We discuss the extent to which measured time-dependent fragment kinetic energy release (KER) spectra and calculated nuclear probability densities can reveal (1) the transition frequencies between stationary vibrational states, (2) the nodal structure of stationary vibrational states, (3) the ground-state adiabatic electronic potential curve of the molecular ion, and (4) the progression of decoherence induced by random interactions with the environment. We illustrate our discussion with numerical simulations for the time-dependent nuclear motion of vibrational wave packets in the $\text{D}_2{}^{+}$ molecular ion caused by the ionization of its neutral ${\text{D}}_2$ parent molecule with an intense pump laser pulse. Based on a harmonic time-series analysis, we suggest a general scheme for the full reconstruction, up to an overall phase factor, of the initial wave packets based on measured KER spectra. We apply this scheme in a numerical simulation for vibrational wave packets in $\text{D}_2{}^{+}$ molecular ions and show how this reconstruction allows the clear distinction between commonly assumed stationary vibrational state distributions of the molecular ion following the ionization of ${\text{D}}_2$.

The stability of a linear ac trap for neutral polar molecules is investigated both theoretically and experimentally. While the overall stability is found to be well described by the linearized equations of motion within the usual framework of stability diagrams, instabilities similar to those observed in anharmonic radio-frequency ion traps occur inside the nominal stable regions. These motional resonances are caused by strong anharmonic contributions to the trapping fields, that inevitably appear in ac traps for polar molecules. Nonlinear resonant energy transfer from the high-frequency source to molecules inside the trap is observed for the particles’ fundamental frequency of transverse oscillation being $\frac{1}{4}$ of the forcing frequency.

A numerical approach that allows for the solution of the time-dependent Schrödinger equation (TDSE) describing molecules exposed to intense short laser pulses was developed. The molecular response to the strong field is described within the single-active electron approximation (SAE). The method is applied in the fixed-nuclei approximation to molecular hydrogen with parallel orientation of the internuclear axis to the laser field. The validity of the SAE is investigated by comparing the ionization and electronic excitation yields to full two-electron solutions of the TDSE. The present results are also used to investigate the validity of approximate SAE methods like the molecular Ammosov-Delone-Krainov and the strong-field approximation.

We demonstrate all-optical control of ultrafast spin polarization upon breakup of a multi-valence-electron system using two-color pump-probe photoionization. For the direct detection of spin polarization, we measure the laser-induced fluorescence of photoions. The experimental results agree well with our ab initio theory.

We numerically study the system of rapidly rotating Bose atoms at the filling factor (ratio of particle number to vortex number) $\nu =1$ with the dipolar interaction. A moderate dipolar interaction stabilizes the incompressible quantum liquid at $\nu =1$. Further addition induces a collapse of it. We show evidence that states after the collapse are compressible states which have phases with stripes and bubbles. Low-energy spectra are consistently interpreted by the presence of particle-hole excitations in which a Bose atom hops between stripes or bubbles. We also investigate models constructed from truncated interactions and the models with the three-body contact interaction. They also have phases with stripes and bubbles.

Transient stimulated rotational Raman scattering induced by a polarization-modulated femtosecond pulse whose polarization varies with time is reported. The peak intensity of the polarization-modulated pulse produced in this study is low compared to that of a pulse without polarization variation, and this leads to the low efficiency of self-phase-modulation and thus the high efficiency of stimulated Raman scattering compared to the case of a pump pulse without polarization modulation. The scattering process is unique in terms of the high peak ratio of the anti-Stokes to Stokes emissions compared to the ratio in the case of the scattering induced by linearly, circularly, and elliptically polarized pump pulses. Under optimum conditions, the ratio approaches 1, which is not realized in the general case of stimulated rotational Raman scattering.

A quasi-isotropic ${\text{CO}}_2$ laser near the resonant condition can present bistability in the polarization state, with spontaneous flips between two orthogonal linear polarization eigenmodes. In this work, we explore the role of the pump and noise on the polarization dynamics, showing a transition from stable to bistable states and the presence of coherent resonance.

