Repulsive Casimir-Lifshitz forces are known to exist between two dissimilar materials if a third material, whose dielectric response is intermediate, separates them. However, the force between two identical materials is almost always attractive. Here we show that the force between two identical, semi-infinite birefringent slabs can be repulsive for particular orientations and compare the conditions for repulsion in this system to those of isotropic materials. We examine the dependence of the Casimir-Lifshitz force on retardation and relative orientation in this system and discuss situations in which the force can be changed from attractive to repulsive as a function of both distance and rotation angle.

A two-dimensional model of the resonant electron-molecule collision processes with one nuclear and one electronic degree of freedom introduced by K. Houfek, T. N. Rescigno, and C. W. McCurdy [Phys. Rev. A 73, 032721 (2006)] is reformulated within the time-dependent framework and solved numerically using the finite-element method with the discrete variable representation basis, the exterior complex scaling method, and the generalized Crank-Nicolson method. On this model we illustrate how the time-dependent calculations can provide deep insight into the origin of oscillatory structures in the vibrational excitation cross sections if one evaluates the cross sections not only at sufficiently large time to obtain the final cross sections, but also at several characteristic times which are given by the evolution of the system. It is shown that all details of these structures, especially asymmetrical peaks, can be understood as quantum interference of several experimentally indistinguishable processes separated in time due to a resonant capture of the electron and the subsequent vibrational motion of the negative molecular ion. Numerical results are presented for the ${\mathrm{N}}_2$-like, NO-like, and ${\mathrm{F}}_2$-like models and compared with ones obtained within the time-independent approach and within the local complex potential approximation.

We consider the Schrödinger equation for the hydrogen atom in a uniform electric field, searching for solutions of this equation in parabolic coordinates in a separable form. With some restrictions on the parameters, we have found the exact analytical expressions for the continuum wave function component and for the most important Stokes multiplier.

We propose and analyze a pumped and damped Bose-Hubbard dimer as a source of continuous-variable Einstein-Podolsky-Rosen (EPR) steering with non-Gaussian statistics. We use and compare the results of the approximate truncated Wigner and the exact positive-$P$ representation to calculate and compare the predictions for intensities, second-order quantum correlations, and third- and fourth-order cumulants. We find agreement for intensities and the products of inferred quadrature variances, which indicate that states demonstrating the EPR paradox are present. We find clear signals of non-Gaussianity in the quantum states of the modes from both the approximate and exact techniques, with quantitative differences in their predictions. Our proposed experimental configuration is extrapolated from current experimental techniques and adds another apparatus to the current toolbox of quantum atom optics.

We present a general method to obtain the stable lasing solutions for the steady-state ab initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2D). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2D rotational symmetry groups. Our method uses a combination of semianalytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closed-form expressions for both circulating modes and other types of lasing solutions as well as for their linearized Maxwell-Bloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its “chiral” intensity pattern, which arises from spontaneous symmetry breaking of mirror symmetry, and whose symmetry group requires that the degeneracy persists even when nonlinear effects become important. Finally, we introduce a numerical technique to solve the degenerate SALT equations far above threshold even when spatial discretization artificially breaks the degeneracy.

Planar microcavities allow the control and manipulation of spin polarization, manifested in phenomena like the optical spin Hall effect due to the intrinsic polarization mode splitting. Here, we study a transparent microcavity with broken rotational symmetry, realized by aligning the optic axis of a uniaxial cavity material in the cavity plane, giving rise to exceptional points in the dispersion relation. These occur pairwise, are circularly polarized, and are cores of polarization vortices. The exceptional points are result of the non-Hermitian character of the system and are in close relationship to singular optic axes in absorptive biaxial systems.

