We propose a method for trapping weak signal pulses by soliton and realizing its trajectory control via electromagnetically induced transparency (EIT). The system we consider is a cold, coherent atomic gas with a tripod or multipod level configuration. We show that, due to the giant enhancement of Kerr nonlinearity contributed by EIT, several weak signal pulses can be effectively trapped by a soliton and cotravel stably with ultraslow propagating velocity. Furthermore, we demonstrate that the trajectories of the soliton and the trapped signal pulses can be manipulated by using a Stern-Gerlach gradient magnetic field. As a result, the soliton and the trapped signal pulses display a Stern-Gerlach deflection and both of them can bypass an obstacle together. The results predicted here may be used to design all-optical switching at very low light level.

We report a rigorous derivation of the power spectral density (PSD) spectrum of the phase noise in the transmitted and reflected signals of a Fabry-Pérot (FP) interferometer. In transmission off and on resonance, the PSD at low frequencies is found to be simply equal to the PSD of the single-pass phase noise (the phase noise acquired by a signal that has traveled once through the FP interferometer) times ${(n_g/n)}^2$, where $n_g$ is the group index and $n$ the phase index of the light inside the FP interferometer. Equivalently, the phase noise (in radians) is equal to the single-pass phase-noise times $n_g/n$. This result states that the phase noise is proportional to the number of passes light makes through the FP interferometer, as expected physically. This simple expression provides a quick means of calculating the phase noise in a linear Fabry-Pérot interferometer of any length in the range of frequencies of interest to the most applications. At high frequencies, we show that the PSD spectrum can also be expressed in a simple closed-form expression on resonance, but that off resonance it must be calculated numerically. Numerical simulations show that the PSD oscillates between 3 dB below the low-frequency PSD and 3 dB below the single-pass PSD. Equivalent expressions are derived for the phase noise in the signal reflected by a Fabry-Pérot interferometer, which is found to have the same magnitude at low frequencies, but to be typically significantly lower at high frequencies.

We investigate how to control single-photon transport along the photonic crystal waveguide with the recent experimentally demonstrated artificial atoms [i.e., $\Lambda$-type quantum dots (QDs)] [S. G. Carter et al., Nat. Photon. 7, 329 (2013)] in an all-optical way. Adopting full quantum theory in real space, we analytically calculate the transport coefficients of single photons scattered by a $\Lambda$-type QD embedded in single- and two-mode photonic crystal cavities (PCCs), respectively. Our numerical results clearly show that the photonic transmission properties can be exactly manipulated by adjusting the coupling strengths of waveguide-cavity and QD-cavity interactions. Specifically, for the PCC with two degenerate orthogonal polarization modes coupled to a $\Lambda$-type QD with two degenerate ground states, we find that the photonic transmission spectra show three Rabi-splitting dips and the present system could serve as single-photon polarization beam splitters. The feasibility of our proposal with the current photonic crystal technique is also discussed.

We study the non-Markovian quantum dynamics of an emitter inside an open multimode cavity, focusing on the case where the emitter is resonant with high-frequency cavity modes. Based on a Green's-function technique suited for open photonic structures, we study the crossovers between three distinct regimes as the coupling strength is gradually increased: (i) overdamped decay with a time scale given by the Purcell modified decay rate, (ii) underdamped oscillations with a time scale given by the effective vacuum Rabi frequency, and (iii) pulsed revivals. The final multimode strong-coupling regime (iii) gives rise to quantum revivals of the atomic inversion on a time scale associated with the cavity round-trip time. We show that the crucial parameter to capture the crossovers between these regimes is the nonlinear Lamb shift, accounted for exactly in our formalism.

We show that the exclusivity (E) principle singles out the set of quantum correlations associated with any exclusivity graph assuming the set of quantum correlations for the complementary graph. Moreover, we prove that, for self-complementary graphs, the E principle, by itself (i.e., without further assumptions), excludes any set of correlations strictly larger than the quantum set. Finally, we prove that, for vertex-transitive graphs, the E principle singles out the maximum value for the quantum correlations assuming only the quantum maximum for the complementary graph. This opens the door for testing the impossibility of higher-than-quantum correlations in experiments.

We focus here on the uncertainty of an observable $Y$ caused by a precise measurement of $X$. We illustrate the effect by analyzing the general scenario of two successive measurements of spin components $X$ and $Y$. We derive an optimized entropic uncertainty limit that quantifies the necessary amount of uncertainty observed in a subsequent measurement of $Y$. We compare this bound to recently derived error-disturbance relations and discuss how the bound quantifies the information of successive quantum measurements.

