The collective spontaneous emission of $N$ multilevel atoms is studied in optical vector theory and without applying the rotating-wave approximation. The counter-rotating terms are included using a unitary transformation method. We analyze the decay dynamics starting from two initial conditions, the standard Dicke and timed Dicke states. In addition to the dependence on ensemble volume and density, we also study the effect of the ensemble geometry on cooperative emission for spheres, cubes, and quasi-two-dimensional shapes in different orientations. Finally, time-dependent cooperative spontaneous emission rates are introduced and investigated.

A variable achromatic optical beam splitter with one input and $N$ output waveguide channels is introduced. The physical mechanism of this multiple beam splitter is adiabatic passage of light between neighboring optical waveguides in a fashion reminiscent of the technique of stimulated Raman adiabatic passage in quantum physics. The input and output waveguides are coupled via a mediator waveguide and the ratios of the light intensities in the output channels are controlled by the couplings of the respective waveguides to the mediator waveguide. Due to its adiabatic nature the beam splitting efficiency is robust to variations in the experimental parameters.

Control of Goos-H$\ddot{\text{a}}$nchen (GH) shift in reflected and transmitted light is revisited for a Gaussian light incident on a cavity. The intracavity atomic medium follows duplicated two-level atomic configurations where two fields, i.e., a strong control field and a relatively weak probe field are employed [F. A. Hashmi and M. A. Bouchene, Phys. Rev. Lett. 101, 213601 (2008)]. The coherent control is achieved via phase shift $\varphi$ between control and probe fields. The effect of incident light width on negative or positive GH shifts and distortion in the reflected and transmitted light is investigated.

The Mott-insulator–superfluid transition for ultracold bosonic atoms in an optical lattice has been extensively studied in the framework of the Bose-Hubbard model with two-body on-site interactions. In this paper, we analyze the additional effect of the three-body on-site interactions on this phase transition in an optical lattice and the transitions between the various phases that arise in an optical superlattice. Using the mean-field theory and the density matrix renormalization group method, we find the phase diagrams depicting the relationships between various physical quantities in an optical lattice and superlattice. We also propose a possible experimental signature to observe the on-site three-body interactions.

In this Rapid Communication we discuss how red-sideband cooling is modified in the single-photon strong-coupling regime of cavity optomechanics where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. Using Fermi's golden rule we calculate the transition rates induced by the optical drive without linearizing the optomechanical interaction. In the resolved-sideband limit we find multiple-phonon cooling resonances for strong single-photon coupling that lead to nonthermal steady states including the possibility of phonon antibunching. Our study generalizes the standard linear cooling theory.

The scattering properties of randomly layered optical media with $\mathcal{PT}$-symmetric index of refraction are studied using the transfer-matrix method. We find that the transmittance decays exponentially as a function of the system size, with an enhanced rate ${\xi }_{\gamma }{\left(W\right)}^{-1}={\xi }_0{\left(W\right)}^{-1}+{\xi }_{\gamma }{\left(0\right)}^{-1}$, where ${\xi }_0\left(W\right)$ is the localization length of the equivalent passive random medium and ${\xi }_{\gamma }\left(0\right)$ is the attenuation and amplification length of the corresponding perfect system with a $\mathcal{PT}$-symmetric refraction index profile. While transmittance processes are reciprocal to left- and right-incident waves, the reflectance is enhanced from one side and is inversely suppressed from the other, thus allowing such $\mathcal{PT}$-symmetric random media to act as unidirectional coherent absorbers.

Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for $\pi /2$ and $\pi$ pulses and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from $\pi /2$ and $\pi$ pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, postfacto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.

The field-free molecular orientation of CO by a terahertz few-cycle pulse was studied theoretically. The effects of the laser intensity and pulse duration on the molecular orientation, which is created by the terahertz few-cycle pulse, were discussed. Furthermore, it was shown that the enhancement or suppression of the molecular orientation can be coherently manipulated by precisely controlling the carrier-envelope phase of the terahertz few-cycle pulse. Compared with other orientation techniques, better orientation can be achieved by a terahertz few-cycle pulse at lower intensities.

We report the experiment on probing the one-body spectral function in a trapped noninteracting ${}^{40}$K Fermi gas by means of the momentum-resolved Raman spectroscopy. The experimental result is in good agreement with the expected quadratic dispersion in the noninteracting regime. Through the comparison with the radio-frequency spectrum, we found that the Raman spectrum shows some new characteristics.

We study the dynamical response of a Tonks-Girardeau gas on a ring induced by a moving $\delta$-barrier potential. An exact solution based on the time-dependent Bose-Fermi mapping allows us to obtain the particle current, its fluctuations and the drag force acting on the barrier. The exact solution is analyzed numerically as well as analytically in the perturbative regime of weak barrier strength. In the weak barrier limit the stirring drives the system into a state with net zero current for velocities $v$ lower than $v_c=\pi \hslash /mL$, with $m$ the atomic mass and $L$ the ring circumference. At $v$ approaching $v_c$, angular momentum can be transferred to the fluid and a nonzero drag force arises. The existence of a velocity threshold for current generation indicates superfluid-like behavior of the mesoscopic Tonks-Girardeau gas, different from the nonsuperfluid behavior predicted for Tonks-Girardeau gas in an infinite tube.

