We solve the time-dependent Schrödinger equation with the method of uniform complex scaling and investigate the possibility to evaluate the solution on a complex time grid. With this approach it is possible to calculate properties that relate directly to the continuum part of the complex scaled wave function, such as the photoelectron spectrum after photoabsorption.

In the dilute limit, the properties of fermionic lattice models with short-range attractive interactions converge to those of a dilute Fermi gas in continuum space. We investigate this connection using mean-field theory, and we show that the existence of finite lattice spacing has consequences down to very small densities. In particular, we show that the reduced translational invariance associated with the lattice periodicity has a pivotal role in the finite-density corrections to the universal zero-density limit. For a parabolic dispersion with a sharp cutoff, we provide an analytical expression for the corrections, and we find that the unavoidable cutoff contributes at leading-order to the corrections to the relevant observables. In a generic lattice we find a universal power-law behavior $n^{1/3}$ which leads to significant corrections already for small densities. Our results place strong constraints on lattice extrapolations of dilute Fermi gas properties.

We analyze the single-particle quantum mechanics of an atom whose dispersion is modified by spin-orbit coupling to Raman lasers. Such a setup can create a double-well-shaped dispersion, which leads to unusual single-particle physics. We show how this dispersion influences the symmetry of the ground-state wave function in different physical-space potentials, including a square well, a harmonic well, and a double well.

We consider $N$ identical two-level systems coupled to a cavity, which is coherently driven by an external field. In the limit of small excitation, the reflection and transmission coefficients for both fields and intensities are calculated analytically. In addition, the frequency content of the cavity field and hence also the emission spectrum of the cavity are determined. A discussion is presented regarding how, in particular, individual collisional dephasing and common energy-level fluctuations prevent the cavity field from being in a coherent state, which in turn affects the outgoing fields.

Entangled photons play a pivotal role in the distribution of quantum information in quantum networks. However, the frequency bands for optimal transmission and storage of photons are often not the same. Here, we experimentally demonstrate the coherent frequency conversion of photons entangled in their polarization, a widely used degree of freedom in photonic quantum information processing. We verify the successful entanglement conversion by violating a Clauser-Horne-Shimony-Holt (CHSH) Bell inequality and fully characterize our near-perfect entanglement transfer using both state and process tomography. Our implementation is robust and flexible, making it a practical building block for future quantum networks.

The deflection of atoms in a $\Lambda$-type configuration passing through two crossed standing light waves is proposed for the probing and visualization of atomic superposition states. For this goal, we use both the large-dispersive and Raman-resonant regimes of atom-field interaction, giving rise to position-dependent phase shifts of fields, and perform double simultaneous spatial measurements on an atom. In this way, it is demonstrated that the deflection spatial patterns of atoms in a $\Lambda$-configuration passing through modes of standing waves are essentially modified if the atoms are initially prepared in coherent superpositions of their low-level states as well as when the superposition states are created during the process of deflection. There are similar results for the joint momentum distributions of atoms. Furthermore, considering both one-photon- and two-photon-excitation regimes of $\Lambda$ atoms, we also illustrate that the two-dimensional patterns of defected atoms qualitatively reflect the efficiency of the Raman processes.

The non-Markovian behavior of a V-type three-level atom coupled to a zero-temperature bosonic Lorentzian reservoir is investigated. The two decay channels from two upper states to the ground one are connected due to the spontaneously generated interference. When the two upper states are degenerate, the two channels can be decoupled, and an analytical lower bound of the non-Markovian behavior can be obtained by the optimal choice of a pair of initial states. The non-Markovian behavior can be enhanced by the interference.

We present an experimental feasible scheme to generate two-mode entangled states of two spatially separated atomic spin ensembles, using superconducting quantum circuits consisting of two coplanar waveguide resonators and a charge qubit. We show that, with the charge qubit as a tunable coupler and the resonator modes as a quantum bus, the collective atomic spins can be steered into a two-mode squeezed state exhibiting Einstein-Podolsky-Rosen entanglement through adiabatic following of the ground state of the system.

Entanglement of formation is an important measure of quantum entanglement. We present an experimental way to measure the entanglement of formation for arbitrary dimensional pure states. The measurement only evolves local quantum mechanical observables.

We discuss the evolution from BCS to Bose-Einstein condensate (BEC) superfluids in the presence of spin-orbit coupling for a balanced mixture of ultracold fermions. The dependence of several thermodynamic properties, such as chemical potential, order parameter, pressure, entropy, isothermal compressibility, and spin susceptibility tensor on the spin-orbit coupling and interaction parameter at low temperatures are analyzed. We studied both equal Rashba and Dresselhaus (ERD) and the Rashba-only (RO) spin-orbit coupling. Comparisons between the two cases reveal several striking differences in the corresponding thermodynamic quantities. Finally, we propose measuring the isothermal compressibility and spin susceptibility as a way of detecting the effects of the spin-orbit coupling.

