We calculate the relativistic correlation function for a hybrid system of a photon and a Dirac particle. Such a system can be produced in decay of another spin-$\frac{1}{2}$ fermion. We show that the relativistic correlation function, which depends on particle momenta, may have local extrema for fermion velocity of the order $0.5c$. This influences the degree of violation of the Clauser-Horne-Shimony-Holt inequality.

For a quantum computer acting on $d$-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect, and we allow access to imperfect nonstabilizer states or operations. If the noise rate affecting the nonstabilizer resource is sufficiently high, then these states and operations can become simulable in the sense of the Gottesman-Knill theorem, reducing the overall power of the circuit to no better than classical. In this paper we find the depolarizing noise rate at which this happens and consequently the most robust nonstabilizer states and non-Clifford gates. In doing so, we make use of the discrete Wigner function and derive facets of the so-called qudit Clifford polytope, i.e., the inequalities defining the convex hull of all qudit Clifford gates. Our results for robust states are provably optimal. For robust gates we find a critical noise rate that, as dimension increases, rapidly approaches the the theoretical optimum of 100%. Some connections with the question of qudit magic state distillation are discussed.

We have calculated triply differential cross sections (TDCS) and doubly differential cross sections (DDCS) for single ionization of ${\mathrm{H}}_2$ by 75-keV proton impact using the molecular three-body distorted-wave–eikonal initial-state (M3DW-EIS) approach. Previously published measured DDCS (differential in the projectile scattering angle and integrated over the ejected electron angles) found pronounced structures at relatively large angles that were interpreted as an interference resulting from the two-centered potential of the molecule. Theory treating ${\mathrm{H}}_2$ as atomic H multiplied by a molecular interference factor only predicts the observed structure when assumptions are made about the molecular orientation. Here we apply the M3DW-EIS method, which does not rely on such an ad hoc approach, but rather treats the interference from first principles.

Polar molecules in selected quantum states can be guided, decelerated, and trapped using electric fields created by microstructured electrodes on a chip. Here we explore how nonadiabatic transitions between levels in which the molecules are trapped and levels in which the molecules are not trapped can be suppressed. We use ${}^{12}\mathrm{C}$O and ${}^{13}\mathrm{C}$O ($a\hspace{0.5em}{}^3{\Pi }_1,v=0$) molecules, prepared in the upper $\Lambda$-doublet component of the $J=1$ rotational level, and study the trap loss as a function of an offset magnetic field. The experimentally observed suppression (enhancement) of the nonadiabatic transitions for ${}^{12}\mathrm{C}$O (${}^{13}\mathrm{C}$O) with increasing magnetic field is quantitatively explained.

We demonstrate a photon-counting technique for detecting Bragg excitation of an ultracold gas of atoms. By measuring the response of the light field to the atoms, we derive a signal independent of traditional time-of-flight atom-imaging techniques. With heterodyne detection we achieve photon shot-noise limited detection of the amplification or depletion of one of the Bragg laser beams. Photon counting for Bragg spectroscopy will be useful for strongly interacting gases where atom-imaging detection fails. In addition, this technique provides the ability to resolve the evolution of excitations as a function of pulse duration.

We study the behavior of two coupled purely dipolar Bose-Einstein condensates (BECs), each located in a cylindrically symmetric pancake-shaped external confining potential, as the separation $b$ between the traps along the tight confining direction is varied. The solutions of the coupled Gross-Pitaevskii and Bogoliubov-de Gennes equations, which account for the full dynamics, show that the system behavior is modified by the presence of the second dipolar BEC. For sufficiently small $b$, the presence of the second dipolar BEC destabilizes the system dramatically. In this regime, the coupled system collapses through a mode that is notably different from the radial roton mode that induces the collapse of the uncoupled system. Finally, we comment on the shortcomings of an approach that employs a separable wavefunction, which is assumed to be a good approximation for highly pancake-shaped dipolar BECs in the literature.

