We investigate the linear instability and the adiabatic fidelity of a dark state in a nonlinear atom-trimer conversion that is implemented by a stimulated Raman adiabatic passage (STIRAP). We find that the interparticle interactions could induce the instability of the atom-trimer dark state in some parameter regimes. We also discuss the adiabatic evolution of the dark state in terms of a newly defined adiabatic fidelity. Based on our theoretical analysis, we propose a feasible two-photon STIRAP scheme that has high adiabatic fidelity, less instability, and therefore could yield high atom-trimer conversion efficiency.

Using mean-field theory, we study the equilibrium properties of boson-fermion mixtures confined in a harmonic pancake-shaped trap at zero temperature. When the modulus of the $s$-wave scattering lengths are comparable to the mixture thickness, two-dimensional scattering events introduce a logarithmic dependence on density in the coupling constants, greatly modifying the density profiles themselves. We show that, for the case of a negative boson-fermion three-dimensional $s$-wave scattering length, the dimensional crossover stabilizes the mixture against collapse and drives it toward spatial demixing.

Using a Luttinger-liquid approach we study the quantum fluctuations of a Bose-Josephson junction, consisting of a Bose gas confined to a quasi-one-dimensional ring trap which contains a localized repulsive potential barrier. For an infinite barrier we study the one-particle and two-particle static correlation functions. For the one-body density-matrix we obtain different power-law decays depending on the location of the probe points with respect to the position of the barrier. This quasi-long-range order can be experimentally probed in principle using an interference measurement. The corresponding momentum distribution at small momenta is also shown to be affected by the presence of the barrier and to display the universal power-law behavior expected for an interacting one-dimensional fluid. We also evaluate the particle-density profile, and by comparing with the exact results in the Tonks-Girardeau limit we fix the nonuniversal parameters of the Luttinger-liquid theory. Once the parameters are determined from one-body properties, we evaluate the density-density correlation function, finding a remarkable agreement between the Luttinger-liquid predictions and the exact result in the Tonks-Girardeau limit, even at the length scale of the Friedel-like oscillations which characterize the behavior of the density-density correlation function at intermediate distance. Finally, for a large but finite barrier we use the one-body correlation function to estimate the effect of quantum fluctuations on the renormalization of the barrier height, finding a reduction in the effective Josephson coupling energy, which depends on the length of the ring and on the interaction strength.

We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the intersite tunneling rate. An ensemble of such lattice dimers is accurately described by an effective Hamiltonian of hard-core bosons with strong nearest-neighbor repulsion, which is equivalent to the $XXZ$ model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system, which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (antiferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the antiferromagnetic density profile and in density-density correlations. We derive a kink model that provides simple quantitative explanation of these features. To describe the long-range correlations of the system, we employ the Luttinger-liquid theory with the relevant Luttinger parameter $K$ obtained exactly using the Bethe-ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density-matrix renormalization-group methods.

The propagation of probe and coupling optical beams through a four-level coherent media is modeled by two coupled nonlinear Schrödinger equations. The nonlinear susceptibilities exhibited by the four-level media are calculated in the nonperturbative regime, i.e., considering the probe and coupling fields as having comparable amplitudes. We address the existence and stability of vector solitons build by the probe and coupling beams in the coupled nonlinear Schrödinger equations.

We report on light slowing down in a rare-earth-metal-ion-doped crystal by persistent spectral hole burning. The absence of motion of the active ions, the large inhomogeneous broadening, the small homogeneous width, and the long lifetime of the hyperfine shelving states make this material convenient for the burning of narrow persistent spectral holes. Since the hole can be burnt long before the arrival of the input signal, there is no need for a strong-coupling field, illuminating the sample simultaneously with the input signal, in contrast with procedures such as electromagnetically induced transparency or coherent population oscillations. Analyzing the slowing down process, we point out the role played by the off-resonant atom. Most of the incoming information is carried over to off-resonant atoms, while the pulse is confined within the sample. The observed speed-of-light reduction factor exceeds ${10}^5$.

Soliton pulses in normally dispersive mode-locked lasers are considered using a nonlinear Schrödinger equation, appropriately modified to model power (intensity) and energy saturations. Strongly chirped, localized pulses are obtained when the effects of nonlinearity, dispersion, saturated gain, filtering, and loss form an appropriate balance. In the case of constant dispersion, perturbation theory yields a set of uncoupled equations for the amplitude and the phase of the soliton pulse. In dispersion-managed (DM) systems, an asymptotic multiple-scale theory is used to analyze the dynamics. This equation, which describes solitons in the anomalous regime, also admits higher-order solitons, the so-called antisymmetric soliton or bisoliton, in both constant dispersion and DM systems. Such pulses have been observed in recent experiments.

Direct measurement of photon bunching ($g_{\left(2\right)}$ correlation function) in one output arm of a spontaneous-parametric-down-conversion source operated with a continuous pump laser in the single-photon regime is demonstrated. The result is in agreement with the statistics of a thermal field of the same coherence length and shows the feasibility of investigating photon statistics with compact continuous-wave-pumped sources. Implications for entanglement-based quantum cryptography are discussed.

