The effective Lagrangian of a test particle, interacting within an ideal gas, is calculated within the closed-time-path formalism in the one-loop approximation and in the leading order of the particle trajectory. The expansion in the time derivative, available for slow enough motion, uncovers diffusive forces and decoherence in the particle coordinate basis. The master equation, generated by the effective Lagrangian, is derived and its consistency is verified for a finite-temperature gas.

An efficient version of the calculable $R$-matrix method, a technique for determination of scattering and bound-state properties, is extended to the Dirac equation. The configuration space is divided into internal and external regions at the channel radius. In both regions, the introduction of a Bloch operator allows restoration of the Hermiticity. The most general Bloch operator contains three free parameters. With a basis without constraint at the channel radius in the internal region, the phase shifts converge to the same value for any choice of these parameters. Nevertheless, some choices provide a faster convergence than others. Determination of the bound-state energies is performed with an extension of the method using a second set of basis functions in the external region. Neither the knowledge of asymptotic expressions nor a large channel radius is required. These $R$-matrix methods are particularly simple and very accurate when combined with the Lagrange-mesh method. No analytical or numerical evaluation of matrix elements is then necessary. Very accurate phase shifts are obtained with a Legendre mesh for various short-range potentials. A combination of Legendre and Laguerre meshes provides accurate energies for the bound states even for potentials with a Coulomb-like asymptotic behavior.

Joint measurements of noncommuting observables are characterized by unavoidable measurement uncertainties that can be described in terms of the error statistics for input states with well-defined values for the target observables. However, a complete characterization of measurement errors must include the correlations between the errors of the two observables. Here, we show that these correlations appear in the experimentally observable measurement statistics obtained by performing the joint measurement on maximally entangled pairs. For two-level systems, the results indicate that quantum theory requires imaginary correlations between the measurement errors of $\widehat{X}$ and $\widehat{Y}$ since these correlations are represented by the operator product $\widehat{X}\widehat{Y}=i\widehat{Z}$ in the measurement operators. Our analysis thus reveals a directly observable consequence of noncommutativity in the statistics of quantum measurements.

Qudit lattice states, as the generalization of qubit lattice states, are the maximally entangled states determined by qudit lattice unitaries in a $p^r\otimes p^r$ quantum system with $p$ being a prime and $r$ being an integer. Based on the partitions of qudit lattice unitaries into commuting sets, we present a sufficient condition for local discrimination of qudit lattice states, in which the commutativity plays an efficient role. It turns out that any set of $l$ qudit lattice states with $2\le l\le p^r$, including $k\le l$ mutually commuting qudit lattice unitaries and satisfying $l(l-1)-(k+1)(k-2)\le 2p^r$, can be locally distinguished, not only extending Fan's result [H. Fan, Phys. Rev. Lett. 92, 177905 (2004)] to the prime power quantum system but also involving the local discrimination of a larger number of maximally entangled states.

This paper defines the fidelity of recovery of a tripartite quantum state on systems $A,B$, and $C$ as a measure of how well one can recover the full state on all three systems if system $A$ is lost and a recovery operation is performed on system $C$ alone. The surprisal of the fidelity of recovery (its negative logarithm) is an information quantity which obeys nearly all of the properties of the conditional quantum mutual information $I(A;B|C)$, including non-negativity, monotonicity with respect to local operations, duality, invariance with respect to local isometries, a dimension bound, and continuity. We then define a (pseudo) entanglement measure based on this quantity, which we call the “geometric squashed entanglement.” We prove that the geometric squashed entanglement is a 1-LOCC monotone (i.e., monotone nonincreasing with respect to local operations and classical communication from Bob to Alice), that it vanishes if and only if the state on which it is evaluated is unentangled, and that it reduces to the geometric measure of entanglement if the state is pure. We also show that it is invariant with respect to local isometries, subadditive, continuous, and normalized on maximally entangled states. We next define the surprisal of measurement recoverability, which is an information quantity in the spirit of quantum discord, characterizing how well one can recover a share of a bipartite state if it is measured. We prove that this discordlike quantity satisfies several properties, including non-negativity, faithfulness on classical-quantum states, invariance with respect to local isometries, a dimension bound, and normalization on maximally entangled states. This quantity, combined with a recent breakthrough of Fawzi and Renner, makes it possible to characterize states with discord nearly equal to zero as being approximate fixed points of entanglement-breaking channels (equivalently, they are recoverable from the state of a measuring apparatus). Finally, we discuss a multipartite fidelity of recovery and several of its properties.

