Coherent transport of atoms trapped in an optical lattice can be controlled by microwave-induced spin flips that correlate with site-to-site hopping. We study the controllability of homogeneous one-dimensional systems of noninteracting atoms in the absence of site addressability. Given these restrictions, we construct a deterministic protocol to map an initially localized Wannier state to a wave packet that is coherently distributed over $n$ sites. As an example, we consider a one dimensional quantum walk in the presence of both realistic photon scattering and inhomogeneous broadening of the microwave transition due to the optical lattice. Using composite pulses to suppress errors, fidelities of over $95\%$ can be achieved for a 25-step walk. We extend the protocol for state preparation to analytic solutions for arbitrary unitary maps given homogeneous systems and in the presence of time-dependent uniform forces. Such control is important for applications in quantum information processing, such as quantum computing and quantum simulations of condensed matter phenomena.

A time-dependent optical lattice with staggered particle current in the tight-binding regime was considered that can be described by a time-independent effective lattice model with an artificial staggered magnetic field. The low-energy description of a single-component fermion in this lattice at half-filling is provided by two copies of ideal two-dimensional massless Dirac fermions. The Dirac cones are generally anisotropic and can be tuned by the external staggered flux $\varphi$. For bosons, the staggered flux modifies the single-particle spectrum such that in the weak coupling limit, depending on the flux $\varphi$, distinct superfluid phases are realized. Their properties are discussed, the nature of the phase transitions between them is established, and Bogoliubov theory is used to determine their excitation spectra. Then the generalized superfluid–Mott-insulator transition is studied in the presence of the staggered flux and the complete phase diagram is established. Finally, the momentum distribution of the distinct superfluid phases is obtained, which provides a clear experimental signature of each phase in ballistic expansion experiments.

We analyze the dynamics of propagation of a Gaussian light pulse through a medium having a negative index of refraction employing the recently reported projection operator technique. The governing modified nonlinear Schrödinger equation, obtained by taking into account the Drude dispersive model, is expressed in terms of the parameters of Gaussian pulse, called collective variables, such as width, amplitude, chirp, and phase. This approach yields a system of ordinary differential equations for the evolution of all the pulse parameters. We demonstrate the dependence of stability of the fixed-point solutions of these ordinary differential equations on the linear and nonlinear dispersion parameters. In addition, we validate the analytical approach numerically utilizing the method of split-step Fourier transform.

Transparent media exhibiting anomalous dispersion have been of considerable interest since Wang, Kuzmich, and Dogariu [Nature 406, 277 (2000)] first observed light propagate with superluminal and negative group velocities without absorption. Here, we propose an atomic model exhibiting these properties, based on a generalization of amplification without inversion in a five-level dressed interacting ground-state system. The system consists of a $\Lambda$ atom prepared as in standard electromagnetically induced transparency (EIT), with two additional metastable ground states coupled to the $\Lambda$ atom ground states by two rf-microwave fields. We consider two configurations by which population is incoherently pumped into the ground states of the atom. Under appropriate circumstances, we predict a pair of new gain lines with tunable width, separation, and height. Between these lines, absorption vanishes but dispersion is large and anomalous. The system described here is a significant improvement over other proposals in the anomalous dispersion literature in that it permits additional coherent control over the spectral properties of the anomalous region, including a possible ${10}^4$-fold increase over the group delay observed by Wang, Kuzmich, and Dogariu.

We show that the universal $1/k^4$ tail in the momentum distribution of dilute Fermi gases implies that the spectral function $A(\mathbf{k},\omega )$ must have weight below the chemical potential for large momentum $k\gg k_F$, with observable consequences in radio-frequency spectroscopy experiments. We find that this incoherent spectral weight is centered around $\omega \simeq -\epsilon (\mathbf{k})$ in a range of energies of order $v_{F}k$. This “bending back” in the dispersion, while natural for superfluids, is quite surprising for normal gases. This universal structure is present in the hard-sphere gas as well as in the Fermi-liquid ground state of the highly imbalanced, attractive gas near unitarity. We argue that, even in the BCS superfluid, this bending back at large $k$ is dominated by interaction effects which do not reflect the pairing gap.