In this paper we discuss a new type of four-dimensional representation of the braid group. The matrices of braid operations are constructed by $q$ deformation of Hamiltonians. One is Dirac’s Hamiltonian for a free electron with mass $m$, the other, which we find, is related to Bogoliubov’s Hamiltonian for quasiparticles in ${}^3\text{H}\text{e}-\text{B}$ with the same free energy and mass being $m/2$. In the process, we choose the free $q$-deformation parameter as a special value in order to be consistent with the anyon description for fractional quantum Hall effect with $\nu =1/2$.

The molecular tetramers can be created in an atomic Bose-Einstein condensate via a bright-state or a dark-state (dimer- or trimer-state-intermediated) scheme. Only the later scheme, realized by the Efimov-resonance-assisted stimulated Raman adiabatic passage, permits the existence of a generalized atom-molecular dark state and thereby leads to stable atom-tetramer conversion.

Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the entanglement of many bound entangled states. The criterion is strictly stronger than the criterion based on Bloch representations, the computable cross-norm or realignment criterion and its optimal nonlinear entanglement witnesses. Furthermore, this criterion can be generalized to an analog of permutation separability criteria in the even-partite systems.

We report on the production of ${}^{52}\mathrm{Cr}$ Bose-Einstein condensates with an all-optical method. We first load $5\times {10}^6$ metastable chromium atoms in a one-dimensional (1D) far-off-resonance optical trap (FORT) from a magneto-optical trap, by combining the use of radio-frequency sweeps and depumping toward the ${}^{5}S_2$ state. The atoms are then pumped to the absolute ground state, and transferred into a crossed FORT in which they are evaporated. The fast loading of the 1D FORT ($35\mathrm{ms}$ $1∕e$ time) and the use of relatively fast evaporative ramps allow us to obtain in $20\mathrm{s}$ about $15000$ atoms in an almost pure condensate.

We demonstrate efficient energy exchange during propagation between four-wave-mixing (FWM) and six-wave-mixing (SWM) signals generated in a four-level inverted-Y atomic system, which fall in the electromagnetically induced transparency window. After an initial growth distance for both FWM and SWM fields in the atomic medium, these two nonlinear optical processes compete and exchange energy between them, and eventually reach their respective steady-state values at long interaction distance. This energy exchange phenomenon can be explained by considering established atomic coherences among various atomic states and quantum interferences between three-photon and five-photon excitation pathways. Understanding these high-order nonlinear optical processes and interplays between them can be very important for correlated FWM (or SWM) photon-pair generations and quantum information processing.

Spatial symmetries inherent to tight focus optical beams are applied to control the field phase generated at interfaces in nonlinear optical processes. We use these symmetries to obtain a background-free pure Raman spectrum in coherent anti-Stokes Raman scattering spectroscopy from a resonant medium forming a transverse interface with a nonresonant medium. We demonstrate that the nonresonant medium acts as a local oscillator with which the Raman spectrum is measured in heterodyne detection. This method is relevant to remove the nonresonant background in other third-order resonant processes excited with focused beams.

In the last few years there has been a lot of interest in quantum repeater protocols using only atomic ensembles and linear optics. Here we show that the local generation of high-fidelity entangled pairs of atomic excitations, in combination with the use of two-photon detections for long-distance entanglement generation, permits the implementation of a very attractive quantum repeater protocol. Such a repeater is robust with respect to phase fluctuations in the transmission channels, and at the same time achieves higher entanglement generation rates than other protocols using the same ingredients. We propose an efficient method of generating high-fidelity entangled pairs locally, based on the partial readout of the ensemble-based memories. We also discuss the experimental implementation of the proposed protocol.

The behavior of one-dimensional quantum random walks is strikingly different from that of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we study the decoherence on both position and “coin” spaces of the particle. We propose an analytical approach to investigate these phenomena and obtain the generating functions which encode all the features of these walks. Specifically, from these generating functions, we find exact analytic expressions of several moments for the time and noise dependence of position. Moreover, the limiting position distributions of decoherent quantum random walks are shown to be Gaussian in an analytical manner. These results explicitly describe the relationship between the system and the level of decoherence.

