Semiclassical approaches of molecular collisions as proposed by Miller and Marcus involve phase indices, related to focal and turning points along trajectories contributing to $S$ matrix elements. The main purpose of the work is to revisit the previous approaches in the case of two degrees of freedom rotationally inelastic collisions so as to make phase indices explicitly appear from first principles. Classical $S$ matrix theory (CSMT) and three semiclassical initial value representation (SCIVR) treatments, respectively involving simple, double, and triple integrals, are considered. The phase index is either the Maslov index of the classical configuration space Green function (CSMT and the first two SCIVR methods), or the Maslov index of the Van Vleck–Gutzwiller space-time propagator (third SCIVR method). In order to assess the validity of the four previous approaches, their predictions are compared with exact quantum scattering results for interaction potentials leading to strong quantum interferences. The Gaussian weighting procedure, recently introduced in the quasiclassical trajectory method, is used here for practical CSMT calculations. We finally discuss the standard application of CSMT in the light of the previous developments and results.

The precession of an electric dipole moment in an external electric field can be reversed by reversing the field direction. This time-reversal operation allows study of coherence in the time evolution of Rydberg Stark wave packets by measuring the resulting echoes. Different sources of reversible dephasing and irreversible dephasing, i.e., decoherence, are discussed in detail. Stochastic interactions with the environment are simulated in a controlled manner by using artificially synthesized noise. The rate of irreversible dephasing is determined from the reduction of the echo amplitude under multiple field reversals.

Cold atoms, loaded into an optical lattice with double-well sites, are considered. Pseudospin representation for an effective Hamiltonian is derived. The system in equilibrium displays two phases, ordered and disordered. The second-order phase transition between the phases can be driven either by temperature or by changing the system parameters. Collective pseudospin excitations have a gap disappearing at the phase-transition point. Dynamics of atoms is studied when they are loaded into the lattice in an initially nonequilibrium state. It is shown that the temporal evolution of atoms, contrary to their equilibrium thermodynamics, cannot be described in the mean-field approximation, since it results in a structurally unstable dynamical system, but a more accurate description is necessary taking into account attenuation effects.

We investigate transmission and reflection of Bose-Einstein-condensate excitations in the low-energy limit across a potential barrier separating two condensates with different densities. The Bogoliubov excitation in the low-energy limit has an incident angle where the perfect transmission occurs. This condition corresponds to Brewster’s law for the electromagnetic wave. The total internal reflection of the Bogoliubov excitation is found to occur at a large incident angle in the low-energy limit. The anomalous tunneling named by Kagan et al. [Yu. Kagan et al., Phys. Rev. Lett. 90, 130402 (2003)] can be understood in terms of the impedance matching. In the case of the normal incidence, comparison with the results in Tomonaga-Luttinger liquids is made.

We formulate a generalized mean-field theory of a mixture of fermionic and bosonic atoms, in which the fermion-boson interaction can be controlled by a Feshbach resonance. The theory correctly accounts for molecular binding energies of the molecules in the two-body limit, in contrast to the most straightforward mean-field theory. Using this theory, we discuss the equilibrium properties of fermionic molecules created from atom pairs in the gas. We also address the formation of molecules when the magnetic field is ramped across the resonance, and we present a simple Landau-Zener result for this process.

We propose a class of path-entangled photon Fock states for robust quantum optical metrology, imaging, and sensing in the presence of loss. We model propagation loss with beam splitters and derive a reduced density-matrix formalism from which we examine how photon loss affects coherence. It is shown that particular entangled number states, which contain a special superposition of photons in both arms of a Mach-Zehnder interferometer, are resilient to environmental decoherence. We demonstrate an order of magnitude greater visibility with loss than possible with path-entangled $\mid N,0⟩+\mid 0,N⟩$ states. We also show that the effectiveness of a detection scheme is related to super-resolution visibility.

A reservoir theory has been used to investigate the spontaneous emission of a two-level atom in a Kerr nonlinear blackbody. It is found that the atomic decay rate is a monotonically increasing function of absolute temperature. Below a transition temperature $T_c$, the spontaneous emission is always inhibited compared to that in a nonabsorbing linear medium. It is also found that the inhibition of spontaneous emission is a monotonically decreasing function of the Kerr nonlinear coefficient. The inhibition of spontaneous emission is interpreted on the basis of a physical mechanism.

We propose a complete tomographic reconstruction of vortex states carrying orbital angular momentum. The scheme determines the angular probability distribution of the state at different times under free evolution. To represent the quantum state, we introduce a bona fide Wigner function defined on the discrete cylinder, which is the natural phase space for the pair angle-angular momentum. The feasibility of the proposal is addressed.

We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment. We conclude that the dynamics of the qubit changes dramatically when the environment passes through a continuous excited state quantum phase transition. If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power law.

