Quantum Ising model in one dimension is an exactly solvable example of a quantum phase transition. We investigate its behavior during a quench caused by a gradual turning off of the transverse bias field. The system is then driven at a fixed rate characterized by the quench time ${\tau }_Q$ across the critical point from a paramagnetic to ferromagnetic phase. In agreement with Kibble-Zurek mechanism (which recognizes that evolution is approximately adiabatic far away, but becomes approximately impulse sufficiently near the critical point), quantum state of the system after the transition exhibits a characteristic correlation length $\widehat{\xi }$ proportional to the square root of the quench time ${\tau }_Q$: $\widehat{\xi }=\sqrt{{\tau }_Q}$. The inverse of this correlation length is known to determine average density of defects (e.g., kinks) after the transition. In this paper, we show that this same $\widehat{\xi }$ controls the entropy of entanglement, e.g., entropy of a block of $L$ spins that are entangled with the rest of the system after the transition from the paramagnetic ground state induced by the quench. For large $L$, this entropy saturates at $\frac{1}{6}{\log }_2\widehat{\xi }$, as might have been expected from the Kibble-Zurek mechanism. Close to the critical point, the entropy saturates when the block size $L\approx \widehat{\xi }$, but—in the subsequent evolution in the ferromagnetic phase—a somewhat larger length scale $l=\sqrt{{\tau }_Q}\ln {\tau }_Q$ develops as a result of a dephasing process that can be regarded as a quantum analog of phase ordering, and the entropy saturates when $L\approx l$. We also study the spin-spin correlation using both analytic methods and real time simulations with the Vidal algorithm. We find that at an instant when quench is crossing the critical point, ferromagnetic correlations decay exponentially with the dynamical correlation length $\widehat{\xi }$, but (as for entropy of entanglement) in the following evolution length scale $l$ gradually develops. The correlation function becomes oscillatory at distances less than this scale. However, both the wavelength and the correlation length of these oscillations are still determined by $\widehat{\xi }$. We also derive probability distribution for the number of kinks in a finite spin chain after the transition.

We consider a one-parameter family of matrix-product states of spin-1 particles on a periodic chain and study in detail the entanglement properties of such a state. In particular, we calculate exactly the entanglement of one site with the rest of the chain, and the entanglement of two distant sites with each other, and show that the derivative of both these properties diverge when the parameter $g$ of the states passes through a critical point. Such a point can be called a point of quantum phase transition, since at this point the character of the matrix-product state, which is the ground state of a Hamiltonian, changes discontinuously. We also study the finite size effects and show how the entanglement depends on the size of the chain. This later part is relevant to the field of quantum computation where the problem of initial state preparation in finite arrays of qubits or qutrits is important. It is also shown that the entanglement of two sites have scaling behavior near the critical point.

It is shown that a large class of weak disturbances on macroscopic quantum superpositions can be canceled by a probabilistic reversing operation on the system. We illustrate this for spin systems undergoing an Ising-type interaction with the environment and demonstrate that both the fidelity to the original state and the purity of the amended state can simultaneously be increased by the reversing operation. A possible experimental scheme to implement our scheme is discussed.

We report the energy and angular distribution of electron double differential cross sections (DDCS) in collision of $6\text{−}\mathrm{MeV}∕\mathrm{u}{\mathrm{C}}^{6+}$ ions with molecular hydrogen. We explain the observed distributions in terms of the two-center effect and the Young-type interference effect. The secondary electrons having energies between 1 and $1000\mathrm{eV}$ are detected at about 10 different emission angles between $30°$ and $150°$. The measured data are compared with the state-of-the-art continuum distorted wave-eikonal initial state and the first Born model calculations which use molecular wave function. The single differential cross sections are derived and compared with the theoretical predictions. The oscillations due to the interference effect are derived in the DDCS ratios using theoretical cross sections for the atomic H target. The effect of the atomic parameters on the observed oscillations is discussed. An evidence of interference effect has also been shown in the single differential cross section. The electron energy dependence of the forward-backward asymmetry parameter shows a monotonically increasing behavior for an atomic target, such as He, which could be explained in terms of the two-center effect only. In contrast, for the molecular ${\mathrm{H}}_2$ the asymmetry parameter reveals an oscillatory behavior due to the Young-type interference effect superimposed with the two-center effect. The asymmetry parameter technique provides a self-normalized method to reveal the interference oscillation which does not require either a theoretical model or complementary measurements on the atomic H target.