Asymmetric steering is an effect whereby an inseparable bipartite system can be found to be described by either quantum mechanics or local hidden variable theories depending on which one of Alice or Bob makes the required measurements. We show that, even with an inseparable bipartite system, situations can arise where Gaussian measurements on one half are not sufficient to answer the fundamental question of which theory gives an adequate description and the whole system must be considered. This phenomenon is possible because of an asymmetry in the definition of the original Einstein-Podolsky-Rosen paradox and in this article we show theoretically that it may be demonstrated, at least in the case where Alice and Bob can only make Gaussian measurements, using the intracavity nonlinear coupler.

Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between spectral singularities in complex crystals and secularities that arise in Bragg diffraction patterns. Signatures of spectral singularities in a scattering process with wave packets are elucidated for a $\mathcal{P}\mathcal{T}$-symmetric complex crystal.

One of the last open problems concerning two qubits in a pure state is to find the exact local content of their correlation, in the sense of Elitzur, Popescu, and Rohrlich (EPR2) [A. C. Elitzur, S. Popescu, and D. Rohrlich, Phys. Lett. A162, 25 (1992)]. We propose an EPR2 decomposition that allows us to prove, for a wide range of states $|\psi (\theta )\rangle =\cos \theta |00\rangle +\sin \theta |11\rangle$, that their local content is $\overline{p_L}(\theta )=\cos 2\theta$. We also share reflections on how to possibly extend this result to all two-qubit pure states.

The origin of Hund’s multiplicity rules has been studied for a system of two electrons confined by a quasi-two-dimensional harmonic-oscillator potential by relying on a full configuration interaction wave function and Cartesian anisotropic Gaussian basis sets. In terms of appropriate normal-mode coordinates the wave function factors into a product of the center-of-mass and the internal components. The ${}^1{\Pi }_u$ singlet state and the ${}^3{\Pi }_u$ triplet state represent the energetically lowest pair of states to which Hund’s multiplicity rule applies. They are shown to involve excitations into different degrees of freedom, namely, into the center-of-mass angular mode and the internal angular mode for the singlet and triplet states, respectively. The presence of an angular nodal line in the internal space allows then the triplet state to avoid the singularity in the electron-electron interaction potential, leading to the energy lowering of the triplet state relative to its counterpart singlet state.

We perform rigorous quantum mechanical calculations for collisions between magnetically trapped Eu atoms to elucidate the results of recent experimental studies. We show that the relaxation from the maximally stretched $m_s=7/2$ level is entirely determined by the magnetic dipole-dipole interaction and analyze the role of the electronic spin-exchange interaction in transitions from the lower-energy Zeeman levels. The relaxation of the $m_s=5/2$ state is shown to be very sensitive to the spin-exchange parameter that determines the splitting between the lowest electronic states of the Eu dimer. We suggest that cold collision experiments with trapped atoms can be used as a tool for obtaining accurate information on the electronic spin anisotropy in complex molecules such as Eu${}_2$.

The temporal evolution of the dissociation probabilities for various vibrational levels of ${\mathrm{H}}_2{}^{+}$ is observed in terms of shifts in the kinetic energy release dissociation spectra, induced by linearly chirped intense laser pulses. In contrast to previous observations, in which no dependence on the chirp sign was observed, the energy spectrum reported here shows peak shifts, up for negative chirp and down for positive chirp. For some vibrational levels, dissociation takes place early on in the pulse; hence, care must be taken while interpreting the effect of pulse duration in photodissociation studies. This interpretation is supported by numerical solutions of the time-dependent Schrödinger equation.

In view of application to a miniaturized spectroscopy system, we consider an optical setup that splits a laser beam into several parallel narrow light sheets allowing an effective beam expansion and consequently longer atom-light interaction times. We analyze the multizone coherent population trapping (MZCPT) spectroscopy of alkali-metal-vapor atoms, without buffer gas, in the presence of a split light beam. We show that the MZCPT signal is largely insensitive to intensity broadening. Experimentally observed spectra are in qualitative agreement with the predictions of a simplified model that describes each spectrum as an integral over the atomic velocity distribution of Ramsey multizone spectra.