We observe high-order harmonic spectra generated from a thin atomic medium, Ar, Kr, and Xe, by intense $800\text{−}\mathrm{nm}$ and $1300\text{−}\mathrm{nm}$ femtosecond pulses. A clear signature of a single-atom response is observed in the harmonic spectra. Especially in the case of Ar, a Cooper minimum, reflecting the electronic structure of the atom, is observed in the harmonic spectra. We successfully extract the photorecombination cross sections of the atoms in the field-free condition with the help of an accurate recolliding electron wave packet. The present protocol paves the way for exploring ultrafast imaging of molecular dynamics with attosecond resolution.

We study the phase diagram of the mixture of a Bose-Einstein condensate and a two-component Fermi gas. In particular, we identify the regime where the homogeneous system becomes unstable against phase separation. We show that, under proper conditions, the phase-separation phenomenon can be exploited as a robust probe of “local” Fermi superfluidity.

A model of a quantum automaton (QA), a transducer, working with $n$ qubits is proposed. The quantum states of the automaton are represented by density operators. The linearity of the QA and of the partial trace operator, jointly with the properties of invariant subspaces and of the quotient spaces, are used to minimize the dimension and the cardinality of the state set of the QA.Two main results are obtained in this paper: (a) The conditions that the unitary evolution operators, representing the quantum gates of the QA, must obey in order to reduce its dimension and its state set. (b) An algorithm is developed to find the minimal QA and its complexity is computed. We show that the necessary and sufficient conditions for minimization depend uniquely in the structure of the unitary evolution operators, and they are independent of the initial quantum state of the QA.

We investigate spectral and temporal features and entanglement of biphoton wave packets formed in spontaneous parametric down-conversion with a pulsed laser pump. The degree of entanglement is characterized by the experimentally measurable parameter $R$ defined as the ratio of the coincidence and single-particle spectral widths. In the frequency representation, this parameter is found as a function of the pump-pulse duration $\tau$. The function $R\left(\tau \right)$ is shown to have a minimum and even in the minimum, at rather natural conditions, the degree of entanglement is found to be very high $(R_{\min }=73)$. The Schmidt number $K$ is found analytically for both short and long pump pulses and interpolated for arbitrary pulse durations. All functional dependences of $R$ and $K$ are found to be identical and numerical coefficients are found to be rather close. Two-time temporal wave function of a biphoton state is investigated in detail, and a rather significant difference between the cases of short and long pump pulses is found to occur. In the case of long pulses, the temporal parameter $R_t$ (defined as the ratio of durations of the single-particle and coincidence signals) is shown to be very close to the Schmidt number $K$.

We present an optimal scheme to realize the transformations between single copies of two bipartite entangled states without classical communication between the sharing parties. The scheme achieves the upper bound for the success probabilities [Phys. Rev. A 63, 022301 (2001); Phys. Rev. Lett. 83, 1455 (1999)] of generating maximally entangled states if applied to entanglement concentration. Such a strategy also dispenses with the interaction with an ancilla system in the implementation. We also show that classical communications are indispensable in realizing the deterministic transformations of a single bipartite entangled state. With a finite number of identical pairs of two entangled bosons, on the other hand, we can realize the deterministic transformation to any target entangled state of equal or less Schmidt rank through an extension of the scheme.

The hyperfine splitting of the ground state of H-, Li-, and B-like ions is investigated in details within the range of nuclear numbers $Z=7–28$. The rigorous QED approach together with the large-scale configuration-interaction Dirac-Fock-Sturm method are employed for the evaluation of the interelectronic-interaction contributions of first and higher orders in $1∕Z$. The screened QED corrections are evaluated to all orders in $\alpha Z$ utilizing an effective potential approach. The influence of nuclear magnetization distribution is taken into account within the single-particle nuclear model. The specific differences between the hyperfine-structure level shifts of H- and Li-like ions, where the uncertainties associated with the nuclear structure corrections are significantly reduced, are also calculated.

The projection-operator formalism of Feshbach is applied to resonance scattering in a single-channel case. The method is based on the division of the full function space into two segments, internal (localized) and external (infinitely extended). The spectroscopic information on the resonances is obtained from the non-Hermitian effective Hamilton operator $H_{\mathrm{eff}}$ appearing in the internal part due to the coupling to the external part. As is well known, additional so-called cutoff poles of the $S$ matrix appear, generally, due to the truncation of the potential. We study the question of spurious $S$ matrix poles in the framework of the Feshbach formalism. The numerical analysis is performed for exactly solvable potentials with a finite number of resonance states. These potentials represent a generalization of Bargmann-type potentials to accept resonance states. Our calculations demonstrate that the poles of the $S$ matrix obtained by using the Feshbach projection-operator formalism coincide with both the complex energies of the physical resonances and the cutoff poles of the $S$ matrix.

