We postulate the existence of a universal uncertainty relation between the quantum and classical mutual informations between pairs of quantum systems. Specifically, we propose that the sum of the classical mutual information, determined by two mutually unbiased pairs of observables, never exceeds the quantum mutual information. We call this the complementary-quantum correlation (CQC) relation and prove its validity for pure states, for states with one maximally mixed subsystem, and for all states when one measurement is minimally disturbing. We provide results of a Monte Carlo simulation suggesting that the CQC relation is generally valid. Importantly, we also show that the CQC relation represents an improvement to an entropic uncertainty principle in the presence of a quantum memory, and that it can be used to verify an achievable secret key rate in the quantum one-time pad cryptographic protocol.

In this paper we propose an expression for the entanglement entropy of several intervals in a stationary state of a free, translational invariant Hamiltonian in a fermionic chain. We check numerically the accuracy of our proposal and conjecture a formula for the asymptotic behavior of principal submatrices of a Toeplitz matrix.

In this paper we propose a scheme for the preparation of steady entanglements in bosonic dissipative networks. We describe its implementation in a system of coupled cavities interacting with an engineered reservoir built up of three-level atoms. Emblematic bipartite ($\text{Bell}$ and $\text{NOON}$) and multipartite ($W$-class) states can be produced with high fidelity and purity.

We prove that the projection on a completely entangled subspace $\mathcal{S}$ of maximum dimension obtained by Parthasarathy [K. R. Parthasarathy, Proc. Indian Acad. Sci. Math. Sci. 114, 365 (2004)] in a multipartite quantum system is not positive under partial transpose. We next show that a large number of positive operators with a range in $\mathcal{S}$ also have the same property. In this process we construct an orthonormal basis for $\mathcal{S}$ and provide a theorem to link the constructions of completely entangled subspaces due to Parthasarathy (as cited above), Bhat [B. V. R. Bhat, Int. J. Quantum Inf. 4, 325 (2006)], and Johnston [N. Johnston, Phys. Rev. A 87, 064302 (2013)].

We consider measurement-based quantum computation that uses scalable continuous-variable cluster states with a one-dimensional topology. The physical resource, known here as the dual-rail quantum wire, can be generated using temporally multiplexed offline squeezing and linear optics or by using a single optical parametric oscillator. We focus on an important class of quantum gates, specifically Gaussian unitaries that act on single quantum modes (qumodes), which gives universal quantum computation when supplemented with multi-qumode operations and photon-counting measurements. The dual-rail wire supports two routes for applying single-qumode Gaussian unitaries: The first is to use traditional one-dimensional quantum-wire cluster-state measurement protocols. The second takes advantage of the dual-rail quantum wire in order to apply unitaries by measuring pairs of qumodes called macronodes. We analyze and compare these methods in terms of the suitability for implementing single-qumode Gaussian measurement-based quantum computation.

We propose approximate kinetic energy (KE) functionals of the pair-density (PD)-functional theory on the basis of the rigorous expression with the coupling-constant integration (RECCI) that has been recently derived [Phys. Rev. A 85, 062508 (2012)]. These approximate functionals consist of the noninteracting KE and correlation energy terms. It is found that the Thomas-Fermi-Weizsäcker functional is shown to be better as the noninteracting KE term than the Thomas-Fermi and Gaussian model functionals. It is also shown that the correlation energy term is also indispensable for the reduction of the KE error, i.e., reductions of both inappropriateness of the approximate functional and error of the resultant PD. Concerning the correlation energy term, we further propose an approximate functional in addition to using the existing familiar functionals. This functional satisfies the scaling property of the KE functional, and yields a reasonable PD in a sense that the KE, electron-electron interaction, and potentials energies tend to be improved with satisfying the virial theorem. The present results not only suggest the usefulness of the RECCI but also provide the guideline for the further improvement of the RECCI-based KE functional.

We study the process of single ionization of Li in collisions with ${\mathrm{H}}^{+}$ and ${\mathrm{O}}^{8+}$ projectile ions at 6-MeV and 1.5-MeV/amu impact energies, respectively. Using the frameworks of the independent-electron model and the impact parameter picture, fully (FDCS) and doubly (DDCS) differential cross sections are evaluated in the continuum distorted wave with eikonal initial-state approximation. Comparisons are made with the recent measurements of LaForge et al. [J. Phys. B 46, 031001 (2013)] for the DDCS and Hubele et al. [Phys. Rev. Lett. 110, 133201 (2013)] for the FDCS, respectively. For ${\mathrm{O}}^{8+}$ impact inclusion of the heavy particle [nucleus-nucleus (NN)] interaction in the calculations is crucial and effects of polarization due to the presence of the projectile ion have also to be taken into account for getting very good agreement with the measured data. Our calculation reproduces the satellite peak structure seen in the FDCS for the Li($2s$) measurement, which we explain as being formed by a combination of the binary and NN interactions.