Joint electron-ion energy spectra for the dissociative ionization of a model ${\mathrm{H}}_2{}^{+}$ in few-cycle, infrared laser pulses are calculated via the numerical ab initio solution of the time-dependent Schrödinger equation. A strong, pulse-dependent modulation of the ionization probability for certain values of the protons' kinetic energy (but almost independent of the electron's energy) is observed. With the help of models with frozen ions, this feature, which mistakenly might be attributed to vibrational excitations, is traced back to the transient population of electronically excited states, followed by ionization. This assertion is further corroborated employing a two-level model incorporating strong-field ionization from the excited state.

We study Bose-Einstein condensation (BEC) in three-dimensional two-component bosonic gases, characterizing the universal behaviors of the critical modes arising at the BEC transitions. For this purpose, we use field-theoretical (FT) renormalization-group (RG) methods and perform mean-field and numerical calculations. The FT RG analysis is based on the Landau-Ginzburg-Wilson ${\mathrm{\Phi }}^4$ theory with two complex scalar fields which has the same symmetry as the bosonic system. In particular, for identical bosons with exchange ${\mathbb{Z}}_2$ symmetry, coupled by effective density-density interactions, the global symmetry is ${\mathbb{Z}}_{2,e}\otimes \mathrm{U}\left(1\right)\otimes \mathrm{U}\left(1\right)$. At the BEC transition, it may break into ${\mathbb{Z}}_{2,e}\otimes {\mathbb{Z}}_2\otimes {\mathbb{Z}}_2$ when both components condense simultaneously, or to $\mathrm{U}\left(1\right)\otimes {\mathbb{Z}}_2$ when only one component condenses. This implies different universality classes for the corresponding critical behaviors. Numerical simulations of the two-component Bose-Hubbard model in the hard-core limit support the RG prediction: when both components condense simultaneously, the critical behavior is controlled by a decoupled XY fixed point, with unusual slowly decaying scaling corrections arising from the onsite interspecies interaction.

Quantum weak measurement has attracted much interest recently [J. Dressel et al., Rev. Mod. Phys. 86, 307 (2014).] because it could amplify some weak signals and provide a technique to observe nonclassical phenomena. Here, we apply this technique to study the interaction between the free atoms and the vacuum in a cavity. Due to the gradient field in the vacuum cavity, the external orbital motions and the internal electronic states of atoms can be weakly coupled via the atom-field electric-dipole interaction. We show that, within the properly postselected internal states, the weak atom-vacuum interaction could generate a large change to the external motions of atoms due to the postselection-induced weak values.

We present a mechanism by which a metamaterial surface, or metasurface, can act as an ideal phase-controlled rotatable linear polarizer. Using coupled-mode theory and the idea of coherent perfect absorption into auxiliary polarization channels, we show how the losses and near-field couplings on the metasurface can be balanced so that, with equal-power linearly polarized beams incident on each side, varying the relative phase rotates the polarization angles of the output beams while maintaining zero ellipticity. The system can be described by a non-Hermitian effective Hamiltonian which is parity-time $\left(PT\right)$ symmetric, although there is no actual gain present; perfect polarization conversion occurs at the eigenfrequencies of this Hamiltonian, and the polarization rotating behavior occurs at the critical point of its $PT$-breaking transition.

