Optical bistability (BI) and self-pulsation (SP) in high-$Q$ silicon microring resonators (MRRs) induced by thermo-optical (TO) effect and other nonlinear effects are theoretically studied with coupled mode theory and linear stability analysis method. It is found that the boundaries for both BI and SP are mainly restricted by two counteracting effects: free carrier dispersion effect and TO effect. If the refractive index changes of a MRR caused by these two effects are on the same order of magnitude, the output power will exhibit much more complicated dependence on the input power and wavelength, namely, input-power-dependent multi-BI and multi-SP regions will exist at certain input wavelength range. The controllability of multi-BI and multi-SP phenomena by the input power and input wavelength could be very useful in all-optical nonlinear devices.

The proposed all-optical amplification scenario is based on the properties of light propagation in two coupled subwavelength metallic slab waveguides where, for a particular choice of waveguide parameters, two eigenmodes coexist: propagating (symmetric) and nonpropagating (antisymmetric). For such a setup incident beams realize boundary conditions for forming a stationary state as a superposition of the mentioned eigenmodes. It is shown both analytically and numerically that the amplification rate in this completely linear mechanism diverges for small signal values.

The Faraday rotation angle $\Theta$ is calculated in a diffusive regime on a three-dimensional disordered slab. It is shown that $\tan \Theta$ is (i) an oscillating function of the magnetic field or the medium's internal properties, and (ii) proportional to the ratio of the inelastic mean-free path $l_{\mathrm{in}}$ to the mean-free path $l$, that is, to the average number of photon scatterings. The maximum rotation is achieved at frequencies when the photon's elastic mean-free path is minimal. We have obtained the rotation angle of backscattered light taking into account the maximally crossed diagrams. The latter leads to an ellipticity in the backscattered wave that can serve as a precursor of weak localization. The critical strength of the magnetic field is $B_c\sim g_c\sim \lambda /l$ beyond which rotation in the backscattered wave disappears. The traversal time of an electromagnetic wave through the slab is estimated in a diffusive regime. The disorder enhanced the traversal time by an additional factor $l_{\mathrm{in}}/l$ in comparison with a free light propagation time. Comparison with the experimental data is carried out.

The interaction between dielectric particles and a laser-driven optical cavity gives rise to both conservative and dissipative dynamics, which can be used to levitate, trap, and cool nanoparticles. We analytically and numerically study a two-mode setup in which the optical potentials along the cavity axis cancel, so that the resulting dynamics is almost purely dissipative. For appropriate detunings of the laser drives, this dissipative optomechanical dynamics can be used to sort particles according to their size, to rectify their velocities, and to enhance transverse cooling.

We investigate algebraic bright and vortex solitons in self-defocusing (SDF) media with a type of spatially inhomogeneous nonlinearity. For a specific choice of the nonlinearity parameters, certain exact analytical solutions for algebraic bright and vortex solitons have been constructed. By applying the linear stability analysis, the stability regions of these algebraic solitons are obtained numerically. In addition, we show analytically that a homogeneous SDF nonlinearity superposed by a localized self-focusing nonlinearity can support exact algebraic bright solitons under certain conditions.

Although there is no consensus regarding the “reality” of the past of a quantum particle, in situations where there is only one trajectory with a nonvanishing quantum wave of the particle between its emission and detection points, it seems “safe” to associate the past of the particle with this trajectory. A method for analyzing the past of a quantum particle according to the weak trace it leaves is proposed. Such a trace can be observed via measurements performed on an ensemble of identically pre- and postselected particles. Examples in which this method contradicts the above common sense description of the past of the particle are presented. It is argued that it is possible to describe the past of a quantum particle, but the naive approach has to be replaced by both forward- and backward-evolving quantum states.

A hybrid quantum system is proposed by coupling the internal hyperfine transitions of a trapped atomic Bose-Einstein condensate (BEC) and a superconducting quantum interference device (SQUID) via the macroscopic quantum field of the flux qubit. The presence of the condensate leads to a bosonic enhancement of the Rabi frequency over the otherwise small single-particle magnetic-dipole transition matrix elements. This enhancement makes it possible to rapidly transfer and store qubit states in the BEC that were originally prepared in the SQUID. The fidelity of this transfer for different states is calculated, and a direct experimental protocol to determine the transfer fidelity by quantum tomography of the BEC qubit is presented.