We propose a special cavity design that is constructed by terminating a one-dimensional waveguide with a perfect mirror at one end and doping a two-level atom at the other. We show that this atom plays the intrinsic role of a semitransparent mirror for single-photon transports such that quasinormal modes emerge spontaneously in the cavity system. This atomic mirror has its reflection coefficient tunable through its level spacing and its coupling to the cavity field, for which the cavity system can be regarded as a two-end resonator with a continuously tunable leakage. The overall investigation predicts the existence of quasibound states in the waveguide continuum. Solid-state implementations based on a dc-superconducting quantum interference device circuit and a defected line resonator embedded in a photonic crystal are illustrated to show the experimental accessibility of the generic model.

The effect of a random-phase diffuser on fluctuations of laser light (scintillations) is studied. Not only spatial but also temporal phase variations introduced by the phase diffuser are analyzed. The explicit dependence of the scintillation index on finite-time phase variations is obtained for long propagation paths. It is shown that for large amplitudes of phase fluctuations, a finite-time effect decreases the ability of phase diffuser to suppress the scintillations.

A system of coherently coupled nonlinear Schrödinger equations relevant to the polarization of light beams is considered. Modulation instability (MI) of plane waves is studied without approximations and two results were presented: (1) MI will be enhanced for a finite birefringence, thus extending earlier works that treated the low birefringence limit; (2) nonlinearity arising from phase coherence introduces unique regimes of cross-phase-modulation-induced MI.

It is discussed that the quantum stability of a metallic cluster system with respect to the variation in the cluster shape transforms a spherical volume distribution of ionic charge core of the cluster into a spherical hollow configuration. Calculations are performed within the jellium model approach based on the Hartree-Fock theory and also within the local-density approximation. It is demonstrated that for such spherical cluster systems, there are two stable states characterized by the different distribution of the positive charge of the ionic core. One of the states corresponds to a spherical charge distribution of the ionic core uniform over the entire cluster volume. The second fullerenelike stable state arises when positive charge is uniformly distributed over a spherical shell of a certain width.

We describe an apparatus for quickly and simply producing ${}^{87}\text{R}\text{b}$ Bose-Einstein condensates. It is based on a magnetic quadrupole trap and a red-detuned optical dipole trap. We collect atoms in a magneto-optical trap (MOT) and then capture the atoms in a magnetic quadrupole trap and force rf evaporation. We then transfer the resulting cold dense cloud into a spatially mode-matched optical dipole trap by lowering the quadrupole field gradient to below gravity. This technique combines the efficient capture of atoms from a MOT into a magnetic trap with the rapid evaporation of optical dipole traps; the approach is insensitive to the peak quadrupole gradient and the precise trapping beam waist. Our system reliably produces a condensate with $N\approx 2\times {10}^6$ atoms every 16 s.

The possibility of using the self-induced transparency effect to achieve laser mode locking has been discussed since the late 1960s but has never been observed. In prior work, we proposed that quantum cascade lasers are the ideal tool to realize self-induced transparency mode locking due to their rapid gain recovery times and relatively long coherence times, and because it is possible to interleave gain and absorbing periods. Here, we present designs of quantum cascade lasers that satisfy the requirements for self-induced transparency mode locking at both 8 and $12\mu \text{m}$, indicating that it is possible to satisfy these requirements over a wide wavelength range. The coupled Maxwell-Bloch equations that define the dynamics in quantum cascade lasers that have both gain and absorbing periods have been solved both analytically and computationally. Analytical mode-locked solutions have previously been found under the conditions that there is no frequency detuning, the absorbing periods have a dipole moment twice that of the gain periods, the input pulse is a $\pi$ pulse in the gain medium, and the gain recovery times in the gain and absorbing periods are much longer than the coherence time $T_2$ and are short compared to the round-trip time. It was shown that the mode-locked pulse durations are on the order of $T_2$, which is typically about 100 fs in quantum cascade lasers. In this work, these analytical results are reviewed and extended to include the effects of partial inversion in the gain and absorbing periods and of frequency detuning. An energy theorem in the limit of long coherence times is derived. The Maxwell-Bloch equations have been solved computationally to determine the robustness of the mode-locked solutions when frequency detuning is present, the dipole moment of the absorbing periods differs from twice that of the gain periods, the gain relaxation time is on the order of 1–10 ps, as is typically obtained in quantum cascade lasers, and the initial pulse is not a $\pi$ pulse in the gain medium. We find that mode-locked solutions exist over a broad parameter range. We have also investigated the evolution of initial pulses that are initially much broader than the final mode-locked pulses. As long as the initial pulse duration is on the order of $T_1$ or shorter and has enough energy to create a $\pi$ pulse in the medium, a mode-locked pulse with a duration on the order of $T_2$ will ultimately form.