We study two-component solitons and their symmetry-breaking bifurcations (SBBs) in linearly coupled photonic systems with a spatially inhomogeneous strength of the coupling. One system models an inverted virtual photonic crystal, built by periodically doping the host medium with atoms implementing the electromagnetically induced transparency (EIT). In this system, two soliton-forming probe beams with different carrier frequencies are mutually coupled by the EIT-induced effective linear interconversion. The system is described by coupled nonlinear Schrödinger (NLS) equations for the probes, with the linear-coupling constant periodically modulated in space according to the density distribution of the active atoms. The type of the SBB changes from sub- to supercritical with the increase of the total power of the probe beams, which does not occur in systems with constant linear-coupling constants. Qualitatively similar results for the SBB of two-component solitons are obtained, in an exact analytical form, in the model of a fused dual-core waveguide, with the linear coupling concentrated at a point.

In this paper, we present a systematic study of beam shifts and angular momenta of paraxial vortex beams at air–left-handed-material (LHM) interfaces. It is shown that, compared to their counterparts at air–right-handed-material (RHM) interfaces, the spatial Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts remain the same, while the angular GH and IF shifts are reversed at air-LHM interfaces. The spatial and angular shifts of paraxial vortex beams have their respective origins in transverse angular momenta and transverse linear momenta. The spatial GH and IF shifts remain unreversed as a result of both reversions of transverse angular momenta and $z$-component linear momentum, while the angular GH and IF shifts are reversed because the $z$-component linear momentum is reversed and the transverse linear momenta are unreversed at air-LHM interfaces. In addition, we perform a quantitative analysis on spin-orbit angular momentum conversion and orbit-orbit angular momentum conversion, which further helps us understand the essence of vortex beam shifts at air-LHM interfaces and their fundamental distinctions from those at air-RHM interfaces.

A scheme for quasi-phase-matching high-harmonic generation is proposed in which polarization beating within a hollow core birefringent waveguide modulates the generation of harmonics. The evolution of the polarization of a laser pulse propagating in a birefringent waveguide is calculated and is shown to periodically modulate the harmonic generation process. The optimum conditions for achieving quasi-phase-matching using this scheme are explored and the growth of the harmonic intensity as a function of experimental parameters is investigated.

We show that a flying particle, such as an electron or a photon, scattering along a one-dimensional waveguide from a pair of static spin-$\frac{1}{2}$ centers, such as quantum dots, can implement a controlled-z gate (universal for quantum computation) between them. This occurs quasideterministically in a single scattering event, with no need for any postselection or iteration and without demanding the flying particle to bear any internal spin. We show that an easily matched hard-wall boundary condition along with the elastic nature of the process are key to such performances.

We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin-Bell inequality. For a small number of outcomes, we verify that our inequalities define facets of the polytope of local correlations. We investigate the quantum violations of these inequalities, in particular with respect to the Hilbert space dimension. We provide strong evidence that the maximal quantum violation can be reached only using systems with local Hilbert space dimension exceeding the number of measurement outcomes. This suggests that our inequalities can be used as multipartite dimension witnesses.

In quantum physics, all measured observables are subject to statistical uncertainties, which arise from the quantum nature as well as the experimental technique. We consider the statistical uncertainty of the so-called sampling method, in which one estimates the expectation value of a given observable by empirical means of suitable pattern functions. We show that if the observable can be written as a function of a single directly measurable operator, the variance of the estimate from the sampling method equals to the quantum-mechanical one. In this sense, we say that the estimate is on the quantum-mechanical level of uncertainty. In contrast, if the observable depends on noncommuting operators (e.g., different quadratures), the quantum-mechanical level of uncertainty is not achieved. The impact of the results on quantum tomography is discussed, and different approaches to quantum tomographic measurements are compared. It is shown explicitly for the estimation of quasiprobabilities of a quantum state, that balanced homodyne tomography does not operate on the quantum-mechanical level of uncertainty, while the unbalanced homodyne detection does.

We propose an experiment that realizes a symmetric informationally complete (SIC) probability-operator measurement (POM) in the four-dimensional Hilbert space of a qubit pair. The qubit pair is carried by a single photon as a polarization qubit and a path qubit. The implementation of the SIC POM is accomplished with the means of linear optics. The experimental scheme exploits an approach to SIC POMs that uses a two-step process: a measurement with full-rank outcomes, followed by a projective measurement on a basis that is chosen in accordance with the result of the first measurement. The basis of the first measurement and the four bases of the second measurements are pairwise unbiased—a hint at a possibly profound link between SIC POMs and mutually unbiased bases.

We consider the implementation of a symmetric informationally complete probability-operator measurement (SIC POM) in the Hilbert space of a $d$-level system by a two-step measurement process: a diagonal-operator measurement with high-rank outcomes, followed by a rank-1 measurement in a basis chosen in accordance with the result of the first measurement. We find that any Heisenberg-Weyl group-covariant SIC POM can be realized by such a sequence where the second measurement is simply a measurement in the Fourier basis, independent of the result of the first measurement. Furthermore, at least for the particular cases studied, of dimensions 2, 3, 4, and 8, this scheme reveals an unexpected operational relation between mutually unbiased bases and SIC POMs; the former are used to construct the latter. As a laboratory application of the two-step measurement process, we propose feasible optical experiments that would realize SIC POMs in various dimensions.

We study the decoherence of a central spin $1/2$ due to a closed environment composed of spin-$1/2$ particles. It is known that a frustrated spin environment, such as a spin glass, is much more efficient for decoherence of the central spin than a similar-size environment without frustration. We construct a Hamiltonian where the degree of frustration is parametrized by a single parameter $\kappa$. By use of this model we find that the environment can be classified by two distinct regimes with respect to the strength of level repulsion. These regimes behave qualitatively different with respect to decoherence of the central spin and might explain the strong enhancement of decoherence observed for frustrated environments.