Coherence properties of light beams generated by optical parametric oscillators (OPOs) are discussed in the region of threshold. Analytic expressions, that are valid throughout the threshold region, for experimentally measurable quantities such as the mean and variance of photon number fluctuations, squeezing of field quadratures, and photon counting distributions are derived. These expressions describe non-Gaussian fluctuations of light in the region of threshold and reproduce Gaussian fluctuations below and above threshold, thus providing a bridge between below and above threshold regimes of operation. They are used to study the transformation of fluctuation properties of light as the OPOs make a transition from below to above threshold. The results for the OPOs are compared to those for the single-mode and two-mode lasers and their similarities and differences are discussed.

We propose a realistic protocol to generate entanglement between quantum memories at neighboring nodes in hybrid quantum repeaters. Generated entanglement includes only one type of error, which enables efficient entanglement distillation. In contrast to the known protocols with such a property, our protocol with ideal detectors achieves the theoretical limit of the success probability and the fidelity to a Bell state, promising higher efficiencies in the repeaters. We also show that the advantage of our protocol remains even with realistic threshold detectors.

Quantum mechanical phases arising from a periodically varying Hamiltonian are considered. These phases are derived from the eigenvalues of a stationary, “dressed” Hamiltonian that is able to treat internal atomic or molecular structure in addition to the time variation. In the limit of an adiabatic time variation, the usual Berry phase is recovered. For more rapid variation, nonadiabatic corrections to the Berry phase are recovered in perturbation theory, and their explicit dependence on internal structure emerges. Simple demonstrations of this formalism are given, to particles containing interacting spins, and to molecules in electric fields.

The low-rotational lines of the $A{}^2\Pi \text{−}X{{}^2\Sigma }^{+}\left(0,0\right)$ band system of the odd isotopologue of strontium monofluoride, ${}^{87}\text{S}\text{rF}$, were recorded and analyzed. The ${}^{87}\text{S}\text{r}\left(I=9/2\right)$ magnetic hyperfine interaction is significant only in the $\left|\Omega \right|=1/2$ spin-orbit component of the $A{}^2\Pi$ state. Optical transitions appropriate for monitoring ultracold samples of ${}^{87}\text{S}\text{rF}$ are identified. The determined fine-structure parameters were used to predict the anisotropic magnetic $g$ factor, $g_l$, for the $X{{}^2\Sigma }^{+}\left(v=0\right)$ state. The $g$ factors were used to predict the magnetic tuning of the $N=0$ $\left(+\text{parity}\right)$ and $N=1$ $\left(-\text{parity}\right)$ levels of the $X{{}^2\Sigma }^{+}\left(v=0\right)$ state. A comparison to spectroscopic parameters for the ${}^{88}\text{S}\text{rF}$ isotopologue is given.

We investigate the phenomenon of fermionic pairing with mismatched Fermi surfaces in a two-species system in the presence of Feshbach resonance, where the resonantly paired fermions combine to form bosonic molecules. We observe that the Feshbach parameters control the critical temperature of the gapped BCS superfluid state, and also determine the range over which a gapless breached pair state may exist. Demanding the positivity of the superfluid density, it is shown that although a breached pair state with two Fermi surfaces is always unstable, its single Fermi-surface counterpart can be stable if the chemical potentials of the two pairing species have opposite signs. This condition is satisfied only over a narrow region in the BEC side, characterized by an upper and a lower limit for the magnetic field. We estimate these limits for a mixture of two hyperfine states of ${}^6\text{L}\text{i}$ using recent experimental data.

Cold atoms in an optical lattice execute Bloch-Zener oscillations when they are accelerated. We have performed a theoretical investigation into the case when the optical lattice is the intracavity field of a driven Fabry-Perot resonator. When the atoms oscillate inside the resonator, we find that their back-action modulates the phase and intensity of the light transmitted through the cavity. We solve the coupled atom-light equations self-consistently and show that, remarkably, the Bloch period is unaffected by this back-action. The transmitted light provides a way to observe the oscillation continuously, allowing high-precision measurements to be made with a small cloud of atoms.

In this paper, the interface between two transformation media or between a transformation medium and vacuum is studied. Strictly from the transformation optics point of view, the consequences of the boundary conditions at such interfaces are addressed in two different ways. First, we analyze a restricted class of reflectionless interfaces, for which the tools of transformation optics allow to describe the electromagnetic fields on both sides of the interface by means of the same vacuum solution of the Maxwell equations. In a second step, we examine interfaces between two arbitrary transformation media. This analysis is extended to the recently suggested generalization of transformation optics by the author. As a basic application it is shown how the standard law of reflection and refraction at an interface between vacuum and a homogeneous and isotropic medium with arbitrary and independent permittivity and permeability can be understood in a completely geometric way by the use of generalized transformation optics.