We consider the evolution of light beams in nonlinear media exhibiting nonlinearities up to the seventh order wherein the beam propagation is governed by the cubic-quintic-septimal nonlinear Schrödinger equation. An exact analytic solution that describes dark solitary wave propagation is obtained, based on a special ansatz. Unlike the well-known $\text{tanh}$-profile dark soliton in Kerr media, the present one has a functional form given in terms of “${\text{sech}}^{2/3}$”. The requirements concerning the optical material parameters for the existence of this localized structure are discussed. This propagating solitary wave exists due to a balance among diffraction, cubic, quintic, and septimal nonlinearities. We also investigate its stability under initial pertubations by employing numerical simulations. The modulational stability of the continuous-wave background, which supports the dark soliton, is also studied analytically. Collisions between stable dark solitons are finally investigated.

We describe a direct method for experimental determination of the negativity of an arbitrary two-qubit state with 11 measurements performed on multiple copies of the two-qubit system. Our method is based on the experimentally accessible sequences of singlet projections performed on up to four qubit pairs. In particular, our method permits the application of the Peres-Horodecki separability criterion to an arbitrary two-qubit state. We explicitly demonstrate that measuring entanglement in terms of negativity requires three measurements more than detecting two-qubit entanglement. The reported minimal set of interferometric measurements provides a complete description of bipartite quantum entanglement in terms of two-photon interference. This set is smaller than the set of 15 measurements needed to perform a complete quantum state tomography of an arbitrary two-qubit system. Finally, we demonstrate that the set of nine Makhlin's invariants needed to express the negativity can be measured by performing 13 multicopy projections. We demonstrate both that these invariants are a useful theoretical concept for designing specialized quantum interferometers and that their direct measurement within the framework of linear optics does not require performing complete quantum state tomography.

A nonrelativistic system such as an ultracold trapped ion may perform a quantum simulation of a Dirac equation dynamics under specific conditions. The resulting Hamiltonian and dynamics are highly controllable, but the coupling between momentum and internal levels poses some difficulties to manipulate the internal states accurately in wave packets. We use invariants of motion to inverse engineer robust population inversion processes with a homogeneous, time-dependent simulated electric field. This exemplifies the usefulness of inverse-engineering techniques to improve the performance of quantum simulation protocols.

We consider the hydrogen atom $\mathrm{H}\left(1s\right)$ exposed to an ultrashort laser pulse with a central frequency ${\omega }_0$ ranging from several hundreds of eV to 1.5 keV ($\approx 55$ a.u.) and a peak intensity of $3.51\times {10}^{16}\mathrm{W}/{\mathrm{cm}}^2$. We study the excitation of the atom by stimulated Raman scattering, a process involving pairs of frequencies (${\omega }_1,{\omega }_2$). These frequencies are non-negligible components of the pulse Fourier transform and they satisfy the condition $E_g+\hslash {\omega }_1=E_b+\hslash {\omega }_2,E_g$ and $E_b\equiv E_n$ being the ground-state and the excited-state energy, respectively. The numerical results obtained by integrating the time-dependent Schrödinger equation (TDSE) are compared with calculations in lowest order perturbation theory (LOPT). In LOPT we consider, in the second order of PT, the contribution of the term $\mathbf{A}·\mathbf{P}$ in the dipole approximation and, in first order of PT, the expression of ${\mathbf{A}}^2$ taken for first-order retardation effects. ($\mathbf{A}$ denotes the vector potential of the field and $\mathbf{P}$ is the momentum operator.) We focus on the Raman excitation of bound states with principal quantum numbers $n$ up to $n=13$. The evaluation in perturbation theory of the $\mathbf{A}·\mathbf{P}$ contribution to $1s-ns$ and $1s-nd$ transition probabilities uses analytic expressions of the corresponding Kramers–Heisenberg matrix elements. At fixed pulse duration $\tau =6\pi$ a.u. ($\approx 0.48$ fs), we find that the retardation effects play an important role at high frequencies: they progressively diminish as the frequency decreases until the contribution of $\mathbf{A}·\mathbf{P}$ dominates over the ${\mathbf{A}}^2$ contribution for ${\omega }_0$ values of a few a.u. We also study the dependence of the Raman process on the pulse duration for several values of ${\omega }_0$. In the case ${\omega }_0=13\mathrm{a}.\mathrm{u}.(\approx 354\mathrm{eV})$ where dipole and nondipole contributions are of the same order of magnitude, we present the Raman excitation probability as a function of the pulse duration for excited $ns,np$, and $nd$ states.