Spin-orbit (SO) coupling can be introduced in a Bose-Einstein condensate (BEC) as a gauge potential acting only in a localized spatial domain. The effect of such a SO “defect” can be understood by transforming the system to the integrable vector model. The properties of the SO BEC change drastically if the SO defect is accompanied by the Zeeman splitting. In such a nonintegrable system, the SO defect qualitatively changes the character of soliton interactions and allows for formation of stable nearly scalar soliton complexes with almost all atoms concentrated in only one dark state. These solitons exist only if the number of particles exceeds a threshold value. We also report on the possibility of transmission and reflection of a soliton upon its scattering on the SO defect. Scattering strongly affects the pseudospin polarization and can induce pseudospin precession. The scattering can also result in almost complete atomic transfer between the dark states.

By applying complementary analytic and numerical methods, we investigate the dynamics of spin-$\frac{1}{2} XXZ$ models with variable-range interactions in arbitrary dimensions. The dynamics we consider is initiated from uncorrelated states that are easily prepared in experiments; it can be equivalently viewed as either Ramsey spectroscopy or a quantum quench. Our primary focus is the dynamical emergence of correlations and entanglement in these far-from-equilibrium interacting quantum systems: We characterize these correlations by the entanglement entropy, concurrence, and squeezing, which are inequivalent measures of entanglement corresponding to different quantum resources. In one spatial dimension, we show that the time evolution of correlation functions manifests a nonperturbative dynamic singularity. This singularity is characterized by a universal power-law exponent that is insensitive to small perturbations. Explicit realizations of these models in current experiments using polar molecules, trapped ions, Rydberg atoms, magnetic atoms, and alkaline-earth and alkali-metal atoms in optical lattices, along with the relative merits and limitations of these different systems, are discussed.

We investigate the thermodynamic properties of a superfluid Fermi gas subject to Rashba spin-orbit coupling and effective Zeeman field. We adopt a $T$-matrix scheme that takes beyond-mean-field effects, which are important for strongly interacting systems, into account. We focus on the calculation of two important quantities: the superfluid transition temperature and the isothermal compressibility. Our calculation shows very distinct influences of the out-of-plane and the in-plane Zeeman fields on the Fermi gas. We also confirm that the in-plane Zeeman field induces a Fulde-Ferrell superfluid below the critical temperature and an exotic finite-momentum pseudogap phase above the critical temperature.

We measure the collective excitation spectrum of a spin-orbit-coupled Bose-Einstein condensate using Bragg spectroscopy. The spin-orbit coupling is generated by Raman dressing of atomic hyperfine states. When the Raman detuning is reduced, mode softening at a finite momentum is revealed, which provides insight into a supersolid-like phase transition. We find that for the parameters of our system, this softening stops at a finite excitation gap and is symmetric under a sign change of the Raman detuning. Finally, using a moving barrier that is swept through the BEC, we also show the effect of the collective excitation on the fluid dynamics.

A theoretical study of interacting bosons in a periodic optical lattice is presented. Instead of the commonly used tight-binding approach (applicable near the Mott-insulating regime of the phase diagram), the present work starts from the exact single-particle states of bosons in a cubic optical lattice, satisfying the Mathieu equation, an approach that can be particularly useful at large boson fillings. The effects of short-range interactions are incorporated using a self-consistent Hartree-Fock approximation, and predictions for experimental observables such as the superfluid transition temperature, condensate fraction, and boson momentum distribution are presented.

We study the propagation of nanofiber-guided light through an array of atomic cesium, taking into account the transitions between the hyperfine levels $6S_{1/2}F=4$ and $6P_{3/2}{F}^{\prime }=5$ of the $D_2$ line. We derive the coupled-mode propagation equation, the input-output equation, the scattering matrix, the transfer matrix, and the reflection and transmission coefficients for the guided field in the linear, quasistationary, weak-excitation regime. We show that, when the initial distribution of populations of atomic ground-state sublevels is independent of the magnetic quantum number, the quasilinear polarizations along the principal axes $x$ and $y$, which are parallel and perpendicular, respectively, to the radial direction of the atomic position, are not coupled to each other in the linear coherent scattering process. When the guided probe field is quasilinearly polarized along the major principal axis $x$, forward and backward scattering have different characteristics. We find that, when the array period is far from the Bragg resonance, the backward scattering is weak. Under the Bragg resonance, most of the guided probe light can be reflected back in a broad region of field detunings even though there is an irreversible decay channel into radiation modes. When the atom number is large enough, two different band gaps may be formed, whose properties depend on the polarization of the guided probe field.

