We present a detailed derivation of a multisite mean-field theory (MSMFT) used to describe the Mott-insulator to superfluid transition of bosonic atoms in optical lattices. The approach is based on partitioning the lattice into small clusters which are decoupled by means of a mean-field approximation. This approximation invokes local superfluid order parameters defined for each of the boundary sites of the cluster. The resulting MSMFT grand potential has a nontrivial topology as a function of the various order parameters. An understanding of this topology provides two different criteria for the determination of the Mott insulator superfluid phase boundaries. We apply this formalism to $d$-dimensional hypercubic lattices in one, two, and three dimensions and demonstrate the improvement in the estimation of the phase boundaries when MSMFT is utilized for increasingly larger clusters, with the best quantitative agreement found for $d=3$. The MSMFT is then used to examine a linear dimer chain in which the onsite energies within the dimer have an energy separation of $\Delta$. This system has a complicated phase diagram within the parameter space of the model, with many distinct Mott phases separated by superfluid regions.

Parametrically modulated optomechanical systems have been recently proposed as a simple and efficient setting for the quantum control of a micromechanical oscillator: relevant possibilities include the generation of squeezing in the oscillator position (or momentum) and the enhancement of entanglement between mechanical and radiation modes. In this paper we further investigate this modulation regime, considering an optomechanical system with one or more parameters being modulated over time. We first apply a sinusoidal modulation of the mechanical frequency and characterize the optimal regime in which the visibility of purely quantum effects is maximal. We then introduce a second modulation on the input laser intensity and analyze the interplay between the two. We find that an interference pattern shows up, so that different choices of the relative phase between the two modulations can either enhance or cancel the desired quantum effects, opening new possibilities for optimal quantum control strategies.

We explore experimentally the effect of nonlinearity on resonant coupling between high-symmetry momentum states in hexagonal photonic lattices. We observe nonlinear Pendellösung oscillations with the power-dependent excitation of additional critical points of the same symmetry in the reciprocal cells closest to the excitation point. In contrast, the nonlinear Landau-Zener tunneling in biased lattices exhibits a sharp transition to the modulational instability with an increase of the input optical power.

We present a detailed theoretical description of laser driven x-ray parametric amplification, which has been experimentally demonstrated by Seres et al. [Nature Phys. 6, 455 (2010)] together with a supporting basic model. The process is based on the parametric interaction of an x-ray photon with a laser accelerated electron in a Coulomb field. With the extended model we are able to estimate the gain cross section also for a finite energy distribution of the interacting electrons as well as to consider dephasing between the electrons and the x-ray field. The improved model is capable of describing the recent experimental findings much more accurately.

We revisit the problem of calculating the probability current for discontinuous states, such as those that may arise in atom trapping or as a result of projective measurements. In the first-passage-time representation, the problem reduces to an evaluation of a localized wave originating from the discontinuity, whose interference with the initial state determines the transfer of probability. Depending on the type of discontinuity, the current behaves as $t^{1/2}$, $t^{3/2}$, or $\text{const}\left(t\right)$. Our approach generalizes earlier work on this subject.

Realizing useful quantum operations with high fidelity is a two-task quantum control problem wherein decoherence is to be suppressed and desired unitary evolution is to be executed. The dynamical decoupling (DD) approach to decoherence suppression has been fruitful but synthesizing DD fields with certain quantum control fields may be experimentally demanding. In the context of spin squeezing, here we explore an unforeseen possibility that continuous DD fields may serve dual purposes at once. In particular, it is shown that a rather simple configuration of DD fields can suppress collective decoherence and yield a $1/N$ scaling of the squeezing performance ($N$ is the number of spins), thus making spin squeezing more robust to noise and much closer to the so-called Heisenberg limit. The theoretical predictions should be within the reach of current spin squeezing experiments.

We extend the Hilbert-Schmidt (square norm) distance, previously used to define the geometric quantum discord, to define also geometric quantifiers of total and classical correlations. We then compare the dynamics of geometric and entropic quantifiers of the different kinds of correlations in a non-Markovian open two-qubit system under local dephasing. We find that qualitative differences occur only for quantum discords. This is taken to imply that geometric and entropic discords are not, in general, equivalent in describing the dynamics of quantum correlations. We then show that geometric and entropic quantifiers of total correlations also present qualitative disagreements in the state space. This aspect indicates that the differences found for quantum discord are not attributable to a different separation, introduced by each measure, between the quantum and classical parts of correlations. Finally, we find that the Hilbert-Schmidt distance formally coincides with a symmetrized form of linear relative entropy.

