We investigate performances of pure continuous variable states in discriminating thermal and identity channels by comparing their $M$-copy error-probability bounds. This offers us a simplified mathematical analysis for quantum target detection with slightly modified features: the object—if it is present—perfectly reflects the signal beam irradiating it, while thermal noise photons are returned to the receiver in its absence. This model facilitates us to obtain analytic results on error-probability bounds, i.e., the quantum Chernoff bound and the lower bound constructed from the Bhattacharya bound on $M$-copy discrimination error probabilities of some important quantum states, like photon number states, $\text{N}$-photon maximally entangled (N00N) states, coherent states and the entangled photons obtained from spontaneous parametric down conversion (SPDC). Comparing the $M$-copy error-bounds, we identify that path-entangled states indeed offer enhanced sensitivity than the photon number state system, when average signal photon number is small compared to the thermal noise level. However, in the high signal-to-noise scenario, N00N states fail to be advantageous than the photon number states. Entangled SPDC photon pairs too outperform conventional coherent state system in the low signal-to-noise case. On the other hand, conventional coherent state system surpasses the performance sensitivity offered by entangled photon pair, when the signal intensity is much above that of thermal noise. We find an analogous performance regime in the lossy target detection (where the target is modeled as a weakly reflecting object) in a high signal-to-noise scenario.

The cross section for resonant ion-pair formation in the collision of low-energy electrons with ${\text{HF}}^{+}$ is calculated by the solution of the time-dependent Schrödinger equation with multiple coupled states using a wave-packet method. A diabatization procedure is proposed to obtain the electronic couplings between quasidiabatic potentials of ${{}^1\Sigma }^{+}$ symmetry for HF. By including these couplings between the neutral states, the cross section for ion-pair formation increases with about 2 orders of magnitude compared to the cross section for direct dissociation. Qualitative agreement with the measured cross section is obtained. The oscillations in the calculated cross section are analyzed. The cross section for ion-pair formation in electron recombination with ${\text{DF}}^{+}$ is calculated to determine the effect of isotopic substitution.

The creation of single collective excitations in atomic ensembles via spontaneous Raman emission plays a key role in several quantum communication protocols, starting with the seminal Duan-Lukin-Cirac-Zoller protocol [L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature (London) 414, 413 (2001)]. This process is usually analyzed theoretically under the assumptions that the write laser pulse inducing the Raman transition is far off resonance and that the atomic ensemble is only homogeneously broadened. Here we study the impact of near-resonance excitation for inhomogeneously broadened ensembles on the collective character of the created atomic excitation. Our results are particularly relevant for experiments with hot atomic gases and for potential future solid-state implementations.

We analytically derive the general pseudopotential operator of an arbitrary isotropic interaction for particles confined in two-dimensional (2D) systems using the frame work developed by Huang and Yang for three-dimensional scattering. We also analytically derive the low-energy dependence of the scattering phase shift for an arbitrary interaction with a power-law decaying tail, $V_{2\text{D}}\left(\rho \right)\propto {\rho }^{-\alpha }$ (for $\alpha >2$). We apply our results to the 2D dipolar gases $\left(\alpha =3\right)$ as an example, calculating the momentum and dipole moment dependences of the pseudopotential for both $s$- and $p$-wave scattering channels if the two scattering particles are in the same 2D layer. Results for the $s$-wave scattering between particles in two different (parallel) layers are also investigated. Our results can be directly applied to the systems of dipolar atoms and/or polar molecules in a general 2D geometry.

We consider an array of waveguides with identical widths but alternating spacings using the discrete nonlinear Schrödinger model (tight-binding approximation). In the highly discrete (anticontinuous) limit when one of the spacings is infinite, the model reduces to an integrable chain of uncoupled dimers. From this limit, we identify the two fundamental, antisymmetric and symmetric, discrete gap solitons, which can be numerically continued to a continuum limit gap soliton at one band edge. Other composite solutions at the uncoupled limit disappear in bifurcations. Similarly to the case of waveguides with alternating widths and constant spacings, oscillatory instabilities appear for the fundamental solutions only for frequencies in the upper half of the gap. In contrast to the alternating-width case, there is no stability exchange between the two fundamental solutions: the symmetric solution is always unstable while the antisymmetric solution is always stable in the lower half of the gap. Thus, the Peierls-Nabarro barrier can vanish only in the continuum limit.

Multi-normal-mode splitting peaks are experimentally observed in a system with Doppler-broadened two-level atoms inside a relatively long optical cavity. In this system, the atom-cavity interaction can reach the “superstrong-coupling” condition with atom-cavity coupling strength $g\sqrt{N}$ to be near or larger than the cavity free-spectral range ${\Delta }_{\text{FSR}}$. In such case, normal-mode splitting can occur in many cavity longitudinal modes to generate the multi-normal-mode splitting peaks, which can be well explained by the linear-dispersion enhancement due to the largely increased atomic density in the cavity. Many new interesting phenomena might come out of this superstrong atom-cavity coupling regime.