We discuss the role of an external phase reference in quantum interferometry. We point out inconsistencies in the literature with regard to the use of the quantum Fisher information (QFI) in phase estimation interferometric schemes. We discuss the interferometric schemes with and without an external phase reference and show a proper way to use QFI in both situations.

I derive an inequality in which the phase damping rates of single qubits set an upper bound for the phase damping rate of entangled states of many qubits. The derivation is based on two assumptions: first, that the phase damping can be described by a dissipator in Lindblad form and, second, that the phase damping preserves the population of qubit states in a given basis.

We observe that changing a phase at a single point in a discrete quantum walk results in a rather surprising localization effect. For certain values of this phase change the possibility of localization strongly depends on the internal coin state of the walker.

While it is usually known that the mean value of a single observable is enough to detect entanglement or its distillability, the counterpart of such an approach in the case of quantum privacy has been missing. Here we develop the concept of a privacy witness, i.e., a single observable that may detect the presence of the secure key even in the case of bound entanglement. Then we develop the notion of secret-key estimation based on few observables and discuss the witness decomposition into local measurements. The surprising property of the witness is that with the help of a low number of product measurements involved it may still report the key values that are strictly above distillable entanglement of the state. For an exemplary four-qubit state studied in a recent experiment [K. Dobek et al., Phys. Rev. Lett. 106, 030501 (2011)] this means 6 Pauli operator product measurements versus 81 needed to carry out the complete quantum state tomography. The present approach may be viewed as a paradigm for the general program of experimentally friendly detection and estimation of task-dedicated quantum entanglement.

We present a fully quantum-mechanical theory of the mutual light-matter effects when two laser pulses interact with three discrete states coupled to a (quasi)continuum. Our formulation uses a single set of equations to describe the time dependence of the discrete and continuum populations, as well as pulse propagation in electromagnetically induced transparency (EIT) and stimulated Raman adiabatic passage (STIRAP) situations, for both weak and strong laser pulses. The theory gives a mechanistic picture of the “slowing down of light” and the state of spontaneously emitted photons during this process. Surprising features regarding the time dependence of material and radiative transients as well as limitations on quantum light storage and retrieval are unraveled.

Nuclear spin conversion (NSC) in water molecules has often been investigated in the gas or solid phase. It has not been observed in the former yet because of the difficulty in producing an efficient disequilibrium of the spin isomer populations. Another, again failed, attempt at such an experiment is presented based on the supposed spin-selective adsorption ability of nanoporous materials. To explain the reason for so many failures, the NSC rate has been calculated in the framework of the quantum relaxation model, using the best available values of the energy levels of the vibrational ground state, the intramolecular magnetic interactions, and the collisional relaxation rates. The characteristic time of NSC in the gas phase is of the order of 1 s at ambient temperature. As NSC is observed in low-temperature matrices, the quantum relaxation model can be adapted to estimate the rate in such environments. Finally, some recent experimental results devoted to astrophysical problems are discussed.

We determine the binding energy of a negative positronium ion in the limits of one spatial dimension and of infinitely many dimensions. The numerical result for the one-dimensional ground-state energy seems to be a rational number, suggesting the existence of an analytical solution for the wave function. We construct a perturbation expansion around the infinitely dimensional limit to compute an accurate estimate for the physical three-dimensional case. That result for the energy agrees to five significant figures with variational studies.

We address an efficient scheme to generate a broadband extreme-ultraviolet (xuv) continuum from high-order harmonic generation emerging from the concept of plasmonic field enhancement in the vicinity of metallic nanostructures [Kim et al., Nature (London) 453, 757 (2008)]. Based on the numerical solution of a time-dependent Schrödinger equation, for moderate field intensities and depending on the inhomogeneity of the field, we are able to increase the plateau region roughly by a factor of two and generate a broadband xuv continuum. The underlying physics of the plasmon enhancement in harmonic generation is investigated in terms of the semiclassical trajectories of strong field-electron dynamics, and perfect consistency is found between quantum mechanical simulations. It is found that the field inhomogeneity plays a critical role in quantum path selection. After a critical value, we observe a systematic suppression in the long trajectories, suggesting the generation of a single isolated attosecond pulse. Finally, we investigate the dependence of cutoff position on the order of field inhomogeneity and find a ${\beta }^{2.3\mp 0.2}$ scaling.

The atomic photoionization by a subcycle linearly polarized laser pulse is studied with numerical solutions of the time-dependent Schrödinger equation for a hydrogenlike atom. In this regime, the presumption for the adiabatic ionization theories that atoms are ionized directly from an initial bound state to the continuum state will fail. The nonadiabatic ionization channels turn out to play important roles: the bound electrons can climb up the energy ladder and get ionized from a certain bound state other than the original one. This process leaves significant fingerprints in carrier-envelope-phase-sensitive phenomena like total ionization yield and momentum asymmetry of the photoelectrons. For the modeling of subcycle pulses, the inconsistency of the popular vector potential definition is noticed and a modified version with an analytic envelope is presented that is capable of describing pulses with arbitrary pulse width.