Experimentally observed strong enhancement of a single high-order harmonic in harmonic generation from low-ionized laser plasma ablation is explained as resonant harmonic generation. The resonant harmonic intensity increases regularly with the increase of the laser intensity, while the phase of the resonant harmonic is almost independent of the laser intensity. This is in sharp contrast with the usual plateau and cutoff harmonics, the intensity of which exhibits wild oscillations while its phase changes rapidly with the laser intensity. The temporal profile of a group of harmonics, which includes the resonant harmonic, has the form of a broad peak in each laser-field half cycle. These characteristics of resonant harmonics can have an important application in attoscience. We illustrate our results using examples of Sn and Sb plasmas.

We consider the evolution of multichannel excitations in longitudinally modulated waveguide arrays where the refractive index either oscillates out-of-phase in all neighboring waveguides or when it is modulated in phase in several central waveguides surrounded by out-of-phase oscillating neighbors. Both types of modulations allow resonant inhibition of light tunneling, but only the modulation of the latter type conserves the internal structure of multichannel excitations. We show that parameter regions where light tunneling inhibition is possible depend on the symmetry and structure of multichannel excitations. Antisymmetric multichannel excitations are more robust than their symmetric counterparts and experience nonlinearity-induced delocalization at higher amplitudes.

The aim of this article is to extend linear quantum dynamical network theory to include static Bogoliubov components (such as squeezers). Within this integrated quantum network theory, we provide general methods for cascade or series connections, as well as feedback interconnections using linear fractional transformations. In addition, we define input-output maps and transfer functions for representing components and describing convergence. We also discuss the underlying group structure in this theory arising from series interconnection. Several examples illustrate the theory.

We study the nonuniform potential effect in a quasi–two-dimensional (2D) Bose gas system at a finite temperature by numerically solving the projected Gross-Pitaevskii equation. The gradual emergence of superfluidity is confirmed by calculating the moment of inertia as the temperature decreases. Reflecting the nonuniformity of the system, the long-distance decay of a phase-correlation function is characterized by a local effective exponent, $\eta (r)$, which depends on the local superfluid density. This “local-density approximation” is endorsed by the 2D Gaussian field theory with the nonuniform coupling constant. Indeed, the effective exponent turns out to be close to $1/4$ at the boundary of the phase-coherent region.

The dynamics behavior of output squeezing and entanglement is investigated, based on the off-resonant interaction of a four-level atom with a low-$Q$ cavity and two classical fields. By means of the input-output theory, we show that the two-mode squeezing and entanglement of the output fields can always exist. It is found that the maximum entanglement is insensitive to the cavity decay rate, but can be optimized by adjusting the ratio between the effective coupling constants.

We investigated energy and charge transfer mechanisms as well as fragmentation dynamics in site-selectively ionized heterogeneous core-shell clusters using a high-resolution photoelectron-ion coincidence technique. We show that after inner-shell photoionization, energy or charge is transferred to neighboring atoms and that the subsequent charge localization depends on the site of ionization. Cluster bulk ionization leads to more distinct fragmentation channels than surface ionization. We attribute this to different electronic decay, charge localization, and fragmentation times and conclude that charge transfer and fragmentation dynamics are strongly influenced by the environment of the initially ionized atom.

We demonstrate how to simulate both discrete and continuous stochastic evolutions of a quantum many-body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a simple representation in terms of matrix product operators is found. The technique is exemplified by numerical simulations of the antiferromagnetic Heisenberg spin-chain model subject to various instances of the measurement model. In particular, we focus on local measurements with small support and nonlocal measurements, which induce long-range correlations.

We propose a simple three-body model of an atom in which one electron on a circular Rydberg orbit is treated as an independent particle and the remaining core electrons are collectively described as a single object. Within this model we predict the existence of stable deformed states of atoms. The deformation is generated by a bootstrap mechanism. The atomic core is polarized by the excited electron and the induced dipole moment keeps this electron localized. The deformed stable states of the atom are similar to the Trojan states observed in recent experiments. However, in the present case the breaking of the rotational symmetry does not require the presence of external fields.