We study theoretically the propagation of a step-modulated optical field as it passes through a dispersive dielectric made up of a dilute collection of oscillators characterized by a single narrow-band resonance. The propagated field is given in terms of an integral of a Fourier type, which cannot be evaluated even for simple models of the dispersive dielectric. The fact that the oscillators have a low number density (dilute medium) and have a narrow-band resonance allows us to simplify the integrand. In this case, the integral can be evaluated exactly, although it is not possible using this method to separate out the transient part of the propagated field known as optical precursors. We also use an asymptotic method (saddle-point method) to evaluate the integral. The contributions to the integral related to the saddle points of the integrand give rise to the optical precursors. We obtain analytic expressions for the precursor fields and the domain over which the asymptotic method is valid. When combined to obtain the total transient field, we find that the agreement between the solutions obtained by the asymptotic and the exact methods is excellent. Our results demonstrate that precursors can persist for many nanoseconds and the chirp in the instantaneous frequency of the precursors can manifest itself in beats in the transmitted intensity. Our work strongly suggests that precursors have been observed in many previous experiments.

In density-functional theory, the exchange-correlation functional can be exactly expressed by the adiabatic connection integral. It had been noticed that as $\lambda \to \infty$, the ${\lambda }^{-1}$ term in the expansion of $W\left(\lambda \right)$ vanishes. We provide a simple derivation of this exact condition in this work. We propose a simple parametric form for the integrand, satisfying this condition, and show that it is highly accurate for weakly correlated two-electron systems.

We observe that the noninteracting kinetic energy, as a functional of the electron density $\rho$, may be obtained from a formula that contains only a single Kohn-Sham orbital, ${\phi }_i\left(\mathbf{r}\right)$, where $i$ is arbitrary. Specifically, $T_s\left[\rho \right]=\left(-1/4\right)\int \left\{{\nabla }^2{\varphi }_i\left[\rho ;\mathbf{r}\right]/{\varphi }_i\left[\rho ;\mathbf{r}\right]\right\}\left[3\rho \left(\mathbf{r}\right)+\mathbf{r}\cdot \nabla \rho \left(\mathbf{r}\right)\right]d\mathbf{r}$.

Relativistic configuration interaction results are presented for the $K\beta$ x rays from $2s3p\text{−}1s2s$ transitions in He-like ions. The x-ray energies and rates are calculated for 23 ions in the range $Z=14$ to 54 using multiconfiguration Dirac-Fock wave functions in the active space approximation. The calculations include finite nuclear size effect, Breit interaction, and quantum electrodynamic corrections. The influence of configuration mixing on the converged x-ray rates is analyzed. Our calculations show that strong configuration mixing reduces substantially the single configuration electric dipole allowed as well the ${{}^3\text{P}}_1\text{−}{{}^1\text{S}}_0$ spin-forbidden transition rates and its contribution decreases with increasing $Z$. While configuration mixing consistently reduces the monoconfiguration rate of ${{}^1\text{P}}_1\text{−}{{}^3\text{S}}_1$ transition in ions with $Z<22$ by as much as 94%, it enhances the spin-forbidden rate of ions with $Z\ge 23$. The contributions from higher order relativistic corrections are seen to be negligible for ${{}^1\text{P}}_1\text{−}{{}^1\text{S}}_0$ and ${{}^1\text{P}}_1\text{−}{{}^3\text{S}}_1$ transitions whereas the effect of Breit interaction is appreciable for the other transitions to ${{}^3\text{S}}_1$ state, especially for the high-$Z$ ions. The results are compared with other available values.

We have made an investigation on the $2s^2{{}^{1}S}^e$ resonances in helium (He) in exponential cosine-screened Coulomb potentials (ECSCP). Highly correlated wave functions are used to take into account of the correlation effect of the charged particles. Resonance energies and widths for the doubly excited He in ECSCP are determined using the stabilization method by calculating the density of the resonance states. Results for resonance energies and widths are reported for the screening parameter in the range 0.0–0.275

We analyze the influence of self-steepening and higher-order dispersion on the process of optical wave thermalization. This study is aimed at developing a thermodynamic formulation of supercontinuum generation in photonic crystal fibers. In the highly nonlinear regime of supercontinuum generation, the optical field exhibits a turbulent dynamics that may be described by the kinetic wave theory. In this respect, the phenomenon of spectral broadening inherent to supercontinuum generation may be interpreted as a natural process of thermalization, which is characterized by an irreversible evolution of the optical field toward a thermodynamic equilibrium state. The numerical simulations show that, under certain conditions, the intensity of the field spontaneously concentrates around two specific frequencies. The theory reveals that these particular frequencies are selected in such a way that the corresponding wave packets propagate with the same group velocity, which is shown to also match the average group velocity of the optical field. This “velocity-locking” effect and the underlying process of spectral fission are interpreted in the light of a fundamental property of statistical equilibrium thermodynamics. It is shown that a velocity locking is required, in the sense that it prevents “a macroscopic internal motion in the wave system.” Furthermore, the kinetic wave theory sheds light on the role of self-steepening in the incoherent regime of supercontinuum generation. A family of equilibrium spectra is derived in the presence of self-steepening. They are found in quantitative agreement with the numerical simulations of the generalized nonlinear Schrödinger equation, without adjustable parameters.