We present a general and mathematically simple method to control two-level systems. It is based on a piecewise time-independent procedure. We assume that some parameters of an external interaction potential can be rapidly switched at specified time instants, and then kept constant during small time intervals $\mathrm{\Delta }t$. By properly setting the parameter values, obtained from algebraic, instead of differential or integral, equations, we can drive the time evolution of arbitrary observables. We illustrate the approach with some examples and discuss important technical aspects, relevant in real concrete situations, such as the robustness of the method to errors in the control parameter values, the influence of the switching mechanism transient times, the appropriate choice for the $\mathrm{\Delta }t$’s, and so on.

We present a semiclassical theory of the sub-Doppler forces in an asymmetric magneto-optical trap where the trap-laser frequencies are unequal to one another. To solve the optical Bloch equations, which contain explicit time dependence, unlike in the symmetric case of equal laser detunings, we have developed a convenient and efficient method to calculate the atomic forces at various oscillating frequencies for each atomic density matrix element. In particular, the theory provides a qualitative understanding of the array of sub-Doppler traps (SDTs) recently observed in such an asymmetric trap. We find that the distances between SDTs are proportional to the relative detuning differences, in good agreement with experimental results. The theory presented here can be applied to a dynamic system with multiple laser frequencies involved; the number of coupled equations to solve is much reduced and the resulting numerical calculation can be performed rather simply and efficiently.

We introduce an analytical formula for the dynamics of light propagation in a two-dimensional waveguide lattice including diagonal coupling. A superposition of infinite arrays created by imaginary sources is used to derive an expression for boundary reflections. It is shown analytically that for large propagation distances the propagating field reaches uniformity. Furthermore, periodic field recovery is studied and discrete anomalous refraction and diffraction are investigated in arbitrary two-dimensional lattices.

We study the transfer of a quantum state through a Heisenberg spin-1 chain prepared in its ground state. We characterize the efficiency of the transfer via the fidelity of retrieving an arbitrarily prepared state and also via the transfer of quantum entanglement. The Heisenberg spin-1 chain has a very rich quantum phase diagram. We show that the boundaries of the different quantum phases are reflected in sharp variations of the transfer efficiency. In the vicinity of the border between the dimer and the ferromagnetic phase (in the conjectured spin-nematic region), we find strong indications for a qualitative change of the excitation spectrum. Moreover, we identify two regions of the phase diagram that give rise to particularly high transfer efficiency; the channel might be nonclassical even for chains of arbitrary length, in contrast to spin-$1∕2$ chains.

We analyze the laser cooling of a gas of polarizable particles by continuous dispersive position detection and active feedback. Microkelvin temperatures can be attained inside an optical resonator, while in free space cooling requires wavelength-size beams. The maximum cooling flux is set by the thermal Doppler width, with typical values between ${10}^5$ and ${10}^9\text{molecules}\text{per}\text{second}$.

We note that an equation governing the dynamics of a polarizable linear polar molecule in a dc electric field coincides with one of two equations describing a hydrogen atom in the prolate spheroidal coordinate system. Using this analogy, as well as the known algebra of the angular momentum and Runge-Lenz-Pauli operators for the case of a hydrogen atom, the energy levels of a polarizable linear polar molecule in a dc electric field are calculated. For some cases, these energy values are exact.

We present a theoretical method for Coulomb three-body rearrangement collisions solving a Chew-Goldberger-type integral equation directly. The scattering boundary condition is automatically satisfied by adiabatically switching on the interaction between the projectile and hydrogen atom. Hence the outgoing wave function is obtained without the tedious procedure of adjusting the total wave function in the asymptotic region. All the dynamical information can be derived from the outgoing wave function obtained on pseudospectral grids numerically. Taking ${\mu }^{-}+\mathrm{H}\left(1s\right)$ and $\overline{p}+\mathrm{H}\left(1s\right)$ collisions as examples, we demonstrate the usefulness and powerfulness of the method and present the state-specified capture cross sections of heavy negatively charged particles by hydrogen atoms. The convergence and accuracy of the numerical procedure are examined with sufficient care.

We theoretically investigate above-threshold ionization by chirped laser pulses. By comparing the photoelectron energy spectra and the photoelectron angular distributions of Na for the laser pulses with different chirp rates but with the identical spectral profile, we find that the ionization processes have a clear dependence on the chirp rate. Further calculations without excited bound states during the time propagation of the wave function reveal practically no chirp dependence, which is clear evidence that the origin of the chirp dependence in above-threshold ionization is the excited bound states.

