We systematically study the parity- and time-reversal ($\mathcal{PT}$) symmetric non-Hermitian version of a quantum network proposed in the paper of   Christandl et al. [Phys. Rev. Lett. 92, 187902 (2004)]. The nature of this model shows that it is a paradigm to demonstrate the complex relationship between the pseudo-Hermitian Hamiltonian and its Hermitian counterpart as well as a candidate in the experimental realization to simulate $\mathcal{PT}$-symmetry breaking. We also show that this model allows a conditional perfect state transfer within the unbroken $\mathcal{PT}$-symmetry region but not an arbitrary one. This is due to the fact that the evolution operator at a certain period is equivalent to the $\mathcal{PT}$ operator for the real-valued wave function in the elaborate $\mathcal{PT}$-symmetric Hilbert space.

Superadditivity effects in the classical capacity of discrete multiaccess channels and continuous variable (CV) Gaussian MACs are analyzed. Several examples of the manifestation of superadditivity in the discrete case are provided, including, in particular, a channel which is fully symmetric with respect to all senders. Furthermore, we consider a class of channels for which input entanglement across more than two copies of the channels is necessary to saturate the asymptotic rate of transmission from one of the senders to the receiver. The five-input entanglement of Shor error correction codewords surpass the capacity attainable by using arbitrary two-input entanglement for these channels. In the CV case, we consider the properties of the two channels (a beam-splitter channel and a “nondemolition” quadratures coupling sum (XP) gate channel) analyzed in Czekaj et al. [Phys. Rev. A 82, 020302(R) (2010)] in greater detail and also consider the sensitivity of capacity superadditivity effects to thermal noise. We observe that the estimates of the amount of two-mode squeezing required to achieve capacity superadditivity are more optimistic than previously reported.

We consider a quantum control problem involving a spin-$1/2$ particle in a magnetic field. The magnitude of the field is held constant, and the direction of the field, which is constrained to lie in the $x–y$ plane, serves as a control parameter that can be varied to govern the evolution of the system. We analytically solve for the time dependence of the control parameter that will synthesize a given target SU(2) transformation in the least possible amount of time, and we show that the time-optimal solutions have a simple geometric interpretation in terms of the fiber bundle structure of SU(2). We also generalize our time-optimal solutions to a control problem that includes a constant bias field along the $\widehat{\mathbf{z}}$ axis and to the case of inhomogeneous control, in which a single control parameter governs the evolution of an ensemble of spin-$1/2$ systems.

Quantum state transfer in the presence of static disorder and noise is one of the main challenges in building quantum computers. We compare the quantum state transfer properties for two classes of qubit chains under the influence of static disorder. In fully engineered chains all nearest-neighbor couplings are tuned in such a way that a single-qubit state can be transferred perfectly between the ends of the chain, while in chains with modified boundaries only the two couplings between the transmitting and receiving qubits and the remainder of the chain can be optimized. We study how the disorder in the couplings affects the state transfer fidelity depending on the disorder model and strength as well as the chain type and length. We show that the desired level of fidelity and transfer time are important factors in designing a chain. In particular we demonstrate that transfer efficiency comparable or better than that of the most robust engineered systems can also be reached in chains with modified boundaries without the demanding engineering of a large number of couplings.

Low-energy electron collisions with formamide are studied using the $R$-matrix method within the static-exchange, static-exchange-polarization, and close-coupling approximations. Twenty target states are included in the close-coupling formalism. The elastic integral, differential, and momentum transfer cross sections and the excitation cross sections from the ground state to the first four low-lying electron excited states are presented in the energy region of 0–10 eV. Besides the low-lying ${}^2{A}^{\prime \prime }$ shape resonance indicating good agreement between the present results and the values available in literature, one core-excited resonance (${}^2{A}^{\prime \prime }$) and three Feshbach resonances (${}^2{A}^{\prime \prime }$, ${}^2{A}^{\prime }$, and ${}^2{A}^{\prime }$) at the higher energies are predicted, and they could be responsible for the fragments observed in a recent experiment of the dissociative electron attachments to formamide.

We report on measurements of total cross sections for positron scattering from the fundamental organic molecule methane (CH${}_4$). The energy range of these measurements was 0.1–50 eV, whereas the energy resolution was $\sim$100 meV when our Ni moderator was used and $\sim$260 meV when the W moderator was employed. To assist us in interpreting these data, Schwinger multichannel calculations were performed at both static and static plus polarization levels of approximation for elastic positron scattering from 0.001 to 10 eV. These calculations are found to be in quite good qualitative agreement with our measured data, and they clearly educe the crucial role played by the target polarization in the low energy positron–CH${}_4$ scattering dynamics.

