A method for the complete characterization of a coherent superposition of atomic states, prepared by a pump pulse, is presented. The technique is based on the measurement of two asymmetry parameters, related to the photoionization of the generated electron wave packet by isolated attosecond pulses. By numerically solving the fully three-dimensional time-dependent Schrödinger equation, it is demonstrated that the temporal evolution of the population of the atomic states involved in the coherent superposition can be mapped onto the amplitude-modulated asymmetry in the direction of the attosecond probe pulse polarization. The results of the numerical simulations show that it is possible to achieve a unique determination of static and time-dependent populations by measuring only a few ionization asymmetry parameters.

Two-dimensional fundamental soliton-soliton pairs are investigated in binary mixtures of Bose-Einstein condensates with attractive interactions between atoms of the same type. Both attractive and repulsive interactions between atoms of different types are considered. The general properties of the stationary states are investigated variationally and numerically. The stability regions of the soliton-soliton pairs are determined.

We perform a numerical study of spin turbulence in a two-dimensional trapped spin-1 spinor Bose-Einstein condensate, focusing on the energy spectrum. The spin turbulence in the trapped system is generated by instability of the helical structure of the spin density vector in the initial state. Our numerical calculation finds that in the trapped system, the spectrum of the spin-dependent interaction energy in the ferromagnetic case exhibits a $-7/3$ power law, which was confirmed in a uniform system by our previous study. The relation between the $-7/3$ power law and the motion of the spin density vector is discussed by investigating the orbits of dynamical variables in the spin space.

We suggest a simple experimental method for probing antiferromagnetic spin correlations of two-component Fermi gases in optical lattices. The method relies on a spin selective Raman transition to excite atoms of one spin species to their first excited vibrational mode where the tunneling is large. The resulting difference in the tunneling dynamics of the two spin species can then be exploited, to reveal the spin correlations by measuring the number of doubly occupied lattice sites at a later time. We perform quantum Monte Carlo simulations of the spin system and solve the optical lattice dynamics numerically to show how the timed probe can be used to identify antiferromagnetic spin correlations in optical lattices.

We investigate properties of an energetic atom propagating through strongly interacting atomic gases. The operator product expansion is used to systematically compute a quasiparticle energy and its scattering rate both in a spin-1/2 Fermi gas and in a spinless Bose gas. Reasonable agreement with recent quantum Monte Carlo simulations even at a relatively small momentum $k/k_{\mathrm{F}}\gtrsim 1.5$ indicates that our large-momentum expansions are valid in a wide range of momentum. We also study a differential scattering rate when a probe atom is shot into atomic gases. Because the number density and current density of the target atomic gas contribute to the forward scattering only, its contact density (measure of short-range pair correlation) gives the leading contribution to the backward scattering. Therefore, such an experiment can be used to measure the contact density and thus provides a new local probe of strongly interacting atomic gases.

We use strong-coupling perturbation theory, the variational cluster approach (VCA), and the dynamical density-matrix renormalization group (DDMRG) method to investigate static and dynamical properties of the one-dimensional Bose–Hubbard model in both the Mott-insulating and superfluid phases. From the von Neumann entanglement entropy we determine the central charge and the transition points for the first two Mott lobes. Our DMRG results for the ground-state energy, momentum distribution function, boson correlation function decay, Mott gap, and single-particle spectral function are reproduced very well by the strong-coupling expansion to fifth order, and by VCA with clusters up to 12 sites as long as the ratio between the hopping amplitude and onsite repulsion, $t/U$, is smaller than 0.15 and 0.25, respectively. In addition, in the superfluid phase VCA captures well the ground-state energy and the sound velocity of the linear phonon modes. This comparison provides an authoritative estimate for the range of applicability of these methods. In strong-coupling theory for the Mott phase, the dynamical structure factor is obtained from the solution of an effective single-particle problem with an attractive potential. The resulting resonances show up as double-peak structures close to the Brillouin zone boundary. These high-energy features also appear in the superfluid phase which is characterized by a pronounced phonon mode at small momenta and energies, as predicted by Bogoliubov and field theory. In one dimension, there are no traces of an amplitude mode in the dynamical single-particle and two-particle correlation functions.

Vortex trimer is predicted in three-component Bose-Einstein condensates (BEC's) with internal coherent couplings. The molecule is made by three constituent vortices which are bounded by domain walls of the relative phases. We show that the shape and the size of the molecule can be controlled by changing the internal coherent couplings.