We propose two schemes to generate the two-dimensional $2\times N$ and $3\times N$ cluster states by using a chain of (two-level) Rydberg atoms in the framework of cavity QED. These schemes work in a completely deterministic way and are based on the resonant interaction of the atoms in a chain with a bimodal cavity that supports two independent modes of the photon field. We demonstrate that a $2\times N$ cluster state can be generated efficiently with only a single bimodal cavity, while two such cavities are needed to produce a $3\times N$ cluster state. It is shown, moreover, how these schemes can be extended toward the generation of $M\times N$ two-dimensional cluster states.

We report here a continuous-wave, high-resolution, and all-optical quadruple resonance laser excitation experiment. To demonstrate this excitation technique, we have used an inhomogeneously broadened molecular sample $\left({\text{Na}}_2\right)$. We emphasize the enhanced ability afforded by the technique to reach new ranges of internuclear separation as well as access to a large range of molecular electronic states. Using the Autler-Townes split line shape of a rovibronic transition and the $E$ field amplitude of the corresponding coupling laser, we have measured with high precision the absolute value of the molecular electronic transition dipole moment matrix elements, with more flexibility than the double and the triple resonance based excitation schemes used previously. This technique may also be used in a stimulated Raman adiabatic passage configuration for effective transfer of ultracold molecules, formed at long internuclear distance, to the lowest vibrational level of the ground electronic state.

The electric dipole polarizabilities and hyperpolarizabilities for the lithium isotopes ${}^6\text{L}\text{i}$ and ${}^7\text{L}\text{i}$ in the ground state $2{}^{2}S$ and the excited states $2{}^{2}P$ and $3{}^{2}D$, as well as the leading resonance and dispersion long-range coefficients for the $\text{Li}\left(2{}^{2}S\right)\text{−}\text{Li}\left(2{}^{2}S\right)$ and $\text{Li}\left(2{}^{2}S\right)\text{-Li}\left(2{}^{2}P\right)$ systems, are calculated nonrelativistically using variational wave functions in Hylleraas basis sets. Comparisons are made with published results, where available. We find that the value of the second hyperpolarizability of the $2{}^{2}S$ state is sensitive to the isotopic mass due to a near cancellation between two terms. For the $3{}^{2}D$ state polarizability tensor, the calculated components disagree with those measured in the sole experiment and with those calculated semiempirically.

We use laser light near resonant with an optical bound-to-bound transition to shift the magnetic field at which a Feshbach resonance occurs. We operate in a regime of large detuning and large laser intensity. This reduces the light-induced atom-loss rate by 1 order of magnitude compared to our previous experiments [D. M. Bauer et al., Nat. Phys. 5, 339 (2009)]. The experiments are performed in an optical lattice and include high-resolution spectroscopy of excited molecular states reported here. In addition, we give a detailed account of a theoretical model that describes our experimental data.

The spontaneous relaxation rates for an atom in free space and close to an absorbing surface are calculated to various orders of the electromagnetic multipole expansion. The spontaneous decay rates for dipole, quadrupole, and octupole transitions are calculated in terms of their respective primitive electric multipole moments and the magnetic relaxation rate is calculated for the dipole and quadrupole transitions in terms of their respective primitive magnetic multipole moments. The theory of electromagnetic-field quantization in magnetoelectric materials is used to derive general expressions for the decay rates in terms of the dyadic Green’s function. We focus on the decay rates in free space and near an infinite half space. For the decay of atoms near to an absorbing dielectric surface, we find a hierarchy of scaling laws depending on the atom-surface distance $z$.

We propose a monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration, the control field is taken as a linear combination of the control field (computed by the standard algorithm) and the filtered field. The parameter of the linear combination is chosen to respect the monotonic behavior of the algorithm and to be as close to the filtered field as possible. We test the efficiency of this method on molecular alignment. Using bandpass filters, we show how to select particular rotational transitions to reach high alignment efficiency. We also consider spectral constraints corresponding to experimental conditions using pulse-shaping techniques. We determine an optimal solution that could be implemented experimentally with this technique.

We derive closed analytical expressions for the order parameter $\Phi \left(x\right)$ and for the chemical potential $\mu$ of a Bose-Einstein condensate loaded into a harmonically confined, one-dimensional optical lattice for sufficiently weak, repulsive, or attractive interaction and not too strong laser intensities. Our results are compared to exact numerical calculations in order to map out the range of validity of the perturbative analytical approach. We identify parameter values where the optical lattice compensates the interaction-induced nonlinearity, such that the condensate ground state coincides with a simple, single-particle harmonic-oscillator wave function.

