We investigate a state discrimination problem in operationally the most general framework to use a probability, including both classical, quantum theories, and more. In this wide framework, introducing closely related family of ensembles (which we call a Helstrom family of ensembles) with the problem, we provide a geometrical method to find an optimal measurement for state discrimination by means of Bayesian strategy. We illustrate our method in two-level quantum systems and in a probabilistic model with square-state space to reproduce, e.g., the optimal success probabilities for binary state discrimination and $N$ numbers of symmetric quantum states. The existences of families of ensembles in binary cases are shown both in classical and quantum theories in any generic cases.

We analyze bipartite quantum states that admit a symmetric extension. Any such state can be decomposed into a convex combination of states that allow a pure symmetric extension. A necessary condition for a state to admit a pure symmetric extension is that the spectra of the local and global density matrices are equal. This condition is also sufficient for two qubits but not for any larger systems. Using this condition, we present a conjectured necessary and sufficient condition for a two-qubit state to admit symmetric extension, which we prove in some special cases. The results from symmetric extension carry over to degradable and antidegradable channels and we use this to prove that all degradable channels with qubit output have a qubit environment.

A theoretical study of the all two-photon transitions from initial bound states with $n_i=2,3$ in hydrogenic ions is presented. High-precision values of relativistic decay rates for ions with nuclear charge in the range $1\le Z\le 92$ are obtained through the use of finite basis sets for the Dirac equation constructed from B splines. We also report the spectral (energy) distributions of several resonant transitions, which exhibit interesting structures, such as zeros in the emission spectrum, indicating that two-photon emission is strongly suppressed at certain frequencies. We compare two different approaches (the line profile approach and the QED approach based on the analysis of the relativistic two-loop self-energy) to regularize the resonant contribution to the decay rate. Predictions for the pure two-photon contributions obtained in these approaches are found to be in good numerical agreement.

The double-resonant laser excitation of nitric oxide, cooled to 1 K in a seeded supersonic molecular beam, yields a gas of $\approx {10}^{12}$ molecules per cubic centimeter in a single selected Rydberg state. This population evolves to produce prompt free electrons, and a durable cold plasma of electrons and intact ${\text{NO}}^{+}$ ions. This plasma travels with the molecular beam through a field-free region to encounter a grid. The atomic weight of the expansion gas controls the beam velocity and hence the flight time from the interaction region to the grid. Monitoring electron production as the plasma traverses this grid measures its longitudinal width as a function of flight time. Comparing these widths to the width of the laser beam that defines the initial size of the illuminated volume allows us to gauge the rate of expansion of the plasma. We find that the plasma created from the evolution of a Rydberg gas of NO expands at a small but measurable rate, and that this rate of expansion accords with the Vlasov equations for an initial electron temperature of $T_e\approx 7\text{K}$.

We present a rigorous quantum study of spin-exchange transitions in collisions of the alkali-metal atoms with ${}^3\text{H}\text{e}$ in the presence of an external magnetic field. Using accurate ab initio interaction potentials, we obtain refined estimates for the Fermi contact interaction constants for complexes of Na, K, and Rb atoms with ${}^3\text{H}\text{e}$. Ab initio calculations show that the Fermi contact interaction in $\text{Li-}{}^3\text{H}\text{e}$ varies more slowly with internuclear distance than predicted by the atomic model [R. M. Herman, Phys. Rev. 37, A1062 (1965)]. The calculated spin-exchange rate constants for Na, K, and Rb atoms in a gas of ${}^3\text{H}\text{e}$ are in good agreement with experimental data. Our calculations demonstrate that at a temperature of 0.5 K, collision-induced spin exchange of the alkali-metal atoms occurs at a very slow rate of $\sim {10}^{-22}{\text{cm}}^3/\text{s}$, suggesting potential applications in cryogenic cooling, precision spectroscopy, and quantum optics.

First time-resolved photoemission experiments employing attosecond streaking of electrons emitted by an extended ultraviolet pump pulse and probed by a few-cycle near-infrared pulse found a time delay of about 100 as between photoelectrons from the conduction band and those from the $4f$ core level of tungsten. We present a microscopic simulation of the emission time and energy spectra employing a classical transport theory. Emission spectra and streaking images are well reproduced. Different contributions to the delayed emission of core electrons are identified: larger emission depth, slowing down by inelastic-scattering processes, and possibly, energy-dependent deviations from the free-electron dispersion. We find delay times near the lower bound of the experimental data.