It remains a challenge to independently manipulate the magnetic dipolar and the spin-exchange interactions, which are entangled in many spin systems, particularly in spin-1 Bose-Einstein condensates. For this purpose, we put forward a sequence of rf pulses and the periodic dynamical decoupling sequence of optical Feshbach resonance pulses to control the dipolar and the spin-exchange interactions, respectively. Our analytic results and the numerical simulations demonstrate that either of the two interactions can be suppressed to make the other dominate the spin dynamics; furthermore, both of the interactions can be simultaneously suppressed to realize spinor-condensate–based magnetometers with a higher sensitivity. This manipulation method may find its wide applications in magnetic resonance and spintronics.

Photonic crystals are periodic systems that consist of dielectrics with different refractive indices. They are designed to act on photons in contrast to semiconductor crystals whose periodicity affects the motion of electrons. Here we consider the interaction of an atomic electron with its own radiation field in the case when the atom is placed in air voids of a photonic crystal and is not in mechanical contact with the vibrational degrees of freedom of the dielectric host. A strong modification of this interaction from that in free space is shown to change the rest mass of the electron, and this has a significant effect on the shift of the atomic energy levels. This shift is investigated by using the example of atomic hydrogen in a high-index-contrast photonic crystal. The found effect may be of interest both from fundamental and practical points of view.

We study electromagnetically induced transparency (EIT) of a probe field in a four-level Y-type atomic system driven by two strong laser (coupling) fields. Both homogeneously (radiative) and Doppler broadened systems are considered. The effect of residual Doppler broadening on EIT is demonstrated for various wave-vector mismatches occurring when the frequency of coupling fields is equal ($k_c$ $=$ $k_p$), higher ($k_c>k_p$), or lesser ($k_c<k_p$) than that of the probe field frequency. Contrary to usual belief it is found that for the $k_c>k_p$ wave-vector mismatch case, the probe absorption profile displays very wide and almost complete single or double EIT windows whose width, depth, and location depend upon the wave-vector mismatch, Rabi frequencies, and atom field detuning of the coupling fields. Analytical results are also obtained to explain these interesting features.

Recent works [Chong et al., Phys. Rev. Lett. 105, 053901 (2010); Wan et al., Science 331, 889 (2011)] have shown that the time-reversed process of lasing at threshold realizes a coherent perfect absorber (CPA). In a CPA, a lossy medium in an optical cavity with a specific degree of dissipation, equal in modulus to the gain of the lasing medium, can perfectly absorb coherent optical waves at discrete frequencies that are the time-reversed counterpart of the lasing modes. Here the concepts of time reversal of lasing and CPA are extended for optical radiation emitted by a laser operated in an arbitrary regime, i.e., for transient, chaotic, or periodic coherent optical fields. We prove that any electromagnetic signal $E\left(t\right)$ generated by a laser system $S$ operated in an arbitrary regime can be perfectly absorbed by a CPA device $S^{\prime }$ which is simply realized by placing inside $S$ a broadband linear absorber (attenuator) of appropriate transmittance. As examples, we discuss CPA devices that perfectly absorb a chaotic laser signal and a frequency-modulated optical wave.

We study effects of nonlocality of the cubic self-focusing nonlinearity on the stability and symmetry-breaking bifurcation (SBB) of solitons in the model of a planar dual-core optical waveguide with nonlocal (thermal) nonlinearity. In comparison with the well-known coupled systems with the local nonlinearity, the present setting is affected by the competition of different spatial scales, viz, the coupling length and correlation radius of the nonlocality $\sqrt{d}$. By means of numerical methods and variational approximation (VA, which is relevant for small $d$), we find that, with the increase of the correlation radius, the SBB changes from subcritical into supercritical, which makes all the asymmetric solitons stable. On the other hand, the nonlocality has little influence on the stability of antisymmetric solitons. Analytical results for the SBB are also obtained (actually, for antisymmetric “accessible solitons”) in the opposite limit of the ultra-nonlocal nonlinearity, using a coupler based on the Snyder-Mitchell model. The results help to grasp the general picture of the symmetry breaking in nonlocal couplers.

Single-photon scattering properties in a coupled-resonator waveguide (CRW) coupled to a nanocavity embedded with a two-level system are investigated theoretically. Two cases are considered: when the nanocavity is locally coupled to one resonator and when it is nonlocally coupled to two resonators of the CRW. The transmission and reflection amplitudes are obtained for the two cases, respectively. The results show that the position of perfect transmission remains unchanged, while the position of perfect reflection is shifted due to the nonlocal coupling. An asymmetric Fano resonance appears in the transmission spectrum and can be controlled by adjusting the coupling strengths in the nonlocal coupling case. The effects of the coupling strengths and dissipation on the transport properties are also analyzed for the two cases.