Kochen-Specker theorems assure the breakdown of certain types of noncontextual hidden-variable theories through the nonexistence of global, holistic frame functions; however, they do not allow us to identify where this breakdown occurs, nor the extent of it. It was recently shown [Phys. Rev. A 86, 062109 (2012)] that this breakdown does not occur everywhere; here we show that it is maximal in that it occurs almost everywhere and thus prove that quantum indeterminacy, often referred to as contextuality or value indefiniteness, is a global property as is often assumed. In contrast to the Kochen-Specker theorem, we only assume the weaker noncontextuality condition that any potential value assignments that may exist are locally noncontextual. Under this assumption, we prove that once a single arbitrary observable is fixed to occur with certainty, almost (i.e., with Lebesgue measure one) all remaining observables are indeterminate.

The adiabatic theorem addresses the dynamics of a target instantaneous eigenstate of a time-dependent Hamiltonian. We use a Feshbach P-Q partitioning technique to derive a closed one-component integro-differential equation. The resultant equation properly traces the footprint of the target eigenstate. The physical significance of the derived dynamical equation is illustrated by both general analysis and concrete examples. We find an interesting phenomenon showing that a dephasing white noise can enhance and even induce adiabaticity. This phenomenon, distinguishing itself from any artificial control process, may occur in natural physical processes. We also show that particular white noises can shorten the total duration of dynamic processing, such as in adiabatic quantum computing.

The classical dynamics for a charged spin particle is governed by the Lorentz force equation for orbital motion and by the Thomas-Bargmann-Michel-Telegdi (T-BMT) equation for spin precession. In static and homogeneous electromagnetic fields, it has been shown that the Foldy-Wouthuysen (FW) transform of the Dirac-Pauli Hamiltonian, which describes the relativistic quantum theory for a spin-$1/2$ particle, is consistent with the classical Hamiltonian (with both the orbital and spin parts) up to the order of $1/m^{14}$ ($m$ is the particle's mass) in the low-energy and weak-field limit. In this paper, we extend this correspondence to the case of inhomogeneous fields. Regardless of the field gradient (e.g. Stern-Gerlach) force, the T-BMT equation is unaltered and thus the classical Hamiltonian remains the same, but subtleties arise and need to be clarified. For the relativistic quantum theory, we apply Eriksen's method to obtain the exact FW transformations for the two special cases, which in conjunction strongly suggest that, in the weak-field limit, the FW transformed Dirac-Pauli Hamiltonian (except for the Darwin term) is in agreement with the classical Hamiltonian in a manner that classical variables correspond to quantum operators via a specific Weyl ordering. Meanwhile, the Darwin term is shown to have no classical correspondence.

Quantum steering is the ability to remotely prepare different quantum states by using entangled pairs as a resource. Very recently, the concept of steering has been quantified with the use of inequalities, leading to substantial applications in quantum information and communication science. Here, we highlight that there exists a natural temporal analog of the steering inequality when considering measurements on a single object at different times. We give nontrivial operational meaning to violations of this temporal inequality by showing that it is connected to the security bound in the Bennett-Brassard 1984 protocol and thus may have applications in quantum communication.

We apply a flexible numerical integrator to the simulation of adiabatic quantum computation with nonlinear paths. We find that a nonlinear path may significantly improve the performance of adiabatic algorithms versus the conventional straight-line interpolations. The employed integrator is suitable for solving the time-dependent Schrödinger equation for any qubit Hamiltonian. Its flexible storage format significantly reduces cost for storage and matrix-vector multiplication in comparison to common sparse matrix schemes.

A major challenge to the control of infinite-dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space domain and show that by utilizing the implications of the quantum recurrence theorem this irreversibility may be overcome, in the case of individual states more generally, but also in certain specified cases over larger subsets of the Hilbert space. We discuss briefly the possibility of using these results in the control of infinite-dimensional coupled harmonic oscillators and also draw attention to some of the issues and open questions arising from this and related work.

In a practical continuous-variable quantum-key distribution (CVQKD), the fluctuations of the local oscillator (LO) not only make the normalization of Bob's measurement outcomes difficult, but also can change the signal-to-noise ratio (SNR) of an imperfect balanced homodyne detector (BHD), which may lead the security of a practical system of CVQKD to be compromised severely. In this paper, we propose that the LO intensity can be manipulated by the legitimate parties, i.e., being tuned and stabilized to a required constant value, to eliminate the impact of LO fluctuations and defeat Eve's potential attack on the LO. Moreover, we show that the secret key rate can be increased over a noisy channel, especially the channels of metropolitan QKD networks, by tuning the intensity of LO and thus the SNR of a practical BHD to an optimal value, and we find that, counterintuitively, the requirement on BHD (i.e., high detection efficiency and low electronic noise) can also be reduced in this case. To realize this manipulation, we give a schematic setup which, thus, can be used to enhance the security of a practical CVQKD system.