We present full three-dimensional numerical calculations of single vortex states in rotating dipolar condensates. We consider a Bose-Einstein condensate of ${}^{52}\text{C}\text{r}$ atoms with dipole-dipole and $s$-wave contact interactions confined in an axially symmetric harmonic trap. We obtain the vortex states by numerically solving the Gross-Pitaevskii equation in the rotating frame with no further approximations. We investigate the properties of a single vortex and calculate the critical angular velocity for different values of the $s$-wave scattering length. We show that, whereas the standard variational approach breaks down in the limit of pure dipolar interactions, exact solutions of the Gross-Pitaevskii equation can be obtained for values of the $s$-wave scattering length down to zero. The energy barrier for the nucleation of a vortex is calculated as a function of the vortex displacement from the rotation axis for different values of the angular velocity of the rotating trap.

The quantum fluctuations and correlations of the output signal and idler beams from a type-II polarization nondegenerate optical parametric amplifier (NOPA) inside an optical cavity are investigated theoretically, which is driven by the different kinds of quantized fields such as the two-mode thermal field, the phase-conjugate state, and a pair of EPR beams at the signal and idler frequency. Spectral line shapes due to quantum interferences between the input quantum fields and the generated down-converted subharmonic fields of NOPA are studied by scanning the length of the NOPA cavity. The entanglement degree of the EPR entangled beams injected into the NOPA as signal and idler beams can be increased or decreased, which are realized by controlling the relative phase between the pump beam and the injected beams for the NOPA. The results demonstrate coherent phenomena of NOPA in the quantum regime and show phase-sensitive manipulations of quantum entanglement for quantum information processing.

The frequency-domain pump-probe signal of a material system interacting with two quantum modes of the radiation field is recast in terms of products of scattering amplitudes ($T$ matrix elements) rather than the third-order susceptibility $\text{Im}{\chi }^{\left(3\right)}$. The resulting expression offers a more intuitive physical picture for the optical process compared with the semiclassical approach which treats the radiation field as classical. It can be derived and interpreted using closed-time-path-loop diagrams which represent the joint state of the matter and the field for each contribution to the signal. The signal has two components representing stimulated Raman scattering ${\omega }_1-{\omega }_2$ and two-photon absorption ${\omega }_1+{\omega }_2$ two-photon resonances. Both are expressed as nonequilibrium steady-state photon and matter fluxes, as is common in the description of dissipative processes in open quantum systems.

We demonstrate how gradient ascent pulse engineering optimal control methods can be implemented on donor-electron-spin qubits in Si semiconductors with an architecture complementary to the original Kane’s proposal. We focus on the high-fidelity-controlled-NOT (CNOT) gate and explicitly find its digitized control sequences by optimizing its fidelity over the external controls of the hyperfine $A$ and exchange $J$ interactions. This high-fidelity-CNOT gate has an error of about ${10}^{-6}$, below the error threshold required for fault-tolerant quantum computation, and its operation time of 100 ns is about three times faster than 297 ns of the proposed global control scheme. It also relaxes significantly the stringent distance constraint of two neighboring donor atoms of 10–20 nm as reported in the original Kane’s proposal to about 30 nm in which surface $A$ and $J$ gates may be built with current fabrication technology. The effects of the control voltage fluctuations, the dipole-dipole interaction, and the electron-spin decoherence on the CNOT gate fidelity are also discussed.

Uncertainty relations emerging from the Tsallis entropy are derived and discussed. In particular we found a positively defined function that saturates the so-called entropic inequalities for entropies characterizing the physical states under consideration.

We propose a simple scheme for hybrid economical telecloning (HETC) of equatorial qubits with the well-known W-type entangled states. The so-called HETC is a synthesis of several types of quantum cloning and quantum teleportation, in which economical symmetric and asymmetric clonings and anticlonings can be simultaneously achieved by teleportation. We use the global fidelity and average-single-qubit fidelity to estimate, respectively, the collective copying quality and show that the two criteria lead to different results. We obtain interesting equalities and inequalities about the fidelities of clones or anticlones. We also introduce controlled HETC of equatorial qubits with recently proposed Greenberger-Horne-Zeilinger (GHZ)–W-type entangled states [L. Chen and Y. X. Chen, Phys. Rev. A 74, 062310 (2006)], in which the achievement of phase-covariant telecloning between the sender (Alice) and the receivers (Bobs) is conditioned on the collaboration of all the supervisors (Charlies). This idea may open a perspective for the applications of such interesting type of entangled states. A method for generating the GHZ–W-type entangled states is also presented.