We assess the two-photon exchange contribution to the Lamb shift in muonic hydrogen with forward dispersion relations. The subtraction constant $\overline{T}(0,Q^2)$ that is necessary for a dispersive evaluation of the forward doubly virtual Compton amplitude, through a finite-energy sum rule, is related to the fixed $J=0$ pole generalized to the case of virtual photons. We evaluated this sum rule using excellent virtual photoabsorption data that are available. We find that the “proton polarizability correction” to the Lamb shift in muonic hydrogen is $-(40\pm 5)\mu$eV. We conclude that nucleon structure-dependent uncertainty by itself is unlikely to resolve the large (300 $\mu$eV) discrepancy between direct measurement of the Lamb shift in $\mu$H and expectations based on conventional hydrogen measurements.

We demonstrate a controllable highly efficient electrostatic surface guide for ND${}_3$ molecules in the weak-field-seeking states on a ceramic substrate over a distance of 840 mm, and study the dependences of the relative molecule number (or the overall transmission efficiency) of our single-wire guide and the guiding-center positions on the guiding voltages, both experimentally and theoretically. Our study shows that the guiding-center position and the number of the guided molecules can be easily controlled by adjusting the guiding voltages, and find that an overall transmission efficiency of higher than 50$\%$ in a single quantum state can be obtained. Our experimental results are consistent with ones of Monte Carlo simulations. Also, we discuss the transverse velocity filtering effect and the acceptance of the guided molecules in four-dimensional phase space. Both the transmission efficiency and the acceptance in two-dimensional position space are higher than that in our previous two-wire guide [Y. Xia, Y. Yin, H. Chen, L. Deng, and J. Yin, Phys. Rev. Lett. 100, 043003 (2008)].

We explore high-order harmonic generation (HHG) from a graphene sheet exposed to intense femtosecond laser pulses based on the Lewenstein model. It is demonstrated that the HHG cutoff frequency increases with graphene size up to the classical limit for distant diatomic systems. In contrast to two-center systems, the cutoff frequency remains constant with increasing power of the harmonics as the graphene diameter extends beyond maximal electron excursion. It is shown that the extended nature of the graphene sheet allows for strong HHG signals at maximum cutoff for linearly as well as circularly polarized laser pulses, the latter opening for generation of strong circularly polarized attosecond pulses.

In photonic crystal (PC) gratings whose structural symmetry is broken owing to one-side corrugations, the Rayleigh-Wood anomalies can appear in a one-way manner. In the combination with the vanishing coupling to the lowest Floquet-Bloch mode at the upper band edge, these anomalies lead to the appearance of the defect-mode-like, i.e., very narrow one-way transmission, peak, which cannot appear in the corresponding slab of PC without corrugations. Such a sole peak can be transformed into a one-way transmission band with a desired width by varying angle of incidence. The nonoverlapping and thus switchable one-way (higher-order) and two-way (zero-order) transmission bands can be obtained in both the frequency and incidence-angle domains. Adjustment of PC lattice and corrugation parameters allows one to obtain two subsequent one-way bands, every being connected with a certain higher diffraction order. Conditions required for the appearance of a narrow one-way transmission band in the vicinity of a Rayleigh-Wood anomaly are well consistent with typical dispersion features of a very large class of PCs and do not need unusual performances.

This paper introduces the exact, analytic integration of all final state variables for the process of nonlinear Compton scattering in an intense plane-wave laser pulse, improving upon a previously slow and challenging numerical approach. Computationally simple and insightful formulas are derived for the total scattering probability and mean energy momentum of the emitted radiation. The general form of the effective mass appears explicitly. We consider several limiting cases and present a quantum correction to Larmor's formula. Numerical results are plotted and analyzed in detail.

We report an experimental study of recently formulated entropic Leggett-Garg inequality (ELGI) by Usha Devi et al. [Phys. Rev. A 87, 052103 (2013)]. This inequality places a bound on the statistical measurement outcomes of dynamical observables describing a macrorealistic system. Such a bound is not necessarily obeyed by quantum systems, and therefore provides an important way to distinguish quantumness from classical behavior. Here we study ELGI using a two-qubit nuclear magnetic resonance system. To perform the noninvasive measurements required for the ELGI study, we prepare the system qubit in a maximally mixed state as well as use the “ideal negative result measurement” procedure with the help of an ancilla qubit. The experimental results show a clear violation of ELGI by over four standard deviations. These results agree with the predictions of quantum theory. The violation of ELGI is attributed to the fact that certain joint probabilities are not legitimate in the quantum scenario, in the sense they do not reproduce all the marginal probabilities. Using a three-qubit system, we also demonstrate that three-time joint probabilities do not reproduce certain two-time marginal probabilities.