Single-mode squeezing and Fourier transformation operations are two essential logical gates in continuous-variable quantum computation, which have been experimentally implemented by means of an optical four-mode cluster state. In this paper, we present a simpler and more efficient protocol based on the use of Einstein-Podolsky-Rosen two-mode entangled states to realize the same operations. The theoretical calculations and the experimental results demonstrate that the presented scheme not only decreases the requirement to the resource quantum states at the largest extent but also enhances significantly the squeezing degree and the fidelity of the resultant modes under an identical resource condition. That is because in our system the influence of the excess noises deriving from the imperfect squeezing of the resource states is degraded. The gate operations applying two-mode entanglement can be utilized as a basic element in a future quantum computer involving a large-scale cluster state.

A quantum electrodynamics (QED) correction surface for the simplest polyatomic and polyelectronic system ${{\mathrm{H}}_3}^{+}$ is computed using an approximate procedure. This surface is used to calculate the shifts to vibration-rotation energy levels due to QED; such shifts have a magnitude of up to 0.25 cm${}^{-1}$ for vibrational levels up to 15 000 cm${}^{-1}$ and are expected to have an accuracy of about 0.02 cm${}^{-1}$. Combining our ${{\mathrm{H}}_3}^{+}$ QED correction surface with existing highly accurate Born-Oppenheimer, relativistic, and adiabatic components suggests that deviations of the resulting ab initio energy levels from observed ones are largely due to nonadiabatic effects.

The two-electron Schrödinger equation at the two-particle coalescences was studied for atomic three-body systems in S states. The general differential equation in three variables was reduced to the centrally symmetric field problem for the case of electron-nucleus and electron-electron coalescence lines. Specific potentials describing attractive and repulsive interactions between the coalesced pair of the electron and nucleus and the two coalesced electrons, respectively, were derived and studied. Interesting features of these potentials in the vicinity of the triple-coalescence point were found. The ground states of the helium atom, the negative ion of hydrogen, and the positive ion of lithium were explored as the typical examples of the helium isoelectronic sequence.

We report our study on coherent population trapping (CPT) in a $\Lambda$ configuration coupled by magnetic dipole interactions. The $\Lambda$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the $nP$ manifold via an optical transition on one of the spectroscopic $D$ lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.

Photoelectron spectra of Ce${}^{-}$ obtained using both 2.33- and 3.49-eV photon energies resolve numerous transitions between the ${}^4{H}_{7/2}$ ($\cdots$4$f$ 5$d^2$ 6$s^2$) anion ground state and excited neutral states, in addition to transitions from excited anion states to the ground and excited neutral states. Building on the theoretical work of O’Malley and Beck [S. M. O’Malley and D. R. Beck, Phys. Rev. A 74, 042509 (2006)] and the known term energies of Ce excited states, we determined the adiabatic electron affinity of Ce to be 0.570(20) eV, which is lower than previously reported experimental values. The term energy of the lowest-energy excited anion state arising from the $\cdots$4$f$ 5$d$ 6$s^2$ 6$p$ configuration was also determined to be 0.210(20) eV.

We employ spin-dependent optical dipole forces to characterize the transverse center-of-mass (COM) motional mode of a two-dimensional Wigner crystal of hundreds of ${}^9$Be${}^{+}$. By comparing the measured spin dephasing produced by the spin-dependent force with the predictions of a semiclassical dephasing model, we obtain absolute mode temperatures in excellent agreement with both the Doppler laser cooling limit and measurements obtained from a previously published technique [B. C. Sawyer et al., Phys. Rev. Lett. 108, 213003 (2012)]. Furthermore, the structure of the dephasing histograms allows for discrimination between initial thermal and coherent states of motion. We also apply the techniques discussed here to measure the ambient-heating rate of the COM mode of a 2D Coulomb crystal in a Penning trap. This measurement places an upper limit on the anomalous single-ion heating rate due to electric field noise from the trap electrode surfaces of $\frac{d\overline{n}}{dt}\sim 5$ s${}^{-1}$ for our trap at a frequency of 795 kHz, where $\overline{n}$ is the mean occupation of quantized COM motion in the axial harmonic well.