A method of purification through Zeno-like measurements has been proposed by Nakazato and co-workers [H. Nakazato, T. Takazawa, and K. Yuasa, Phys. Rev. Lett. 90, 060401 (2003); H. Nakazato, M. Unoki, and K. Yuasa, Phys. Rev. A 70, 012303 (2004)]. A series of frequent measurements on a quantum system is demonstrated to result in the purification of another quantum system in interaction with the former. Inspired by this idea, we have designed a strategy to obtain entangled states through only two measurements. A deterministic purification method is also provided in this article.

We present a procedure for direct characterization of the dephasing noise acting on a single qubit by making repeated measurements of the qubit coherence under suitably chosen sequences of controls. We show that this allows a numerical reconstruction of the short-time noise correlation function and that it can be combined with a series of measurements under free evolution to allow a characterization of the noise correlation function over many orders of magnitude range in time scale. We also make an analysis of the robustness and reliability of the estimated correlation functions. Application to a simple model of two uncorrelated noise fluctuators using decoupling pulse sequences shows that the approach provides a useful route for the experimental characterization of dephasing noise and its statistical properties in a variety of condensed phase and atomic systems.

Nonclassical states of light play a central role in many quantum information protocols. Very recently, their quantum features have been exploited to improve the readout of information from digital memories, modeled as arrays of microscopic beam splitters [Pirandola, Phys. Rev. Lett. 106, 090504 (2011)]. In this model of “quantum reading,” a nonclassical source of light with Einstein-Podolski-Rosen correlations has been proven to retrieve more information than any classical source. In particular, the quantum-classical comparison has been performed under a global energy constraint, i.e., by fixing the mean total number of photons irradiated over each memory cell. In this paper we provide an alternative analysis which is based on a local energy constraint, meaning that we fix the mean number of photons per signal mode irradiated over the memory cell. Under this assumption, we investigate the critical number of signal modes after which a nonclassical source of light is able to beat any classical source irradiating the same number of signals.

We present an implementation of four-component relativistic coupled-cluster theory for the treatment of electronically excited states of molecules containing heavy elements, allowing for a consistent and accurate treatment of relativistic effects such as the spin-orbit interaction and electron correlations as well as their intertwining. Our approach uses general excitation ranks in the cluster operator and, moreover, allows for the definition of active-space selected excitations of variable excitation rank. Initial applications concern the silicon atom and the heavier pnictogen monohydride molecules, where we focus on the first vertical excitation energy to the $\Omega =1$ electronic state. We discuss the problem of adequately choosing a reference state (Fermi vacuum) and addressing electron correlation in the presence of effects of special relativity of increasing importance. For the heaviest homolog, BiH, where dynamic electron correlation is of major importance, we obtain vertical excitation energies with a deviation of less than 1% from the experimental value.

We propose a method for sensitive parallel detection of low-frequency electromagnetic fields based on the fine structure interactions in paramagnetic polar molecules. Compared to the recently implemented scheme employing ultracold ${}^{87}$Rb atoms by Böhi et al. [Appl. Phys. Lett. 97, 051101 (2010)], the technique based on molecules offers a 100-fold higher sensitivity, the possibility to measure both the electric and magnetic field components, and a probe of a wide range of frequencies from the dc limit to the THz regime.

We apply a numerical-basis-state method to study dynamical processes in the interaction of atoms with strong laser pulses. The method is based on the numerical representation of finite-space energy eigenstates of the field-free atomic Hamiltonian in a box on a grid and the expansion of the solution of the full time-dependent Schrödinger equation, including the interaction with the field, in this numerical basis. We apply the method to the hydrogen atom and present results for excitation and ionization probabilities as well as photoelectron momentum distributions. Convergence of the results with respect to the size of the basis as well as the parallel efficiency of the numerical algorithm is studied. The results of the numerical-basis-state method are in good agreement with those of two-dimensional numerical grid calculations. The computation times for the numerical-basis-state method usually are found to be significantly smaller than those for the two-dimensional grid calculations, whereas, even higher excited states can be well represented. We further apply this method to study a few recently reported phenomena related to strong-field excitation of atoms, such as the dependence of the excitation probabilities on the carrier-envelope phase in ultrashort pulses as well as the so-called frustrated ionization.