We present an iterative analytic solution for the time dynamics of the ${}^{87}\text{R}\text{b}$ four-level atoms excited by a train of ultrashort pulses. It enables fast and accurate calculation of the system time evolution circumventing the use of time-consuming numerical procedures. The obtained solution is used to study the complex interaction of atoms with the pulse-train electric field, both in time and frequency domain. We investigate the influence of pulse-train physical parameters, such as the pulse peak power, the repetition frequency and the central laser wavelength on the accumulation of population and coherence in the system characterized by relaxation times larger than the pulse repetition period.

We report an experimental study of the $1.064\mu \text{m}$ transition dipoles in neodymium-doped yttrium aluminum garnet (Nd:YAG) by measuring the coupling constant between two orthogonal modes of a laser cavity for different cuts of the YAG gain crystal. We propose a theoretical model in which the transition dipoles, slightly elliptic, are oriented along the crystallographic axes. Our experimental measurements show a very good quantitative agreement with this model and predict a dipole ellipticity between 2% and 3%. This work provides an experimental evidence for the simple description in which transition dipoles and crystallographic axes are collinear in Nd:YAG (with an accuracy better than $1°$), a point that has been discussed for years.

A scheme is proposed for realizing geometric quantum computation with one-qubit unitary gates and $N$-qubit $\left(N\ge 2\right)$ phase gates in cavity QED. In the scheme, the cavity field and excited states are virtually excited by controlling appropriately atom-field couplings and engineering adiabatic passage; thus the gate operations are insensitive to the cavity decay and the atomic spontaneous emission. Furthermore, the $N$-qubit $\left(N\ge 2\right)$ geometric phase gates can be realized just by one step and the required time does not increase with the number of qubits, which can significantly reduce complexity of physical realization of practical quantum computation and quantum algorithms.

We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential in the presence of a uniform magnetic field. It is shown that the unstable system exhibits a rich structure, with complex normal modes as well as nonstandard modes of evolution characterized by equations of motion which cannot be decoupled (nonseparable cases). It is also shown that in some unstable cases the dynamics can be stabilized by increasing the magnetic field or tuning the rotational frequency, giving rise to dynamical stability or instability windows. The evolution in general nondiagonalizable cases is as well discussed.

Initial switching refers to the way in which the decay of an initially confined state begins, as the barrier isolating it from the exterior is relaxed. We study these effects in the context of Longhi’s version of the Fano-Anderson model. Most authors assume the sudden approximation where the coupling is turned on instantaneously. We consider a finite rise time $T$ both numerically and analytically. When the coupling is ramped up linearly over a switching time $T$, we show that the asymptotic survival amplitude acquires a phase $T$ and is modulated by a factor $\left(\text{sin}T\right)/T$. Several other results relating to the solution of the model are obtained. All site amplitudes have the same decay constant during the exponential decay regime. In the asymptotic regime, the amplitude and phase of decay oscillations depend on the initial-switching profile, but the period does not.

We implemented an optical one-way potential barrier that allows ultracold ${}^{87}\text{R}\text{b}$ atoms to transmit through when incident on one side of the barrier but reflect from the other. This asymmetric barrier is a realization of Maxwell’s demon, which can be employed to produce phase-space compression and has implications for cooling atoms and molecules not amenable to standard laser-cooling techniques. The barrier comprises two focused Gaussian laser beams that intersect the focus of a far-off-resonant single-beam optical dipole trap that holds the atoms. The main barrier beam presents a state-dependent potential to incident atoms, while the repumping barrier beam optically pumps atoms to a trapped state. We investigated the robustness of the barrier asymmetry to changes in the barrier-beam separation, the initial atomic potential energy, the intensity of the second beam, and the detuning of the first beam. We performed simulations of the atomic dynamics in the presence of the barrier, showing that the initial three-dimensional momentum distribution plays a significant role, and that light-assisted collisions are likely the dominant loss mechanism. We also carefully examined the relationship to Maxwell’s demon and explicitly accounted for the apparent decrease in entropy for our particular system.

We consider an atomic Fermi gas confined in a uniform optical lattice potential, where the atoms can pair into molecules via a magnetic field controlled narrow Feshbach resonance. Thus by adjusting the magnetic field the portion of fermionic and bosonic particles in the system can be continuously varied. We analyze the statistical mechanics of this system and consider the interplay of the lattice physics with the atom-molecule conversion. We study the entropic behavior of the system and characterize the temperature changes that occur during adiabatic ramps across the Feshbach resonance. We show that an appropriate choice of filling fraction can be used to reduce the system temperature during such ramps.