We consider the ground state of an attractively interacting atomic Bose-Einstein condensate in a prolate, cylindrically symmetric harmonic trap. If a true quasi-one-dimensional limit is realized, then for sufficiently weak axial trapping this ground state takes the form of a bright soliton solution of the nonlinear Schrödinger equation. Using analytic variational and highly accurate numerical solutions of the Gross-Pitaevskii equation, we systematically and quantitatively assess how solitonlike this ground state is, over a wide range of trap and interaction strengths. Our analysis reveals that the regime in which the ground state is highly solitonlike is significantly restricted and occurs only for experimentally challenging trap anisotropies. This result and our broader identification of regimes in which the ground state is well approximated by our simple analytic variational solution are relevant to a range of potential experiments involving attractively interacting Bose-Einstein condensates.

We propose an experimental scheme to detect macroscopic Klein tunneling with spin-orbit-coupled Bose-Einstein condensates (BECs). We show that a nonlinear Dirac equation with tunable parameters can be realized with such BECs. Through numerical calculations, we demonstrate that macroscopic Klein tunneling can be clearly detected under realistic conditions. Macroscopic quantum coherence in such relativistic tunneling is clarified and a BEC with a negative energy is shown to be able to transmit transparently through a wide Gaussian potential barrier.

Remarkable demonstrations of a cavity-induced giant reduction of the Raman lasing threshold in silica microspheres have been reported in Spillane et al. [Nature (London) 415, 621 (2002)], yet a complete quantum electrodynamics (QED) treatment of this process including the rigorous expressions for the electromagnetic modes of the sphere is lacking. In this paper, we employ a cavity QED approach to describe Raman lasing in microscopic spherical dielectric resonators with third-order nonlinearity to derive explicit expressions for the Raman gain and lasing threshold in terms of mode-overlapping coefficients determined from full analytic expressions of the electromagnetic eigenmodes of a dielectric sphere. We present dependencies of the Raman lasing threshold on the the order $n$ of overlapping whispering gallery modes for microspheres with diameter in the range 20–35 $\mu$m, demonstrating ultralow thresholds of between 70 and 90 $\mu$W, consistent with recent experimental results. We explain the reduction of the lasing threshold as due to an increase in the overlapping coefficients as the mode order is increased toward the regime where the modal energy is mostly confined to the surface region of the resonator. The presented theory can be easily generalized to any microcavity of regular morphology and for any combination of interacting whispering gallery modes.

A field configuration utilizing local static fields and a few continuous-wave driving fields is constructed to achieve universal (but low-order) protection of two-qubit states. That is, two-qubit states can be protected against arbitrary system-environment coupling with control fields if their frequencies are sufficiently large as compared with the cutoff frequency of the environment. Equally important, we show that it is possible to construct driving fields to protect two-qubit entangling gates against decoherence, without assuming any particular form of system-environment coupling. Using a non-Markovian master equation, we further demonstrate the effectiveness of our continuous dynamical decoupling fields in protecting entanglement and the excellent performance of protected two-qubit gates in generating entanglement. The results are complementary to current studies of entanglement protection using universal dynamical decoupling pulse sequences.

We use relativistic Hartree-Fock and correlation potential methods to calculate nuclear spin-dependent, parity-nonconserving amplitudes (dominated by the nuclear anapole moment) between hyperfine structure components of the ground state of odd isotopes of K, Rb, Cs, Ba${}^{+}$, Yb${}^{+}$, Tl, Fr, and Ra${}^{+}$. The results will be used for interpretation of current and future measurements.

We present a simple and computationally efficient method to calculate excited-state nuclear forces on adiabatic potential-energy surfaces (APES) from linear-response time-dependent density-functional theory within a real-space framework. The Casida ansatz, which has been validated for computing first-order nonadiabatic couplings in previous studies, was applied to the calculation of the excited-state forces. Our method is validated by the consistency of results in the lower excited states, which reproduce well those obtained by the numerical derivative of each APES. We emphasize the usefulness of this technique by demonstrating the excited-state molecular-dynamics simulation.

The phenomenon whereby features associated with certain vibrational levels in molecular states of mixed electronic character disappear under specific scattering conditions in electron energy-loss spectra is investigated. In particular, using a combination of experimental measurements and coupled-channel calculations, anomalous vibrational intensities in the mixed valence-Rydberg ${}^1{\Pi }_u\leftarrow X{}^1{\Sigma }_g^{+}$ transition of N${}_2$ are explained. A single parameter, i.e., the ratio of the generalized electronic transition moments to the diabatic valence and Rydberg components of the mixed states, dependent on the experimental scattering conditions, is found to be essentially capable of describing all observed relative vibrational intensities, including the near disappearance of the $b{}^1{\Pi }_u(v=5)$ feature for momentum-transfer-squared values $K^2\approx 0.3$ a.u. This result highlights the interesting possibility of experimental control of molecular quantum-interference effects in electron energy-loss spectra, something that is not possible in optical spectra.

