglement between highly mixed states can be generated via a direct unitary interaction even when both states have purities arbitrarily close to zero. This indicates that purity of a subsystem is not required for entanglement generation. This result is in contrast to previous studies where the importance of the subsystem purity was emphasized.

We study the information provided by a detector click about the state of an initially excited two-level system. By computing the time evolution of the corresponding conditioned probability beyond the rotating-wave approximation, we show that a click in the detector is related to the decay of the source only for long interaction times. For short times, non-rotating-wave approximation effects such as self-excitations of the detector forbid a naive interpretation of the detector readings. These effects might appear in cQED experiments.

An open quantum system with multiple levels coupled to a bosonic environment at zero temperature is investigated systematically using the non-Markovian quantum-state-diffusion (QSD) method [W. T. Strunz, L. Diósi, and N. Gisin, Phys. Rev. Lett. 82, 1801 (1999)]. We have established exact time-local QSD equations for a set of interesting multilevel open systems, including high-spin systems, multiple-transition atomic models, and multilevel atomic models driven by time-dependent external fields. These exact QSD equations have paved the way to evaluate the dynamics of open multilevel atomic systems in the general non-Markovian regimes without any approximation.

We consider the differential cross section of electron-positron pair production by a high-energy photon in a strong Coulomb field close to the end of the electron or positron spectrum. When the momentum transfer $Q$ largely exceeds the electron mass, the cross section is obtained analytically in a compact form, and it is proportional to $1/Q^4$. Coulomb corrections essentially modify the cross section even for moderate values of the nuclear charge number $Z$. In the same kinematical region, the angular distribution for bound-free pair production, bremsstrahlung, and photorecombination is also obtained.