Various types of solitary wave pulses are obtained theoretically based on the analytic solutions for the higher-order nonlinear Schrödinger equation. Different from the previous results, the bright solitons are observed in the normal group-velocity dispersion regime. Depending on the parameters’ values, the properties of both bright and dark solitons are analyzed. Furthermore, the soliton types are found to be interchangeable after the collision, and the transfer mode of the solitons can be controlled under certain conditions. This might be of potential applications in the design of optical switch, pulse signal converters, and optical communication systems.

We propose the use of a superconducting charge qubit capacitively coupled to two resonant nanomechanical resonators to generate Yurke-Stoler states, i.e., quantum superpositions of pairs of distinguishable coherent states $180°$ out of phase with each other. This is achieved by effectively implementing Kerr nonlinearities induced through the application of a strong external driving field in one of the resonators. A simple study of the effect of dissipation on our scheme is also presented and lower bounds of fidelity and purity of the generated state are calculated. Our procedure to implement a Kerr nonlinearity in this system may be used for high-precision measurements in nanomechanical resonators.

We show by means of numerical simulations that the quantum wake of impulsive molecular alignment provides a simple system to achieve frequency tuning of the broadband spectrum of a few-cycle pulse. A femtosecond pump pulse serves both to form a filament in a molecular gas and to align the molecules. A delayed few-cycle pulse probing the quantum wake is shown to experience a guiding mechanism. Its spectrum is red- or blueshifted while its duration remains comparable to the duration of the incident pulse, resulting in a controllable process to tune the frequency of a few-cycle laser pulse.

Approximate analytic expressions for haze (and gloss) of Gaussian randomly rough surfaces for various types of correlation functions are derived within phase-perturbation theory. The approximations depend on the angle of incidence, polarization of the incident light, the surface roughness, $\sigma$, and the average of the power spectrum taken over a small angular interval about the specular direction. In particular it is demonstrated that haze (gloss) increase (decrease) with $\sigma /\lambda$ as $\text{exp}\left[-A{\left(\sigma /\lambda \right)}^2\right]$ and decreases (increase) with $a/\lambda$, where $a$ is the correlation length of the surface roughness, in a way that depends on the specific form of the correlation function being considered. These approximations are compared to what can be obtained from a rigorous Monte Carlo simulation approach, and a good agreement is found over large regions of parameter space. Some experimental results for the angular distribution of the transmitted light through polymer films and their haze are presented and compared to the analytic approximations derived in this paper. A satisfactory agreement is found. In the literature haze of blown polyethylene films has been related to surface roughness. Few authors have quantified the roughness and others have pointed to the difficulty in finding the correct roughness measure.

We report measurement of the inelastic and elastic collision rates for ${}^{88}\text{S}\text{r}$ atoms in the $\left(5s5p\right){{}^{3}P}_0$ state in a crossed-beam optical dipole trap. Since the $\left(5s5p\right){{}^{3}P}_0$ state is the lowest level of the triplet manifold, large loss rates indicate the importance of principle-quantum-number-changing collisions at short range. We also provide an estimate of the collisional loss rates for the $\left(5s5p\right){{}^{3}P}_2$ state. Large loss-rate coefficients for both states indicate that evaporative cooling toward quantum degeneracy in these systems is unlikely to be successful.

We carry out a decoherent-histories analysis of the arrival-time problem, taking advantage of a recently demonstrated connection between time-ordered strings of projection operators and evolution in the presence of a complex potential of step-function form. We concentrate on the limit of a weak potential, in which the resulting arrival-time distribution function is closely related to the quantum-mechanical current. We first consider the analogous classical arrival-time problem involving an absorbing potential, and this sheds some light on certain aspects of the quantum case. We use the path-decomposition expansion to give a derivation of the standard arrival-time distribution defined using a complex potential. This derivation is then used in the decoherent-histories analysis to obtain very simple and plausible expressions for the class operators (describing the amplitudes for crossing the origin during intervals of time). We show that decoherence of histories is obtained for a wide class of initial states (such as simple wave packets and superpositions of wave packets). We find that the decoherent-histories approach gives results with a sensible classical limit that are fully compatible with standard results on the arrival-time problem. We also find some interesting connections between backflow and decoherence.