$\mathcal{PT}$-symmetric systems can have a real spectrum even when their Hamiltonian is non-Hermitian, but develop a complex spectrum when the degree of non-Hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous $\mathcal{PT}$-symmetry breaking can occur via two distinct mechanisms, whose predominance is associated to different universality classes. Present optical experiments fall into the orthogonal class, where symmetry-induced level crossings render the characteristic absorption rate independent of the coupling strength between the symmetry-related parts of the system.

We develop the constrained adiabatic trajectory method (CATM), which allows one to solve the time-dependent Schrödinger equation constraining the dynamics to a single Floquet eigenstate, as if it were adiabatic. This constrained Floquet state (CFS) is determined from the Hamiltonian modified by an artificial time-dependent absorbing potential whose forms are derived according to the initial conditions. The main advantage of this technique for practical implementation is that the CFS is easy to determine even for large systems since its corresponding eigenvalue is well isolated from the others through its imaginary part. The properties and limitations of the CATM are explored through simple examples.

Many properties of current ab initio approaches to the quantum many-body problem, both perturbational and otherwise, are related to the singularity structure of the Rayleigh-Schrödinger perturbation series. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the Hamiltonian matrix on a vector and does not rely on the terms in the perturbation series. The method can be useful for studying perturbation series of typical systems of moderate size, for fundamental development of resummation schemes, and for understanding the structure of singularities for typical systems. Some illustrative model problems are studied, including a helium-like model with $\delta$-function interactions for which Møller-Plesset perturbation theory is considered and the radius of convergence found.

High-resolution dissociative recombination rate coefficients of rotationally cool and hot ${\mathrm{H}}_3^{+}$ in the vibrational ground state have been measured with a 22-pole trap setup and a Penning ion source, respectively, at the ion storage-ring TSR. The experimental results are compared with theoretical calculations to explore the dependence of the rate coefficient on ion temperature and to study the contributions of different symmetries to probe the rich predicted resonance spectrum. The kinetic energy release was investigated by fragment imaging to derive internal temperatures of the stored parent ions under differing experimental conditions. A systematic experimental assessment of heating effects is performed which, together with a survey of other recent storage-ring data, suggests that the present rotationally cool rate-coefficient measurement was performed at 380${}_{-130}^{+50}$ K and that this is the lowest rotational temperature so far realized in storage-ring rate-coefficient measurements on ${\mathrm{H}}_3^{+}$. This partially supports the theoretical suggestion that temperatures higher than assumed in earlier experiments are the main cause for the large gap between the experimental and the theoretical rate coefficients. For the rotationally hot rate-coefficient measurement a temperature of below 3250 K is derived. From these higher-temperature results it is found that increasing the rotational ion temperature in the calculations cannot fully close the gap between the theoretical and the experimental rate coefficients.

Providing a femtosecond optical pulse with a proper transverse spatial profile represents a fast and relatively simple method to force a quantum system to follow a prescribed temporal evolution. In the present work, we show that the quantum system presents a surprisingly high sensitivity with respect to the spatial shape of the pulse. We discuss an explicit example where differences on the order of a few nanometers in the initial pulse’s spot size induce completely different responses in the system under study.

After deriving the isothermal Hellmann-Feynman theorem (IHFT) that is suitable for mixed states in a canonical ensemble, we use this theorem to obtain the isothermal magnetic-field sweep theorems for the free, average, and trapping energies and for the entropy, specific heat, pressure, and atomic compressibility of strongly correlated ultracold quantum gases. In particular, we apply the sweep theorems to two-component Fermi gases in the weakly interacting Bardeen-Cooper-Schrieffer and Bose-Einstein condensate limits, showing that the temperature dependence of the contact parameter can be determined by varying either the entropy or specific heat with respect to the scattering length. We also use the IHFT to obtain the virial theorem in a canonical ensemble and discuss its implications for quantum gases.