The exact reduced dynamics for two independent qudits dephasingly coupled to a common zero-temperature, super-Ohmic, bosonic environment is studied. It is shown that the qudit-qudit subsystem initially prepared in a separable state evolves into an entangled state. Details of the entanglement origination depend on both the coupling strength and the spectral properties of the environment as well as on the dimension of the qudit; the environment-induced entanglement can survive in the long-time limit. The entanglement dynamics of initially maximally entangled qudit-qudit states is analyzed for two examples: the qubit-qubit and qutrit-qutrit systems. The theory is applied to negative partial transposition entangled states of a two-qutrit system, which are shown to be distillable (for the assumed initial state) for arbitrary environment parameters.

The Lamb shift of a hydrogen atom due to the surface plasmon polariton (SPP) modes is calculated and we observe both band edge and surface enhancement. The atom sits inside a thin metal slab which is sandwiched by two semi-infinite dielectrics. The SPP dispersion relation shows a band gap if the two dielectrics have different dielectric constants. We find the magnitude of the $2P_{1/2}$ level shift increases rapidly when the level separation is close to the high band edge. But the low band edge enhancement can be overwhelmed by the decreasing trend of the shift. If the atom is placed close to either surface or if the slab is narrow, all the level shifts would be large because of the surface enhancement. An interesting feature is that the $2P_{1/2}$ level shift can be larger than the $2S$ level shift due to the nonisotropic fields.

We demonstrate an accurate method for measuring the lifetime of long-lived metastable magnetic states using a magneto-optical trap (MOT). Through optical pumping, the metastable $\left(3s3p\right){{}^{3}P}_1$ level is populated in a standard MOT. During the optical pumping process, a fraction of the population is captured in the magnetic quadrupole field of the MOT. When the metastable atoms decay to the $\left(3s^2\right){{}^{1}S}_0$ ground state they are recaptured into the MOT. In this system no alternative cascading transition is possible. The lifetime of the metastable level is measured directly as an exponential load time of the MOT. We have experimentally tested our method by measuring the lifetime of the $\left(3s3p\right){{}^{3}P}_1$ of ${}^{24}\text{M}\text{g}$. This lifetime has been measured numerous times previously, but with quite different results. Using our method we find the $\left(3s3p\right){{}^{3}P}_1$ lifetime to be $\left(4.4\pm 0.2\right)\text{ms}$. Theoretical values point toward a lower value for the lifetime.

We determine the exact many-body properties of a bosonic Tonks-Girardeau gas confined in a harmonic potential with a tunable $\delta$-function barrier at the trap center. This is done by calculating the reduced single-particle density matrix, the pair-distribution function, and the momentum distribution of the gas as a function of barrier strength and particle number. With increasing barrier height we find that the ground-state occupation in a diagonal basis diverges from the $\sqrt{N}$ behavior that is expected for the case of a simple harmonic trap. In fact, the scaling of the occupation number depends on whether one has an even or odd number of particles. Since this quantity is a measure of the coherence of our sample we show how the odd-even effect manifests itself in both the momentum distribution of the Bose gas and interference fringe visibility during free temporal evolution.

The response of a ${\text{Nd}}^{3+}$-doped yttrium-aluminum-garnet laser is examined experimentally when the pump polarization direction is abruptly changed from one to the other stress-induced principal axis of the cavity. As a result, the laser output polarization changes direction but only after a significant delay. We numerically solve rate equations that describe the evolution of the two polarization fields coupled to the population inversion. The simulations indicate that the polarization switching (PS) delay depends on two successive processes that we analyze using multi-time-scale techniques. The analysis predicts two qualitatively different PS responses depending on how close the laser is from its threshold. Finally, we compare quantitatively the experimental and theoretical estimates of the PS delay.