$S$-matrix theory of high-order harmonic generation (HHG) is generalized to multielectron atoms. In the multielectron case the harmonic power is expressed via a coherent sum of the time-dependent dipoles, while for the one-electron models a corresponding incoherent sum appears. This difference is important for the inert atomic gases having a $p$ ground state as used in a recent HHG experiment with a bicircular field [Nat. Photonics 9, 99 (2015)]. We investigate HHG by such a bicircular field, which consists of two coplanar counter-rotating circularly polarized fields of frequency $r\omega$ and $s\omega$. Selection rules for HHG by a bicircular field are analyzed from the aspects of dynamical symmetry of the system, conservation of the projection of the angular momentum on a fixed quantization axis, and the quantum number of the initial and final atomic ground states. A distinction is made between the selection rules for atoms with closed [J. Phys. B 48, 171001 (2015)] and nonclosed shells. An asymmetry in emission of the left- and right-circularly polarized harmonics is found and explained by using a semiclassical model and the electron probability currents which are related to a nonzero magnetic quantum number. This asymmetry can be important for the application of such harmonics to the exploration of chirality-sensitive processes and for generation of elliptic or even circular attosecond pulse trains. Such attosecond pulse trains are analyzed for longer wavelengths than in Opt. Lett. 40, 2381 (2015), and for various field-component intensities.

The electron-nuclei interaction affects the internuclear motion in slow ion-atom collisions, which in turn affects theoretical results for the cross sections of various collision processes. The results are especially sensitive to the details of the internuclear dynamics in the presence of a strong isotope effect on the cross sections, as is the case, e.g., for the charge transfer in low-energy collisions of ${\text{He}}^{2+}$ with H, D, and T. By considering this system as an example, we show that internuclear trajectories defined by the Born-Oppenheimer (BO) potential in the entrance collision channel, which effectively accounts for the electron-nuclei interaction, are in much better agreement with trajectories obtained in the ab initio electron-nuclear dynamics approach [R. Cabrera-Trujillo et al., Phys. Rev. A 83, 012715 (2011)] than the corresponding Coulomb trajectories. We also show that the use of the BO trajectory instead of the Coulomb trajectory in the calculations of the charge-transfer cross sections within the adiabatic approach improves the agreement of the results with ab initio calculations.

We study the effect of disorder on the propagation of collective excitations in a disordered Bose superfluid. We incorporate local-density depletion induced by strong disorder at the mean-field level and formulate the transport of the excitations in terms of a screened scattering problem. We show that the competition of disorder, screening, and density depletion induces a strongly nonmonotonic energy dependence of the disorder parameter. In three dimensions, it results in a rich localization diagram with four different classes of mobility spectra, characterized by either no or up to three mobility edges. Implications on experiments with disordered ultracold atoms are discussed.

We show that several aspects of the low-temperature hydrodynamics of a discrete Gross-Pitaevskii equation (GPE) can be understood by mapping it to a nonlinear version of fluctuating hydrodynamics. This is achieved by first writing the GPE in a hydrodynamic form of a continuity and a Euler equation. Respecting conservation laws, dissipation and noise due to the system's chaos are added, thus giving us a nonlinear stochastic field theory in general and the Kardar-Parisi-Zhang (KPZ) equation in our particular case. This mapping to KPZ is benchmarked against exact Hamiltonian numerics on discrete GPE by investigating the nonzero temperature dynamical structure factor and its scaling form and exponent. Given the ubiquity of the Gross-Pitaevskii equation (also known as the nonlinear Schrödinger equation), ranging from nonlinear optics to cold gases, we expect this remarkable mapping to the KPZ equation to be of paramount importance and far reaching consequences.

We theoretically and numerically study the quantum dynamics of two degenerate optical parametric oscillators with mutual injections. The cavity mode in the optical coupling path between the two oscillator facets is explicitly considered. Stochastic equations for the oscillators and mutual injection path based on the positive $P$ representation are derived. The system of two gradually pumped oscillators with out-of-phase mutual injections is simulated, and its quantum state is investigated. When the incoherent loss of the oscillators other than the mutual injections is small, the squeezed quadratic amplitudes $\widehat{p}$ in the oscillators are positively correlated near the oscillation threshold. It indicates finite quantum correlation, estimated via Gaussian quantum discord, and the entanglement between the intracavity subharmonic fields. When the loss in the injection path is low, each oscillator around the phase transition point forms macroscopic superposition even under a small pump noise. It suggests that the squeezed field stored in the low-loss injection path weakens the decoherence in the oscillators.