We study the interplay of quantum statistics, strong interactions, and finite temperatures in the two-component (spinor) Bose gas with repulsive delta-function interactions in one dimension. Using the Thermodynamic Bethe Ansatz, we obtain the equation of state, population densities, and local density correlation numerically as a function of all physical parameters (interaction, temperature, and chemical potentials), quantifying the full crossover between low-temperature ferromagnetic and high-temperature unpolarized regimes. In contrast to the single component, Lieb-Liniger gas, nonmonotonic behavior of the local density correlation as a function of temperature is observed.

The only information available about an alleged source of entangled quantum states is the amount $S$ by which the Clauser-Horne-Shimony-Holt inequality is violated: nothing is known about the nature of the system or the measurements that are performed. We discuss how the quality of the source can be assessed in this black-box scenario, as compared to an ideal source that would produce maximally entangled states (more precisely, any state for which $S=2\sqrt{2}$). To this end, we present several inequivalent notions of fidelity, each one related to the use one can make of the source after having assessed it, and we derive quantitative bounds for each of them in terms of the violation $S$. We also derive a lower bound on the entanglement of the source as a function of $S$ only.

We develop a determinantal method in a quantum scattering system for direct evaluation of various quantities including the local field amplitude and transition amplitude ($S$-matrix element). This method is applicable to multichannel elastic and inelastic scattering systems without rearranging the particles. The underlying principle of our formulation is that requested information can be extracted from a wave operator without solving the wave equation. The wave operator is the master operator maintaining all of the information about a system; the determinant of the inverse wave operator is just the Fredholm determinant. In the 1960s, a similar determinantal method was developed for the $S$-matrix element or equivalently the far-field amplitude of the wave function. Until now, however, no determinantal method for near-field quantities existed, although de Broglie and electromagnetic near fields are observable using scanning probe microscopes. Additionally, we prove that our formula for $S$-matrix element covers the known formula (the Le Couteur-Newton formula).

We demonstrate an atom detector based on field ionization and subsequent ion counting. We make use of field enhancement near tips of carbon nanotubes to reach extreme electrostatic field values of up to $9\times {10}^9\text{V}/\text{m}$, which ionize ground-state rubidium atoms. The detector is based on a carpet of multiwall carbon nanotubes grown on a substrate and used for field ionization, and a channel electron multiplier used for ion counting. We measure the field enhancement at the tips of carbon nanotubes by field emission of electrons. We demonstrate the operation of the field ionization detector by counting atoms from a thermal beam of a rubidium dispenser source. By measuring the ionization rate of rubidium as a function of the applied detector voltage we identify the field ionization distance, which is below a few tens of nanometers in front of nanotube tips. We deduce from the experimental data that field ionization of rubidium near nanotube tips takes place on a time scale faster than ${10}^{-10}\text{s}$. This property is particularly interesting for the development of fast atom detectors suitable for measuring correlations in ultracold quantum gases. We also describe an application of the detector as partial pressure gauge.

Population transfer to the excited electronic state $E{{}^1\Sigma }_{\text{g}}$ of ${\text{Li}}_2$ by transform limited delayed femtosecond pulses has been investigated. The validity of the usual neglect of some field-molecule coupling terms in such transfers, accomplished using counterintuitively ordered pulses through “adiabatic passage on light-induced potentials,” has been reexamined. It has been found that such an approximation cannot be justified in the case of the ladder system $X{}^1\Sigma ^{+}{}_{\text{g}}\text{−}A{}^1\Sigma ^{+}{}_{\text{u}}\text{−}E{}^1\Sigma ^{+}{}_{\text{g}}$ of ${\text{Li}}_2$. However, the transfer can be successfully accomplished over a range of pulse parameters, which is more restricted than those obtained with the usual approximation. In this scheme, when two pulses with a small frequency difference between them are used, the lower-frequency pulse must precede the higher-frequency pulse for a successful transfer. We introduce an adiabatic representation, appropriate to this full coupling case, for examining the mechanism of transfer. In our representation the initial wave packet may be prepared on more than one adiabatic state, and at an early stage it is transferred to a single adiabatic surface after which the evolution mostly proceeds adiabatically. The vibrational analysis of the final wave packet shows that for short pulses high vibrational states are generally excited, while for pulses with larger width low-lying vibrational states are preferred in cases where successful transfer occurs. These results can be understood in terms of the motion of the wave packet on the time-dependent adiabatic potentials.

