We discuss the dynamical behavior of the entanglement between the internal and the external degrees of freedom of a trapped atom in electromagnetically induced transparency laser cooling. It is shown that essential features of the intricate entanglement dynamics observed in full numerical simulations of the underlying quantum master equation can be understood in terms of a two-state model on the basis of Landau-Zener splittings in the atom-laser field Hamiltonian. An extension of this model to an effective non-Hermitian Hamiltonian is constructed which describes the decay of entanglement by spontaneous emission processes. We also discuss schemes for the control of entanglement and demonstrate that a permanent entanglement can be imprinted on trapped atoms through a rapid switch-off of the driving fields.

We investigate for the existence of the weakly bound He-He-Ca molecules. By employing the best empirical interaction between each pair of particles, the Schrödinger equation for the triatomic system is solved using hyperspherical coordinates in the adiabatic approximation. The bound states are found for each of the ${}^3$He-${}^3$He-${}^{40}$Ca, ${}^3$He-${}^4$He-${}^{40}$Ca, and ${}^4$He-${}^4$He-${}^{40}$Ca trimers, respectively. The binding energies of such molecules are estimated. We discuss the features of the channel functions associated with the hyperspherical potential curves of each system to obtain insight into the geometry of the molecules.

Angular distributions of molecular above-threshold ionization (MATI) in bichromatic attosecond extreme ultraviolet (XUV) linear polarization laser pulses have been theoretically investigated. Multiphoton ionization in a prealigned molecular ion H${}_2$${}^{+}$ produces clear MATI spectra which show a forward-backward asymmetry in angular and momentum distributions which is critically sensitive to the carrier envelope phase (CEP) $\phi$, the time delay $\Delta \tau$ between the two laser pulses, and the photoelectron kinetic energies $E_e$. The features of the asymmetry in MATI angular distributions are described well by multiphoton perturbative ionization models. Phase differences of continuum electron wave functions can be extracted from the CEP $\phi$ and time delay $\Delta \tau$ dependent ionization asymmetry ratio created by interfering multiphoton ionization pathways. At large internuclear distances MATI angular distributions exhibit more complex features due to laser-induced electron diffraction where continuum electron wavelengths are less than the internuclear distance.

We present high-resolution two-dimensional momentum distributions and energy-angular distributions of photoelectrons from xenon atoms, ionized by an 800-nm, 25-fs linearly polarized laser at intensities of (1.8–4.4) × 10${}^{13}$ W/cm${}^2$. The angular distributions of low-energy photoelectrons exhibit pronounced intensity-dependent features. The photoelectron angular distributions (PADs) of nonresonant ionization, Freeman resonance, and main order above-threshold ionization at different laser intensities are analyzed. We have characterized the PADs of above-threshold ionization up to the fourth order and have confirmed the angular momentum selection rule of $\Delta l=1$ for above-threshold ionization at all laser intensities. We observe that the channel of nine-photon resonant ionization has switched to a ten-photon process but nine-photon nonresonance still remains for xenon.

An analytical expression for the optical field of an Airy beam partially blocked by an opaque obstacle is derived. The self-healing properties of the Airy beam are studied and discussed in detail. The study shows that the self-healing process of the Airy beam is affected by many factors such as the opaque obstacle size, propagation distance, wavelength, and parameters of the Airy beam. The self-healing process is caused by the convergence of energy from the side to the position of the opaque obstacle and is finished when the convergence of energy flow disappears. When the propagation distance is short, the main lobe of the Airy beam is affected by the obstruction located near the main lobe. When the propagation distance is long, the main lobe of the Airy beam can be affected by the obstruction located far away from the main lobe. The result agrees with the existing results and can be explained by the caustic of the Airy beam.