We use the operator product expansion (OPE) and dispersion relations to obtain model-independent “Borel-resummed” sum rules for both shear and bulk viscosity of many-body systems of spin-1/2 fermions with predominantly short-range $S$-wave interactions. These sum rules relate Gaussian weights of the frequency-dependent viscosities to the Tan contact parameter $\mathcal{C}\left(a\right)$. Our results are valid for arbitrary values of the scattering length $a$, but receive small corrections from operators of dimension $\Delta >5$ in the OPE and can be used to study transport properties in the vicinity of the $a\to \infty$ fixed point. In particular, we find that the exact dependence of the shear viscosity sum rule on scattering length is controlled by the function $\mathcal{C}\left(a\right)$. The sum rules that we obtain depend on a frequency scale ${\omega }_0$ that can be optimized to maximize their overlap with low-energy data.

We investigate a system of fermions on a two-dimensional optical square lattice in the strongly repulsive coupling regime. In this case, the interactions can be controlled by laser intensity as well as by Feshbach resonance. We compare the energetics of states with resonating valence bond $d$-wave superfluidity, antiferromagnetic long-range order, and a homogeneous state with coexistence of superfluidity and antiferromagnetism. Using a variational formalism, we show that the energy density of a hole $e_{\mathrm{hole}}\left(x\right)$ has a minimum at doping $x=x_c$ that signals phase separation between the antiferromagnetic and $d$-wave paired superfluid phases. The energy of the phase-separated ground state is, however, found to be very close to that of a homogeneous state with coexisting antiferromagnetic and superfluid orders. We explore the dependence of the energy on the interaction strength and on the three-site hopping terms and compare with the nearest-neighbor hopping t-J model.

We address the phenomenon of diffraction of nonrelativistic matter waves on openings in absorbing screens. To this end, we expand the full quantum propagator, connecting two points on the opposite sides of the screen, in terms of the free particle propagator and spatiotemporal properties of the opening. Our construction, based on the Huygens-Fresnel principle, describes the quantum phenomena of diffraction in space and diffraction in time, as well as the interplay between the two. We illustrate the method by calculating diffraction patterns for localized wave packets passing through various time-dependent openings in one and two spatial dimensions.

We present a theoretical technique for solving the quantum transport problem of a few photons through a one-dimensional, strongly nonlinear waveguide. We specifically consider the situation where the evolution of the optical field is governed by the quantum nonlinear Schrödinger equation. Although this kind of nonlinearity is quite general, we focus on a realistic implementation involving cold atoms loaded in a hollow-core optical fiber, where the atomic system provides a tunable nonlinearity that can be large even at a single-photon level. In particular, we show that when the interaction between photons is effectively repulsive, the transmission of multiphoton components of the field is suppressed. This leads to antibunching of the transmitted light and indicates that the system acts as a single-photon switch. On the other hand, in the case of attractive interaction, the system can exhibit either antibunching or bunching, which is in stark contrast to semiclassical calculations. We show that the bunching behavior is related to the resonant excitation of bound states of photons inside the system.

We propose a setup for quantum memory based on a single two-level atom in a half cavity with a moving mirror. We show that various temporal shapes of incident photon can be efficiently stored and read out by shaping the time-dependent decay rate $\gamma \left(t\right)$ between the atom and the light. This is achieved uniquely by an appropriate motion of the mirror without the need for additional control laser or atomic level. We present an analytical expression for the efficiency of the process and study its dependence on the ratio between the incident light field bandwidth and the atomic decay rate. We discuss possible implementations and experimental issues, particularly for a single atom or ion in a half cavity quantum optical setup as well as a superconducting qubit in the context of circuit QED.

We report the experimental observation of generation of four and six strongly correlated and anticorrelated laser fields via atomic spin coherence in triple- and quadruple-Λ-type ${}^{85}$Rb atomic systems. The anticorrelated Stokes and anti-Stokes fields, simultaneously produced through scattering of the applied laser fields off the atomic spin coherence established in advance by the coupling and probe fields, are also highly anticorrelated, respectively, with the corresponding scattering fields. This method can, in principle, be used to create correlated and anticorrelated narrowband multiple fields of any desired order with long correlation times. It paves the way to further study of the generation of multifield quantum correlations and anticorrelations of arbitrarily high order.

We predict the existence of antihydrogen atom long-living quasistationary states, localized near a curved material surface due to quantum reflection from the van der Waals–Casimir potential. Such states are an atom-wave analog of the whispering-gallery (WG) modes, known in acoustics, optics, and neutron physics. We argue that the WG states of antihydrogen atoms could be regarded as a close analog of recently predicted gravitational states of antihydrogen where the centrifugal potential plays the role of the linear gravitational potential. We point out a method for the precision measurement of anti-atom-matter interactions, based on the study of interference of WG antihydrogen states.