We estimate the Stark and Zeeman shifts in the transition frequencies of the ${{}^{16}\mathrm{O}_2}^{+}$ molecular ion as a step in the search for the variation in the proton-to-electron mass ratio $\mu$. The $X^2\mathrm{\Pi }v=21-a^4\mathrm{\Pi }v=0$ or the $X^2\mathrm{\Pi }v=21-a^4\mathrm{\Pi }v=1$ transition frequencies (THz region) of the ${{}^{16}\mathrm{O}_2}^{+}$ molecular ion have particularly high sensitivity to the variation in $\mu$. Note also that the Stark shift in the ${{}^{16}\mathrm{O}_2}^{+}$ transition frequencies is expected to be much smaller than that for heteronuclear diatomic molecules. However, the actual systematic uncertainties for the ${{}^{16}\mathrm{O}_2}^{+}$ transition frequencies have never been estimated. We estimated the Stark and Zeeman shifts in the different ${{}^{16}\mathrm{O}_2}^{+}$ transition frequencies. When the molecular ions in a string crystal formed in a linear trap (trap electric field $<0.1$ V/cm, and Stark shift $<{10}^{-20}$) are used, the $X^2{\mathrm{\Pi }}_{1/2}(v,J)=(0,1/2)-(v^{\prime },1/2)(v^{\prime }\ge 1)$ transition frequencies are most advantageous for the search for the variation in $\mu \left(\mathrm{\Delta }\mu /\mu <{10}^{-17}\right)$ because the Zeeman shift is easily suppressed to lower than ${10}^{-18}$ and the electric quadrupole shift is zero. On the other hand, the $X^2{\mathrm{\Pi }}_{1/2}\left(v,J\right)=\left(21,1/2\right)-a^4{\mathrm{\Pi }}_{1/2}\left(v,J\right)=\left(0,1/2\right)$ transition frequency has another merit in that the positive Stark shift induced by the trap electric field can be canceled by the quadratic Doppler shift. Therefore, the measurement using molecular ions in a Coulomb crystal broadened in the radial direction is also possible, when the Zeeman shift is effectively eliminated.

The eigenstate thermalization hypothesis provides one picture of thermalization in a quantum system by looking at individual eigenstates. However, it is also important to consider how local observables reach equilibrium values dynamically. Quench protocol is one of the settings to study such questions. A recent numerical study [Bañuls, Cirac, and Hastings, Phys. Rev. Lett. 106, 050405 (2007)] of a nonintegrable quantum Ising model with longitudinal field under such a quench setting found different behaviors for different initial quantum states. One particular case called the “weak-thermalization” regime showed apparently persistent oscillations of some observables. Here we provide an explanation of such oscillations. We note that the corresponding initial state has low energy density relative to the ground state of the model. We then use perturbation theory near the ground state and identify the oscillation frequency as essentially a quasiparticle gap. With this quasiparticle picture, we can then address the long-time behavior of the oscillations. Upon making additional approximations which intuitively should only make thermalization weaker, we argue that the oscillations nevertheless decay in the long-time limit. As part of our arguments, we also consider a quench from a BEC to a hard-core boson model in one dimension. We find that the expectation value of a single-boson creation operator oscillates but decays exponentially in time, while a pair-boson creation operator has oscillations with a $t^{-3/2}$ decay in time. We also study dependence of the decay time on the density of bosons in the low-density regime and use this to estimate decay time for oscillations in the original spin model.

We study, by first-principles computer simulations, the low-temperature phase diagram of bosonic dipolar gases in a bilayer geometry as a function of the two control parameters, i.e., the in-plane density and the interlayer distance. We observe four distinct phases, namely, paired and decoupled superfluids, as well as a crystal of dimers and one consisting of two aligned crystalline layers. A direct quantum phase transition from a dimer crystal to two independent superfluids is observed in a relatively wide range of parameters. No supersolid phase is predicted for this system.