Photoionization of a laser-cooled and compressed atomic beam from a high-flux thermal source can be used to create a high-brightness ion beam for use in focused-ion-beam instruments. Here we show using calculations and Doppler cooling simulations that an atomic rubidium beam with an equivalent brightness of $2.1\times {10}^7 \mathrm{A}/\left(\mathrm{m}{}^2 \mathrm{sr} \mathrm{eV}\right)$ can be created using a compact 5 cm long two-dimensional magneto-optical compressor. If this can be conserved during the photoionization process, this leads to an ion beam brightness an order of magnitude higher than produced by a liquid metal ion source. The source is also capable of producing a flux of $6.2\times {10}^9 \mathrm{s}{}^{-1}$ that results in a substantial beam current of 1 nA once fully ionized.

Here we demonstrate that photocurrent noise reduction below the standard quantum limit and modal anticorrelation can arise in a two-mode coupled vertical external cavity surface emitting laser system with a common pump. This effect occurs due to correlated loss of laser modes. It is possible to suppress noise below the standard quantum limit even for Poissonian coherent pumping, whereas the regularity of the pump can be harmful for nonclassicality.

We describe and quantify the emergence of coherence between quantum systems that are initially at thermal equilibrium. We show that the coherence can be induced by a conditional locking method based on a feasible joint detection of photons spontaneously emitted by the systems. The energy employed by the locking method comes solely from the initial thermal excitation of the systems, which makes the method suitable for a wide range of experimental platforms. We show that the same method can be applied to a pair of two-level systems or to a pair of quantum oscillators and we compare the results with regard to their first- and second-order correlation functions. We also propose feasible experimental tests to verify the thermally induced coherence.

We present analytical solutions for the mean-field master equation of the driven-dissipative Bose-Hubbard model for cavity photons, in the limit of both weak pumping and weak dissipation. Instead of pure Mott-insulator states, we find statistical mixtures with the same second-order coherence $g^{\left(2\right)}\left(0\right)$ as a Fock state with $n$ photons, but a mean photon number of $n/2.$ These mixed states occur when $n$ pump photons have the same energy as $n$ interacting photons inside the nonlinear cavity and survive up to a critical tunneling coupling strength, above which a crossover to a classical coherent state takes place. We also explain the origin of both antibunching and superbunching predicted by P-representation mean-field theory at higher pumping and dissipation. In particular, we show that the strongly correlated region of the associated phase diagram cannot be described within the semiclassical Gross-Pitaevskii approach.

We study numerically the spectrum of the non-Hermitian effective Hamiltonian that describes the dipolar interaction of a gas of $N\gg 1$ atoms with the radiation field. We analyze the interplay between cooperative effects and disorder for both scalar and vectorial radiation fields. We show that for dense gases, the resonance width distribution follows, both in the scalar and vectorial cases, a power law $P\left(\Gamma \right)\sim {\Gamma }^{-4/3}$ that originates from cooperative effects between more than two atoms. This power law is different from the $P\left(\Gamma \right)\sim {\Gamma }^{-1}$ behavior, which has been considered as a signature of Anderson localization of light in random systems. We show that in dilute clouds, the center of the energy distribution is described by Wigner's semicircle law in the scalar and vectorial cases. For dense gases, this law is replaced in the vectorial case by the Laplace distribution. Finally, we show that in the scalar case the degree of resonance overlap increases as a power law of the system size for dilute gases, but decays exponentially with the system size for dense clouds.

We study the polarization properties of elliptical femtosecond-laser-written waveguide arrays. An analytical model is presented to explain the asymmetry of the spatial transverse profiles of linearly polarized modes in these waveguides. This asymmetry produces a polarization-dependent coupling coefficient, between adjacent waveguides, which strongly affects the propagation of light in a lattice. Our analysis explains how this effect can be exploited to tune the final intensity distribution of light propagated through the array and links the properties of a polarizing beam splitter in integrated optical circuits to the geometry of the waveguides.