We study the properties of Bose-Einstein condensates with the realistic van der Waals two-body interaction for large numbers of trapped atoms, solving the many-body Schrödinger equation by the potential harmonic expansion method. The effect of different $C_6$ parameters has been critically examined, starting from very few to 14 000 atoms to analyze and justify the idea of a shape-independent approximation. It is found that the condensate properties almost remain unchanged when the number of atoms are quite small $(\sim 100)$, in good agreement with earlier results of Blume and Greene [Phys. Rev. A 63, 063601 (2001)], but we observe the appreciable effect of a long attractive tail when $N$ is large, even in the low-density limit. The above reference considered only 20 atoms which is far from a real experimental situation. Our calculation gives a realistic scenario which justifies the use of a shape-dependent two-body interaction in many-body theories.

We study the phase diagram of a two component Fermi system with a weak attractive interaction. Our analysis includes the leading order Hartree energy shifts and pairing correlations at finite temperature and chemical potential difference between the two fermion species. We show that in an asymmetric system, the Hartree shift to the single particle energies is important for the phase competition between normal and superfluid phase and can change the phase transition curve qualitatively. At large chemical potential asymmetry we find that a somewhat fragile superfluid state can be favored due to finite-temperature effects. We also investigate the transition between the normal phase and an inhomogeneous superfluid phase to study how gradient instabilities evolve with temperature and asymmetry. Finally, we adopt our analysis to study the density profiles of similar asymmetric Fermi systems that are being observed in cold-atom experiments.

Quantum state exchange between light and matter is an important ingredient for future quantum information networks as well as other applications. Photons are the fastest and simplest carriers of information for transmission but in general, it is difficult to localize and store photons, so usually one prefers choosing matter as quantum memory elements. Macroscopic superposition and nonlocal quantum interactions have received considerable interest for this purpose over recent years in fields ranging from quantum computers to cryptography, in addition to providing major insights into physical laws. However, these experiments are generally performed either with equipment or under conditions that are unrealistic for practical applications. Ideally, the two can be combined using conventional equipment and conditions to generate a “quantum teleportation”-like state, particularly with a very small amount of purity existing in an overall highly mixed thermal state (relatively low decoherence at high temperatures). In this study we used an experimental design to demonstrate these principles. We performed optical coherence tomography (OCT) using a thermal source at room temperatures of a specifically designed target in the sample arm. Here, position uncertainty (i.e., dispersion) was induced in the reference arm. In the sample arm (target) we placed two glass plates separated by a different medium while altering position uncertainty in the reference arm. This resulted in a chirped signal between the glass plate reflective surfaces in the combined interferogram. The chirping frequency, as measured by the fast Fourier transform (FFT), varies with the medium between the plates, which is a nonclassical phenomenon. These results are statistically significant and occur from a superposition between the glass surface and the medium with increasing position uncertainty, a true quantum-mechanical phenomenon produced by photon pressure from two-photon interference. The differences in chirping frequency with medium disappears when second-order correlations are removed by dual balanced detection, confirming the proposed mechanism. We demonstrated that increasing position uncertainty at one site leads to position uncertainty (quantum position probability amplitude) nonlocally via second-order correlations (two-photon probability amplitude) from a low coherence thermal source (low purity, high local entropy). The implications, first, are that the phenomenon cannot be explained through classical mechanisms but can be explained within the context of quantum mechanics, particularly relevant to the second-order correlations where controversy exists. More specifically, we provide the theoretical framework that these results indicate a nonlocal macroscopic superposition is occurring through a two-photon probability amplitude-induced increase in the target position probability amplitude uncertainty. In addition, as the experiments were performed with a classical source at room temperature, it supports both the quantum-mechanical properties of second-order correlations and that macroscopic superposition is obtainable in a target not in a single coherent state (mixed state). Future work will focus on generalizing the observations outside the current experimental design and creating embodiments that allow practical application of the phenomenon.

We present a fully quantum-electrodynamical formalism suitable to evaluate the spontaneous emission rate and pattern from a dipole embedded in a nonabsorbing and lossless multilayer dielectric structure. In the model here developed the electromagnetic field is quantized by a proper choice of a complete and orthonormal set of classical spatial modes, which consists of guided and radiative (partially and fully) states. In particular, by choosing a set of radiative states characterized by a single outgoing component, we get rid of the problem related to the quantum interference between different outgoing modes, which arises when the standard radiative basis is used to calculate spontaneous emission patterns. After the derivation of the local density of states, the analytical expressions for the emission rates are obtained within the framework of perturbation theory. First we apply our model to realistic silicon-based structures such as a single Si/air interface and a silicon waveguide in both the symmetric and asymmetric configurations. Then, we focus on the analysis of the spontaneous emission process in a silicon-on-insulator (SOI) slot waveguide (a six-layer model structure) doped with ${\mathrm{Er}}^{3+}$ ions (emitting at the telecom wavelength). In this latter case we find a very good agreement with the experimental evidence [M. Galli et al., Appl. Phys. Lett. 89, 241114 (2006)] of an enhanced TM/TE photoluminescence signal. Hence, this model is relevant to study the spontaneous emission in silicon-based multilayer structures which nowadays play a fundamental role for the development of highly integrated multifunctional devices.