A strongly correlated Luttinger-liquid behavior is found to emerge well beyond the Tonks-Girardeau (TG) regime in a one-dimensional Bose gas with dipolar repulsions at $T=0$, persisting for a wide range of densities. After combining reptation quantum Monte Carlo and bosonization techniques, we provide a unifying theory of the underlying crossover physics, evolving from the TG gas at low density into a classical quasiordered state at high density. The density dependent Luttinger parameters extracted from the numerical data provide all that is needed to determine the low-energy behavior from analytical expressions. Our quantitative predictions, in the whole crossover, for measurable quantities such as the structure factor and the momentum distribution, are estimated to be accessible in underway experiments with ultracold polar molecules.

We give an overview of different types of entanglement that can be generated in experiments, as well as of various protocols that can be used to verify or quantify entanglement. We propose several criteria that, we argue, should be applied to experimental entanglement verification procedures. Explicit examples demonstrate that not following these criteria will tend to result in overestimating the amount of entanglement generated in an experiment or in inferring entanglement when there is none. We distinguish protocols meant to refute or eliminate hidden-variable models from those meant to verify entanglement.

Highly entangled states called cluster states are a universal resource for measurement-based quantum computing (QC). Here we propose an efficient method for producing large cluster states using superconducting quantum circuits. We show that a large cluster state can be efficiently generated in just one step by turning on the interqubit coupling for a short time. Because the interqubit coupling is only switched on during the time interval for generating the cluster state, our approach is also convenient for preparing the initial state for each qubit and for implementing one-way QC via single-qubit measurements. Moreover, the cluster state is robust against parameter variations.

Differential measurements for single and multiple ionization of Kr by 240 and $500\mathrm{eV}$ electron impact are presented. Using a pulsed extraction field, ${\mathrm{Kr}}^{+}$, ${\mathrm{Kr}}^{2+}$, and ${\mathrm{Kr}}^{3+}$ ions were measured in coincidence with scattered electrons for energy losses up to $120\mathrm{eV}$ and scattering angles between 16° and 90°. Scaling properties of the doubly differential cross sections (DDCS) are investigated as a function of energy loss, scattering angle, and momentum transfer. It is shown that scaling the DDCS as outlined by Kim and Inokuti and plotting them versus a parameter consisting of the momentum transfer divided by the square root of the impact energy times $1-\cos \left(\theta \right)$, where $\theta$ is the scattering angle, yielded similar curves, but with different magnitudes, for single and multiple ionization. Normalizing these curves together produced two universal curves, one appropriate for single and multiple electron emission at larger scattering angles $(\theta ⩾30°)$ and one appropriate for small scattering angles $(\theta <30°)$.

Efimov physics refers to universal phenomena associated with a discrete scaling symmetry in the three-body problem with a large scattering length. The first experimental evidence for Efimov physics was the recent observation of a resonant peak in the three-body recombination rate for ${}^{133}\mathrm{Cs}$ atoms with large negative scattering length. There can also be resonant peaks in the atom-dimer relaxation rate for large positive scattering length. We calculate the atom-dimer relaxation rate as a function of temperature and show how measurements of the relaxation rate can be used to determine accurately the parameters that govern Efimov physics.

We show that an effective quadratic Zeeman effect for trapped atoms can be generated by proper laser configurations and, in particular, by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, e.g., for a degenerate ${}^{52}\mathrm{Cr}$ gas, can be used to induce topological defects by controllably quenching across transitions between phases of different symmetries, allows for the observability of the Einstein–de Haas effect for relatively large magnetic fields, and may be employed to create $S=1∕2$ systems with spinor dynamics. Similar ideas could be explored in other atomic species opening an exciting new control tool in spinor systems.

We give a unified approach to macroscopic QED in arbitrary linearly responding media, based on the quite general, nonlocal form of the conductivity tensor as it can be introduced within the framework of linear response theory, and appropriately chosen sets of bosonic variables. The formalism generalizes the quantization schemes that have been developed previously for diverse classes of linear media. In particular, it turns out that the scheme developed for locally responding linear magnetodielectric media can be recovered from the general scheme as a limiting case for weakly spatially dispersive media. With regard to practical applications, we furthermore address the dielectric approximation for the conductivity tensor and the surface impedance method for the calculation of the Green tensor of the macroscopic Maxwell equations, the two central quantities of the theory.

An approach for performing a local measurement on a set of complete $n$-qubit maximally entangled states via cavity QED is presented. The method operates essentially by creating a single photon in the cavity through one qubit and then performing a joint multiqubit phase shift on the remaining qubits with the assistance of the photon. It is shown that for three-level qubit systems, a complete set of $2^n$ $n$-qubit maximally entangled states can be measured simultaneously, deterministic and independent of the number of qubits. Hence, the method is very efficient for realizing multiqubit GHZ-state measurement which is important to quantum information processing and communication.