A so-called two centers problem (TCP) has the following two mathematically equivalent, but physically different embodiments. The first one is the motion of an electron in the field of two stationary Coulomb centers of charges $Z$ and $Z$′ separated by a distance $R$, which is one of the most fundamental problems in quantum mechanics. The second one is the motion of a planet in the gravitational field of two stationary stars of generally different masses, which is one of the most fundamental problems in celestial mechanics. At least, two groups of authors claimed that for the TCP they derived a supergeneralized Runge-Lenz vector, whose projection on the internuclear (or interstellar) axis is conserved. In the present paper, first, we show that their claims are incorrect: the projection of their supergeneralized Runge-Lenz vector is not conserved. Second, we derive a correct supergeneralized Runge-Lenz vector whose projection on the internuclear or interstellar axis does conserve. Third, since in the literature there are several expressions for the separation constant for the TCP—the expressions not having the form of a projection of any vector on the internuclear or interstellar axis—we provide relations between those expressions and our result.

We study analytically and numerically the dynamical Casimir effect in a cavity containing two stationary two-level atoms that interact with the resonance field mode via the Tavis-Cummings Hamiltonian. We determine the modulation frequencies for which the field and atomic excitations are generated and study the corresponding dynamical behaviors in the absence of damping. It is shown that the two-atom setup allows for monitoring of photon generation without interrupting the growth, and different entangled states can be generated during the process.

We present the first experimental implementation of a multifunctional device for the optimal cloning of one to two qubits. Previous implementations have always been designed to optimize the cloning procedure with respect to one single type of a priori information about the cloned state. In contrast, our “all-in-one” implementation is optimal for several prominent regimes such as universal cloning, phase-covariant cloning, and also the first ever realized mirror phase-covariant cloning, when the square of the expected value of Pauli's $Z$ operator is known in advance. In all these regimes the experimental device yields clones with almost maximum achievable average fidelity (97.5$\%$ of theoretical limit). Our device has a wide range of possible applications in quantum information processing, especially in quantum communication. For instance, one can use it for incoherent and coherent attacks against a variety of cryptographic protocols, including the Bennett-Brassard 1984 protocol of quantum key distribution through the Pauli damping channels. It can be also applied as a state-dependent photon multiplier in practical quantum networks.

Quantum-state transfer with fidelity higher than $0.99$ can be achieved in the ballistic regime of an arbitrarily long one-dimensional chain with uniform nearest-neighbor interaction, except for the two pairs of mirror-symmetric extremal bonds, say $x$ (first and last) and $y$ (second and penultimate). These have to be roughly tuned to suitable values $x\sim 2N^{-1/3}$ and $y\sim 2^{3/4}{N}^{-1/6}$, where $N$ is the chain length. The general framework can describe the end-to-end response in different models, such as fermion or boson hopping models and $XX$ spin chains.

We propose a startling hybrid quantum architecture for simulating a localization-delocalization transition. The concept is based on an array of superconducting flux qubits which are coupled to a diamond crystal containing nitrogen-vacancy centers. The underlying description is a Jaynes-Cummings lattice in the strong-coupling regime. However, in contrast to well-studied coupled cavity arrays, the interaction between lattice sites is mediated here by the qubit rather than by the oscillator degrees of freedom. Nevertheless, we point out that a transition between a localized and a delocalized phase occurs in this system as well. We demonstrate the possibility of monitoring this transition in a nonequilibrium scenario, including decoherence effects. The proposed scheme allows the monitoring of localization-delocalization transitions in Jaynes-Cummings lattices by use of currently available experimental technology. Contrary to cavity-coupled lattices, our proposed recourse to stylized qubit networks facilitates (i) investigating localization-delocalization transitions in arbitrary dimensions and (ii) tuning the intersite coupling in situ.

It was shown [Cubitt et al., IEEE Trans. Inf. Theory 57, 8114 (2011)] that there exist quantum channels where a single use cannot transmit classical information perfectly yet two uses can. This phenomenon is called the superactivation of the zero-error classical capacity, which does not occur in classical channels. In this paper, it is shown that qubit channels cannot generate the superactivation.

We develop a quantum-mechanical coupled-channel theory to simulate spatial distributions of electron current densities, produced in photoionization for nonhydrogenic atoms in the presence of a uniform external electric field. The coupled Schrödinger equations are numerically solved using the renormalized Numerov method. The expression for the outgoing wave function for photoelectrons ejected from the nonhydrogenic atomic source is derived. The theory is applied to investigations of photoionization for ground-state Li atoms. The distributions of electron current densities are computed and compared to the corresponding experimental images. Excellent agreement is obtained. It is, furthermore, found that the presence of the nonhydrogenic residual ion significantly changes the differential cross sections and/or electron current densities with respect to the hydrogenic case. Finally, the implications of the presence of the atomic core for quantum resonance tunneling are also analyzed.