We report on a teleportation scheme, in which a controllable orbital angular momentum (OAM) generator is teleported. Via our scheme, Alice is able to—according to another independent photon’s spin state (polarization) sent by Carol—electrically control the remote OAM generation on Bob’s photon. To this end, we introduce a local electrically tunable and spin-dependent OAM generator to transfer a preliminary OAM-OAM entanglement to a spin-OAM hybrid entanglement, which then makes a joint Bell-state measurement on Alice and Carol’s photons play its role. We show that the quantum state tomography can be introduced to evaluate the performance of the teleportation.

We report on the experimental observation of two-dimensional surface solitons residing at the interface between a homogeneous square lattice and a superlattice that consists of alternating “deep” and “shallow” waveguides. By exciting single waveguides in the first row of the superlattice, we show that solitons centered on deep sites require much lower powers for their excitation than their respective counterparts centered on shallow sites. Despite the fact that the average refractive index of the superlattice waveguides is equal to the refractive index of the homogeneous lattice, the interface results in clearly asymmetric output patterns.

Several wave-function approximations describing spontaneous parametric down-conversion can be found in the literature. Basically all cases are derived from the standard Hamiltonian for parametric down-conversion. Most frequently, particular cases describing collinear or paraxial approximations are described. This work presents a wave function in compact form, valid for all cases of single photon-pair conversion (Type I or Type II), for all angles allowed by the phase-matching conditions and for all orbital angular momentum values $l$. Examples are given of coincidence structures to be expected for signal and idler photons. Partial transfer of orbital angular momentum from the pump laser to the photon pair is discussed. Some hypothesis for the decay channels of the nontransferred part of the orbital angular momentum is made.

In order to characterize the statistical aspect of the energy loss in particle penetration, Bohr developed a kinetic theory and applied it to a beam of fast $\alpha$ particles interacting with free electrons. The present study rests on this classical theory of collisional straggling, and it is implemented by using a partially screened Coulomb potential to model the electron-projectile interaction. The deflection angle of electron scattering in this long-ranged field is calculated analytically within the framework of classical mechanics. The transport fluctuation cross section, which is the basic quantity to the collisional straggling in Bohr’s modeling, is determined numerically. By varying the number of bound electrons around the swift He ions, the effect of prefixed charge states in the collisional energy-loss straggling is quantified. An incoherent weighted summation of different fixed charge-state channels is discussed as well, by using normalized probabilities.

We present a fundamental concept—closed sets of correlations—for studying nonlocal correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical theories, must be closed under a natural set of operations. Hence, studying the closure of sets of correlations gives insight into which information-theoretic principles are genuinely different, and which are ultimately equivalent. This concept also has implications for understanding why quantum nonlocality is limited, and for finding constraints on physical theories beyond quantum mechanics.

The resources required to solve the general interacting quantum $N$-body problem scale exponentially with $N$, making the solution of this problem very difficult when $N$ is large. In a previous series of papers we develop an approach for a fully interacting wave function for a confined system of identical bosons with a general two-body interaction. This method tames the $N$ scaling by developing a perturbation series that is order-by-order invariant under a point group isomorphic with $S_N$. Group theory and graphical techniques are then used to solve for the wave function exactly and analytically at each order, yielding a solution for the general $N$-body problem which scales as $N^0$ at any given order. Recently this formalism has been used to obtain the first-order fully interacting wave function for a system of harmonically confined bosons interacting harmonically. In this paper, we report the application of this $N$-body wave function to a system of $N$ fully interacting bosons in three dimensions. We derive an expression for the density profile for a confined system of harmonically interacting bosons. Choosing this simple interaction is not necessary or even advantageous for our method, however this choice allows a direct comparison of our exact results through first order with exact results obtained in an independent solution. Our density profile for the wave function through first order in three dimensions is indistinguishable from the first-order exact result obtained independently and shows strong convergence to the exact result to all orders.

Using a dynamical quantum Zeno effect, we propose a general approach to control the coupling between a two-level system (TLS) and its surroundings, by modulating the energy-level spacing of the TLS with a high-frequency signal. We show that the TLS-surroundings interaction can be turned off when the ratio between the amplitude and the frequency of the modulating field is adjusted to be a zero of a Bessel function. The quantum Zeno effect of the TLS can also be observed by the vanishing of the photon reflection at these zeros. Based on these results, we propose a quantum switch to control the transport of a single photon in a one-dimensional waveguide. Our analytical results agree well with numerical results using Floquet theory.

We investigate the connection between local minima in the problem Hamiltonian and first-order quantum phase transitions during adiabatic quantum computation. We demonstrate how some properties of the local minima can lead to an extremely small gap that is exponentially sensitive to the Hamiltonian parameters. Using perturbation expansion, we derive an analytical formula that cannot only predict the behavior of the gap, but also provide insight on how to controllably vary the gap size by changing the parameters. We show agreement with numerical calculations for a weighted maximum independent set problem instance.