We introduce a fast, dependable algorithm to solve for the exit surface wave of a specimen in coherent diffractive imaging for a set of illumination conditions that are not unduly restrictive. It is shown that a direct solution of the phase problem from a diffraction pattern is obtained efficiently and uniquely. The algorithm is deterministic and is known a priori to converge to the correct solution in less than a predetermined number of steps. It is based on the conjugate gradient least-squares method implemented with Fourier transforms and offers the possibility of real-time solutions. We also extend the formulation to allow for imaging of extended objects in a manner similar to ptychography.

Recent experiments have demonstrated single-site resolved observation of cold atoms in optical lattices. Thus, in the future it may be possible to take repeated snapshots of an interacting quantum many-body system during the course of its evolution. Here we address the impact of the resulting quantum (anti-)Zeno physics on the many-body dynamics. We use the time-dependent density-matrix renormalization group to obtain the time evolution of the full wave function, which is then periodically projected in order to simulate realizations of stroboscopic measurements. For the example of a one-dimensional lattice of spinless fermions with nearest-neighbor interactions, we find regimes for which many-particle configurations are stabilized or destabilized, depending on the interaction strength and the time between observations.

We propose to exploit a continuous-variable measurement, based on displacing the input field at different points of the phase space, over a multiphoton state produced by a high-gain optical parametric amplifier. We show that by correlating the different values of the displaced parity operators obtained from the two separated parties, it is possible to violate a Bell's inequality and thus demonstrate the nonlocality of the overall state. The robustness of the results against two independent sources of error, loss and dephasing, is also discussed.

Entanglement between the constituents of a quantum system is an essential resource in the implementation of many quantum processes and algorithms. Indeed, universal quantum computation is possible by measuring individual qubits that constitute highly entangled “cluster states.” In this work, it is shown that the unique gapped ground state of noninteracting fermions hopping on a specially prepared lattice is equivalent to a cluster state, where the entanglement between qubits results from fermionic indistinguishability and antisymmetry. A deterministic strategy for universal measurement-based quantum computation with this resource is described. Because most matter is composed of fermions, these results suggest that resources for quantum information processing might be generic in nature.

In order to understand how stochastic processes might enter and influence coherent atomic dynamics, we have studied the behavior of a Λ system under periodic polarization modulation. Polarization, in addition to amplitude and phase, is a defining feature of a classical vector field. However, to date, there has been little study concerning the response of quantum systems to temporal variations in polarization, even though some lasers are known to exhibit stochastic polarization fluctuations. In our work, we square-wave modulate the polarization of a laser that induces coherent-population trapping (CPT) in ${}^{87}$Rb. At low-modulation frequencies, we find that the amplitude of the CPT resonance increases with modulation frequency because the polarization variations limit the number of atoms confined to the system's trapping state. Surprisingly, at higher-modulation frequencies, we find that the CPT resonance splits into a doublet. We have developed an analytical theory of CPT in the presence of polarization modulation that captures the primary features of our experimental findings and shows that the doublet is a consequence of ground-state coherence modulation in the Λ system. The present results lay a foundation for understanding how more complicated (i.e., stochastic) temporal variations in laser polarization could influence Λ-system dynamics.

We study the effective one-dimensional (1D) scattering of two distinguishable atoms confined individually by separatedtransverse harmonic traps. With equal trapping frequency for two $s$-wave interacting atoms, we find that by tuning the trap separations, the system can undergo double 1D scattering resonance, named as the separation-induced resonance (SIR), when the ratio between the confinement length and $s$-wave scattering length is within $(0.791,1.46]$. Near SIR, the scattering property shows unique dependence on the resonance position. The universality of a many-body system on scattering branch near SIR is demonstrated by studying the interaction effect of a localized impurity coupled with a Fermi sea of light atoms in a quasi-1D trap.