Recently it was shown that broadband supercontinuum harmonics can be produced from the long-trajectory electrons in the single-atom response by the coherent control of the electron trajectories through optimized two-color laser fields. Such supercontinuum harmonics can be superposed to generate an isolated sub-30-attosecond (as) pulse [Liu et al., Phys. Rev. A 84, 033414 (2011)]. In this paper, we investigate the effect of macroscopic propagation on the supercontinuum harmonic spectra and the subsequent attosecond-pulse generation of atomic hydrogen. The time-dependent Schrödinger equation is solved accurately and efficiently by means of the time-dependent generalized pseudospectral method. The effects of macroscopic propagation are investigated in near and far field by solving Maxwell's equation. The results show that the contribution of short-trajectory electron emission is increased when the macroscopic propagation is considered. However, the characteristics of the dominant long-trajectory electron emission (in the single-atom response case) are not changed, and an isolated 53 as pulse can be generated in the near field. Moreover, in the far field, the contribution of long-trajectory electron emission is still dominant for both on-axis and off-axis cases. As a result, an isolated 42 as pulse can be generated directly. Similar results are obtained when the atomic target position is changed. Therefore, the proposed method for the single ultrashort attosecond-pulse generation can be realized by means of the coherent control of the electron quantum paths in appropriately optimized two-color laser fields.

We suggest a type of imaging technique that uses optical nonlinearities and spatiotemporal modulation to achieve nanoscale resolution in the far field. The technique utilizes intense laser beams to produce an optical excitation with spatial features that are much smaller than the wavelength of light. Nonlinear mixing with the excitation can then be used to imprint the information contained in high spatial frequencies into the propagating region. As a specific example, we study the implementation of this technique using coherent anti-Stokes Raman scattering (CARS) near maximum molecular coherence. Our simulations suggest that it may be possible to resolve the structure of complex biological molecules at the nanometer scale in the far field using near-infrared light.

A theoretical model describing the Raman scattering process in atomic vapors is constructed. The treatment investigates the low-excitation regime suitable for modern experimental applications. Despite the incorporated decoherence effects (possibly mode dependent) it allows for a direct separation of the time evolution from the spatial degrees of freedom. The impact of noise on the temporal properties of the process is examined. The model is applied in two experimentally relevant situations of ultracold and room-temperature atoms. The spatial eigenmodes of the Stokes photons and their coupling to atomic excitations are computed. Similarly, dynamics and the waveform of the collective atomic state are derived for quantum memory implementations.

We analyze the excitation spectrum of a superfluid Bose-Einstein condensate rotating in a ring trap. We identify two important branches of the spectrum related to outer and inner edge surface modes that lead to the instability of the superfluid. Depending on the initial circulation of the annular condensate, either the outer or the inner modes become first unstable. This instability is crucially related to the superfluid nature of the rotating gas. In particular, we point out the existence of a maximal circulation above which the superflow decays spontaneously, which cannot be explained by invoking the average speed of sound.

We propose a method to maximize the fidelity of quantum memory implemented by a spectrally inhomogeneous spin ensemble. The method is based on preselecting the optimal spectral portion of the ensemble by judiciously designed pulses. This leads to significant improvement of the transfer and storage of quantum information encoded in the microwave or optical field.

We analyze the structure and stability of singular singly quantized vortices in a rotating spin-1 Bose-Einstein condensate. We show that the singular vortex can be energetically stable in both the ferromagnetic and polar phases despite the existence of a lower-energy nonsingular coreless vortex in the ferromagnetic phase. The spin-1 system exhibits an energetic hierarchy of length scales resulting from different interaction strengths, and we find that the vortex cores deform to a larger size determined by the characteristic length scale of the spin-dependent interaction. We show that in the ferromagnetic phase the resulting stable core structure, despite apparent complexity, can be identified as a single polar core with an axially symmetric density profile which is nonvanishing everywhere. In the polar phase, the energetically favored core deformation leads to a splitting of a singly quantized vortex into a pair of half-quantum vortices that preserves the topology of the vortex outside the extended core region, but breaks the axial symmetry of the core. The resulting half-quantum vortices exhibit nonvanishing ferromagnetic cores.