In a hybrid optomechanical setup consisting of a two-level atom in a cavity with a pendular end mirror, the interplay between the light field's radiation pressure on the mirror and the dipole interaction with the atom can lead to an effect, which manifests itself in the suppression of Rabi oscillations of the atomic population. This effect is present when the system is in the single-photon strong-coupling regime and has an analogy in the photon blockade of optomechanics.

We analyze how chirality can generate pulling optical forces and left-handed torques by cross-coupling linear-to-angular momenta between the light field and the chiral object. In the dipolar regime, we reveal that such effects can emerge from a competition between nonchiral and chiral contributions to dissipative optical forces and torques, a competition balanced by the strength of chirality of the object. We extend the analysis to large chiral spheres where the interplay between chirality and multipolar resonances can give rise to a break of symmetry that flips the signs of both optical forces and torques.

We derive the optical theorem for scattering of electromagnetic waves in nonlinear media. This result is used to obtain the power extinguished from a field by a nonlinear scatterer. The cases of second-harmonic generation and the Kerr effect are studied in some detail. Applications to nonlinear apertureless scanning near-field optical microscopy are considered.

Classical optics can be used to efficiently implement certain quantum information processing tasks with a high degree of control, for example, one-dimensional quantum walks through the space of orbital angular momentum of light directed by its polarization. To explore the potential of quantum information processing with classical light, we here suggest a method to realize $d$-dimensional quantum walks with classical optics—an important step towards robust implementation of certain quantum algorithms. In this scheme, different degrees of freedom of light, such as frequency, orbital angular momentum, and time bins, represent different directions for the walker while the coin to decide which direction the walker takes is realized by employing the polarization combined with different light paths.

Compared with the traditional protocols of quantum key distribution (QKD), the reference-frame-independent (RFI)–QKD protocol has been generally proved to be very useful and practical, since its experimental implementation can be simplified without the alignment of a reference frame. In most RFI-QKD systems, the encoding states are always taken to be perfect, which, however, is not practical in realizations. In this paper, we consider the security of RFI QKD with source flaws based on the loss-tolerant method proposed by Tamaki et al. [Phys. Rev. A 90, 052314 (2014)]. As the six-state protocol can be realized with four states, we show that the RFI-QKD protocol can also be performed with only four encoding states instead of six encoding states in its standard version. Furthermore, the numerical simulation results show that the source flaws in the key-generation basis $(Z$ basis) will reduce the key rate but are loss tolerant, while the ones in $X$ and $Y$ bases almost have no effect and the key rate remains almost the same even when they are very large. Hence, our method and results will have important significance in practical experiments, especially in earth-to-satellite or chip-to-chip quantum communications.

We study collective modes of superfluid Bose gases in optical lattices combined with potential barriers. We assume that the system is in the vicinity of the quantum phase transition to a Mott insulator at a commensurate filling, where emergent particle-hole symmetry gives rise to two types of collective mode, namely a gapless Nambu-Goldstone (NG) phase mode and a gapful Higgs amplitude mode. We consider two kinds of potential barrier: One does not break the particle-hole symmetry while the other does. In the presence of the former barrier, we find Higgs bound states that have binding energies lower than the bulk Higgs gap and are localized around the barrier. We analyze tunneling properties of the NG mode incident to both barriers to show that the latter barrier couples the Higgs bound states with the NG mode, leading to Fano resonance mediated by the bound states. Thanks to the universality of the underlying field theory, it is expected that Higgs bound states may be present also in other condensed-matter systems with a particle-hole symmetry and spontaneous breaking of a continuous symmetry, such as quantum dimer antiferromagnets, superconductors, and charge-density-wave materials.