We investigate how to apply a high-frequency driving field to the quantum control of a single particle in an open double-well system. The linear stability analysis points out that the stability depends on the external-field parameters and the loss (or gain) coefficients of the system, and the instability leads to a transition of the Floquet quasienergy from real to complex values and results in decaying probabilities for the particle to be in the double well. By combining analytical solutions in the high-frequency approximation with numerical calculations based on an accurate model, we exhibit quantum-dynamical behavior of the particle such as Floquet oscillation, coherent destruction of tunneling, quasi-NOON-state population, partial one-particle tunneling, and the decay of the probabilities of occupation, which are due to the competition and balance between the quantum coherence and the loss (or gain) effect. The results suggest an experimental method for testing quantum motion in an open system by adjusting the driving field.

Electromagnetically-induced-transparency-like behavior in the extreme-ultraviolet region is studied theoretically, including the effect of intense 800 nm laser dressing of He 2s2p(${}^1{P}^o$) and 2p${}^2$${(}^1{S}^e)$ autoionizing states. We present an ab initio solution of the time-dependent Schrödinger equation in an $LS$-coupling configuration-interaction basis set. The method enables a rigorous treatment of optical field ionization of these coupled autoionizing states into the $N=2$ continuum in addition to $N=1$. Our calculated transient absorption spectra show encouraging agreement with experiment.

We consider the effects of radiation damping on the electron dynamics in a Gaussian-beam model of a laser field. For high intensities, i.e., with dimensionless intensity $a_0\gg 1$, it is found that the dynamics divides into three regimes. For low-energy electrons (low initial $\gamma$ factor, ${\gamma }_0$) the radiation damping effects are negligible. At higher energies, but still at $2{\gamma }_0<a_0$, the damping alters the final displacement and the net energy change of the electron. For $2{\gamma }_0>a_0$ one is in a regime of radiation-reaction-induced electron capture. This capture is found to be stable with respect to the spatial properties of the electron beam and results in a significant energy loss of the electrons. In this regime the plane-wave model of the laser field provides a good description of the dynamics, whereas for lower energies the Gaussian-beam and plane-wave models differ significantly. Finally the dynamics is considered for the case of an x-ray free-electron laser field. It is found that the significantly lower intensities of such fields inhibit the damping effects.

Based on the mean-field approximation and the phase-space analysis, we study the dynamics of atom-molecule conversion systems subject to particle losses. Starting from the many-body dynamics described by a master equation, an effective nonlinear Schrödinger equation is introduced. The classical phase space is then specified and classified by fixed points. The boundaries, which separate different dynamical regimes, have been established and discussed. The effect of particle loss on the conversion efficiency and the self-trapping is explored. By numerically solving the master equation, we show that the mean-field approximation is a good approach to study the dynamics of this atom-molecule conversion system.

We investigate theoretically Bose-Einstein condensation of an ideal, trapped Bose gas in the presence of Rashba spin-orbit coupling. Analytic results for the critical temperature and condensate fraction are derived based on a semiclassical approximation to the single-particle-energy spectrum and density of states and are compared with exact results obtained by explicitly summing discrete energy levels for a small number of particles. We find a significant decrease of the critical temperature and of the condensate fraction due to finite spin-orbit coupling. For a large coupling strength and a finite number of particles $N$, the critical temperature scales as $N^{2/5}$ and $N^{2/3}$ in three and two dimensions, respectively, contrasted to the predictions of $N^{1/3}$ and $N^{1/2}$ in the absence of spin-orbit coupling. Finite-size corrections in three dimensions are also discussed.

Cavity electromagnetically induced transparency (EIT) in a coherently prepared cavity-atom system is manifested as a narrow transmission peak of a weak probe laser coupled into the cavity mode. We show that, with a resonant pump laser coupling the cavity-confined four-level atoms from free space, the narrow transmission peak of the cavity EIT is split into two peaks. The two peaks represent the dressed intracavity dark states and have a frequency separation approximately equal to the Rabi frequency of the free-space pump laser. We experimentally observed the dressed intracavity dark states in cold Rb atoms confined in a cavity, and the experimental results agree with theoretical calculations based on a semiclassical analysis.