A one-dimensional periodic array of circular dielectric cylinders surrounded by air is a simple structure on which guided modes above the light line, also called bound states in the continuum (BICs), may exist. Recent studies reveal that such an array supports not only antisymmetric standing waves which are symmetry-protected BICs, but also propagating Bloch BICs and symmetric standing waves. Near a BIC, there is a family of resonant modes (depending on the Bloch wave number $\beta$) with arbitrarily large quality factors. Using a perturbation method, we show that the quality factor of the resonant mode typically depends on $\beta$ like $1/{(\beta -{\beta }_{*})}^2$, where ${\beta }_{*}$ is the Bloch wave number of the BIC, but near a symmetric standing wave $({\beta }_{*}=0)$, the quality factor blows up like $1/{\beta }^4$. This indicates that strong resonances can be more easily induced near a symmetric standing wave. As an application, we numerically study optical bistability for the periodic array assuming the cylinders have a Kerr nonlinearity. With the nonlinear effects enhanced by the resonances, it is possible to have optical bistability for weak incident waves. The numerical results confirm that the weakest incident wave for optical bistability is realized through the resonances near the symmetric standing waves.

It is shown that the single-particle spin-orbit coupling terms, which—in the cold atom context—are associated with synthetic gauge fields, can significantly and nontrivially modify the phase accumulation at small interparticle distances even if the length scale ${\left(k_{\text{so}}\right)}^{-1}$ associated with the spin-orbit coupling term is significantly larger than the van der Waals length $r_{\text{vdW}}$ that characterizes the two-body interaction potential. A theoretical framework, which utilizes a generalized local frame transformation and accounts for the phase accumulation analytically, is developed. Comparison with numerical coupled-channel calculations demonstrates that the phase accumulation can, to a very good approximation, be described over a wide range of energies by the free-space scattering phase shifts—evaluated at a scattering energy that depends on $k_{\text{so}}$—and the spin-orbit coupling strength $k_{\text{so}}$.

We study non-Markovian effects present in a driven qubit coupled to a finite environment using a recently proposed model developed in the context of calorimetric measurements of open quantum systems. To quantify the degree of non-Markovianity we use the Breuer-Laine-Piilo (BLP) measure [H.-P. Breuer, Phys. Rev. Lett. 103, 210401 (2009)]. We show that information backflow only occurs in the case of driving, in which case we investigate the dependence of memory effects on the environment size, driving amplitude, and coupling to the environment. We show that the degree of non-Markovianity strongly depends on the ratio between the driving amplitude and the coupling strength. We also show that the degree of non-Markovianity does not decrease monotonically as a function of the environment size.

Asymmetry of quantum states is a useful resource in applications such as quantum metrology, quantum communication, and reference frame alignment. However, asymmetry of a state tends to be degraded in physical scenarios where environment-induced noise is described by covariant operations, e.g., open systems constrained by superselection rules, and such degradations weaken the abilities of the state to implement quantum information processing tasks. In this paper, we investigate under which dynamical conditions asymmetry of a state is totally unaffected by the noise described by covariant operations. We find that all asymmetry measures are frozen for a state under a covariant operation if and only if the relative entropy of asymmetry is frozen for the state. Our finding reveals the existence of universal freezing of asymmetry, and provides a necessary and sufficient condition under which asymmetry is totally unaffected by the noise.

We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically motivated assumptions, we provide strong numerical evidence that threefold degenerate X states of purity $P$ reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.

We present an approach for the quantification of quantumness of correlations in fermionic systems. We study the multipartite relative entropy of quantumness in such systems and show how the symmetries in the states can be used to obtain analytical solutions. Numerical evidence of the uniqueness of such solutions is also presented. Supported by these results, we show that the minimization of the multipartite relative entropy of quantumness, over certain choices of its mode multipartitions, reduces to the notion of quantumness of indistinguishable particles. By means of an activation protocol, we characterize the class of states without quantumness of correlations. As an example, we calculate the dynamics of quantumness of correlations for a purely dissipative system, whose stationary states exhibit interesting topological nonlocal correlations.