We investigate the Stückelberg oscillations of a spin-1 Bose-Einstein condensate subject to a spatially inhomogeneous transverse magnetic field and a periodic longitudinal field. We show that the time-domain Stückelberg oscillations result in modulations in the density profiles of all spin components due to the spatial inhomogeneity of the transverse field. This phenomenon represents the Landau-Zener-Stückelberg interference in the space domain. Since the magnetic dipole-dipole interaction between spin-1 atoms induces an inhomogeneous effective magnetic field, interference fringes also appear if a dipolar spinor condensate is driven periodically. We also point out some potential applications of this spatial Landau-Zener-Stükelberg interference.

A simple optical structure, termed a pillar-slit structure, is proposed to enhance the contrast ratio of the weak optical signal. The structure consists of a metal slit surrounded by two metal pillars and can be directly incorporated onto optical sensors. The waves excited on the incident surface are modulated by the pillars and then scattered by the slit entrance so as to generate the in-slit surface plasmon polaritons passing through the slit. The transmission power is modified by the surface wave intensity. This structure is capable of suppressing background and enhancing signal light simultaneously. A calculated illustration by the numerical simulation method shows that an increase of the contrast ratio can be exceeded 900 times.

It is shown that broadband chaos suitable for fast nondeterministic random-bit generation in small devices can be achieved in a semiconductor laser with a short external cavity. The design of the device is based on a theoretical model for nondeterministic random-bit generation by amplification of microscopic noise. Moreover, it is demonstrated that bit sequences passing common tests of statistical randomness at rates up to 2.08 Gbits/s can be generated using on-chip lasers with a monolithically integrated external cavity, amplifiers, and a photodetector.

X-ray emission originating in charge-exchange collisions between Ar${}^{18+}$ and neutral argon is studied at impact energies of 5–4000 eV/amu by means of the classical trajectory Monte Carlo method (CTMC). Line emission and charge-exchange cross sections obtained from different CTMC versions based on the one-active electron approximation are contrasted among themselves and against the results obtained by means of a three-active electron code that lets us infer the role of multiple electron capture. The present results are compared to the recent experimental data available from the EBIT groups operating at Livermore, NIST, and Berlin. We were not able to reconcile the major difference in x-ray emission cross sections obtained from in situ measurements made in EBIT, versus those made in an exterior, field-free collision chamber using ions extracted from the EBIT. Our calculations support the extracted beam results.

We analyze paired phases of cold bosonic atoms with spin $S=1$ and with an attractive interaction. We derive mean-field self-consistent equations for the matrix order parameter describing such paired bosons on an optical lattice. The possible solutions are classified according to their symmetries. In particular, we find that the self-consistent equations for the SO(3) symmetric phase are of the same form as those for scalar bosons with attractive interactions. This singlet phase may exhibit either the BCS-type pairing instability (BCS phase) or the Bose-Einstein condensation (BEC) quasiparticle condensation together with the BCS-type pairing (BEC phase) for an arbitrary attraction $U_0$ in the singlet channel of the two-body interaction. We show that both condensate phases become stable if a repulsion $U_2$ in the quintet channel is above a critical value, which depends on $U_0$ and other thermodynamic parameters.

We propose a simple and robust mechanism to achieve unidirectional emission in a microcavity comprised of two half-ellipses. The microcavity has two geometrical parameters, two eccentricities, which permit a control of the directional emissions. For the microcavity with two small eccentricities, the positions of secondary islands near primary islands in the survival probability distributions determine the directionality of emissions. We obtain the optimized values of the eccentricities for unidirectional emission.

Spontaneous parametric down-conversion has been shown to be a reliable source of entangled photons. Among the wide range of properties shown to be entangled, it is the orbital angular momentum that is the focus of our study. We investigate, in particular, the bi-photon state generated using a Gaussian pump beam. We derive an expression for the simultaneous correlations in the orbital angular momentum, $\ell$, and radial momentum, $p$, of the down-converted Laguerre-Gaussian beams. Our result allows us, for example, to calculate the spiral bandwidth with no restriction on the geometry of the beams: $\ell$, $p$, and the beam widths are all free parameters. Moreover, we show that, with the usual paraxial and collinear approximations, a fully analytic expression for the correlations can be derived.