We formulate entropic Leggett-Garg inequalities, which place constraints on the statistical outcomes of temporal correlations of observables. The information theoretic inequalities are satisfied if macrorealism holds. We show that the quantum statistics underlying correlations between time-separated spin component of a quantum rotor mimics that of spin correlations in two spatially separated spin-$s$ particles sharing a state of zero total spin. This brings forth the violation of the entropic Leggett-Garg inequality by a rotating quantum spin-$s$ system in a similar manner as does the entropic Bell inequality [S. L. Braunstein and C. M. Caves, Phys. Rev. Lett. 61, 662 (1988)] by a pair of spin-$s$ particles forming a composite spin singlet state.

Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with memory by endowing the walker with multiple recycled coins and using a physical memory function via a history dependent coin flip. By numerical simulation we observe several phenomena. First in one dimension, walkers with memory have persistent quantum ballistic speed up over classical walks just as found in previous studies of multicoined walks with trivial memory function. However, measurement of the multicoin state can dramatically shift the mean of the spatial distribution. Second, we consider spatial entanglement in a two-dimensional quantum walk with memory and find that memory destroys entanglement between the spatial dimensions, even when entangling coins are employed. Finally, we explore behavior in the presence of spatial randomness and find that in the time regime where single-coined walks localize, multicoined walks do not and in fact a memory function can speed up the walk relative to a multicoin walker with no memory. We explicitly show how to construct linear optics circuits implementing the walks, and discuss prospects for classical simulation.

We measure the collision-rate coefficient between laser-cooled rubidium (Rb) atoms in a magneto-optical trap (MOT) and optically dark Rb${}^{+}$ ions in an overlapping Paul trap. In such a mixture, the ions are created from the MOT atoms and allowed to accumulate in the ion trap, which results in a significant reduction in the number of steady-state MOT atoms. A theoretical rate-equation model is developed to describe the evolution of the MOT atom number due to ionization and ion-atom collisions, and we derive an expression for the ion-atom collision-rate coefficient. The loss of MOT atoms is studied systematically by sequentially switching on the various mechanisms in the experiment. Combining the measurements with the model allows the direct determination of the ion-atom collision-rate coefficient. Finally, the scope of the experimental technique developed here is discussed.

Nonlinear optics experiments measuring phase shifts induced in a weak probe pulse by a strong pump pulse must account for coherent effects that only occur when the pump and probe pulses are temporally overlapped. It is well known that a weak probe beam experiences a greater phase shift from a strong pump beam than the pump beam induces on itself. The physical mechanism behind the enhanced phase shift is diffraction of pump light into the probe direction by a nonlinear refractive index grating produced by interference between the two beams. For an instantaneous third-order response, the effect of the grating is to simply double the probe phase shift, but when delayed nonlinearities are considered, the effect is more complex. A comprehensive treatment is given for both degenerate and nondegenerate pump-probe experiments in noble and diatomic gases. Results of numerical calculations are compared to a recent transient birefringence measurement [Loriot et al., Opt. Express 17, 13429 (2009)] and a recent spectral interferometry experiment [Wahlstrand et al., Phys. Rev. A 85, 043820 (2012)]. We also present results from two new experiments using spectrally resolved transient birefringence with 800 nm pulses in Ar and air and degenerate chirped pulse spectral interferometry in Ar. Both experiments support the interpretation of the negative birefringence at high intensity as arising from a plasma grating.

We present a theoretical study of a multiatom cavity quantum electrodynamics system consisting of three-level atoms confined in a cavity and interacting with a control laser from free space. A probe laser is coupled into the cavity, and the transmitted cavity field and reflected probe field from the cavity are analyzed. We show that the free-space control laser induces large nonlinearities for the intracavity probe field, which can be used to control the amplitude and phase of the reflected probe light and the transmitted probe light. Under appropriate conditions, large cross-phase modulation for the reflected and transmitted light fields can be obtained with a weak control field, which renders the system useful for studies of all-optical switching and quantum phase gates.

The partial transposition of a two-qubit state has at most one negative eigenvalue and all the eigenvalues lie in $[-1/2,1]$. In this Brief Report, we extend this result by Sanpera et al. [A. Sanpera, R. Tarrach, and G. Vidal, Phys. Rev. A 58, 826 (1998)] to arbitrary bipartite states. We show that partial transposition of an $m\otimes n$ state cannot have more than $(m-1)(n-1)$ number of negative eigenvalues. Low-dimensional states have been studied to show the tightness of this result and explicit examples have been provided for $mn\le 9$. It is also shown that all the eigenvalues of partial transposition lie within $[-1/2,1]$. Some possible applications are also discussed.

We discuss representation of single-mode purity-preserving conditional Gaussian quantum operations by complex symplectic matrices. This formalism allows us to efficiently determine the result of concatenation of several probabilistic purity-preserving Gaussian operations. We present several examples of application of this formalism and discuss canonical forms of the considered single-mode conditional Gaussian operations.