We study the properties of coupled linear and nonlinear resonances. The fundamental phenomena and the level crossing scenarios are introduced for a nonlinear two-level system with one decaying state, describing the dynamics of a Bose-Einstein condensate in a mean-field approximation (Gross-Pitaevskii or nonlinear Schrödinger equation). An important application of the discussed concepts is the dynamics of a condensate in tilted optical lattices. In particular the properties of resonance eigenstates in double-periodic lattices are discussed, in the linear case as well as within mean-field theory. The decay is strongly altered, if an additional period-doubled lattice is introduced. Our analytic study is supported by numerical computations of nonlinear resonance states, and future applications of our findings for experiments with ultracold atoms are discussed.

We propose a strategy to physically implement a universal set of quantum gates based on geometric phases accumulated in the nondegenerate eigenstates of a designated invariant operator in a periodic physical system. The system is driven to evolve in such a way that the dynamical phase shifts of the invariant operator eigenstates are identical (or mod $2\pi$) while the corresponding geometric phases are nontrivial. We illustrate how this strategy works in a simple but typical NMR-type qubit system.

We study a scheme for a local quantum measurement discrimination, i.e., the estimation via local measurements on $B$ of previous measurements done in $A$ for a composed bipartite system $AB$. The common bath plays a crucial role in the process.

The passage-time distribution for a spread-out quantum particle to traverse a specific region is calculated using a detailed quantum model for the detector involved. That model, developed and investigated in earlier works, is based on the detected particle’s enhancement of the coupling between a collection of spins (in a metastable state) and their environment. We treat the continuum limit of the model, under the assumption of the Markov property, and calculate the particle state immediately after the first detection. An explicit example with 15 boson modes shows excellent agreement between the discrete model and the continuum limit. Analytical expressions for the passage-time distribution as well as numerical examples are presented. The precision of the measurement scheme is estimated and its optimization discussed. For slow particles, the precision goes like $E^{-3∕4}$, which improves previous $E^{-1}$ estimates, obtained with a quantum clock model.

We present a scheme, based only on linear optics and standard photon detection, that allows to generate heralded multiphoton entangled states of arbitrary photon number from spontaneous parametric downconversion (PDC) in the weak interaction regime. The scheme also works in the strong interaction regime, i.e., for the production of large photon numbers, when photon-number resolving detectors with nearly perfect quantum efficiency are used. In addition, the same setup can be used for quantum metrology as multiphoton interferometer with sensitivity at the Heisenberg limit.

Realization of controllable interaction between subsystems is one of the major problems in solid-state quantum computing. We study a current-biased Josephson junction (CBJJ) as a tunable coupler for superconducting transmission-line resonators (TLR). By modulating the bias current, the junction can be tuned in and out of resonance with the TLRs connected to it. Various inter-TLR quantum operations can be reliably implemented by controlling the mediating CBJJ. The main decoherence sources are analyzed in detail. This work may offer improvement to scalable quantum computing in coupled TLR-cavity array system.

We address the problem of broadcasting $N$ copies of a generic qubit state to $M>N$ copies by estimating its direction and preparing a suitable output state according to the outcome of the estimate. This semiclassical broadcasting protocol is more restrictive than a general one, since it requires an intermediate step where classical information is extracted and processed. However, we prove that a suboptimal superbroadcasting, namely broadcasting with simultaneous purification of the local output states with respect to the input ones, is possible. We show that in the asymptotic limit of $M\to \infty$ the purification rate converges to the optimal one, proving the conjecture that optimal broadcasting and state estimation are asymptotically equivalent. We also show that it is possible to achieve superbroadcasting with simultaneous inversion of the Bloch vector direction (universal NOT). We prove that in this case the semiclassical procedure of state estimation and preparation turns out to be optimal. We finally analyze semiclassical superbroadcasting in the phase-covariant case.

We study ground state properties of spinless, quasi one-dimensional bosons which are confined in a harmonic trap and interact via repulsive delta-potentials. We use the exact diagonalization method to analyze the pair correlation function, as well as the density, the momentum distribution, different contributions to the energy and the population of single-particle orbitals in the whole interaction regime. In particular, we are able to trace the fascinating transition from bosonic to fermi-like behavior in characteristic features of the momentum distribution which is accessible to experiments. Our calculations yield quantitative measures for the interaction strength limiting the mean-field regime on one side and the Tonks-Girardeau regime on the other side of an intermediate regime.

We address the issue of determining an effective two-body interaction for mean-field calculations of the energies of many-body systems. We show that the effective interaction is proportional to the phase shift and demonstrate this result in the quasiclassical approximation when there is a trapping potential in addition to the short-range interaction between a pair of particles. We calculate numerically energy levels for the case of an interaction with a short-range square well and a harmonic trapping potential and show that the numerical results agree well with the analytical expression. We derive a generalized Gross-Pitaevskii equation which includes effective range corrections and discuss the form of the electron-atom effective interaction to be used in calculations of Rydberg atoms and molecules.

The structure of multiply quantized or giant vortex states in atomic Fermi gases across a Feshbach resonance is studied within the context of self-consistent Bogoliubov–de Gennes theory. The particle density profile of vortices with $\kappa >1$ flux quanta is calculated. Owing to $\kappa$ discrete branches of vortex-core bound states, inside the core the density oscillates as a function of the distance from the vortex line and displays a nonmonotoic dependence on the interaction strengths, in marked contrast to the singly quantized case, in which the density depletes monotonically. This feature can make a direct visualization of the giant vortices in atomic Fermi gases.

Two noninteracting qubits are coupled to an environment. Both coupling and environment are chosen as random matrices to obtain generic results. The initial state of the pair ranges from a Bell state to a product state. Decoherence of the pair is evaluated analytically in terms of purity; Monte Carlo calculations confirm these results and also yield concurrence of the pair. Entanglement within the pair accelerates decoherence. Numerics displays the relation between concurrence and purity known for Werner states. A closed albeit heuristic formula for concurrence decay ensues.

We provide a class of inequalities for detecting entanglements in multimode systems. Necessary conditions for fully separable, biseparable, and sufficient conditions for fully entangled states are explicitly presented.

We propose a practical decoy-state method with heralded single-photon source for quantum key distribution (QKD). In the protocol, three intensities are used and one can estimate the fraction of single-photon counts. The final key rate over transmission distance is simulated under various parameter sets. Due to the lower dark count than that of a coherent state, it is shown that a three-intensity decoy-state QKD with a heralded source can work for a longer distance than that of a coherent state.

We investigate the quantum interference between the resonant process of nuclear excitation by electron capture (NEEC) followed by the radiative decay of the excited nucleus, and radiative recombination (RR). In order to derive the interference cross section, a Feshbach projection operator formalism is used. The electromagnetic field is considered by means of multipole fields. The nucleus is described by a phenomenological collective model and by making use of experimental data. The Fano profile parameters as well as the interference cross section for electric and magnetic multipole transitions in various heavy ions are presented. We discuss the experimental possibility of discerning NEEC from the RR background.

The Stark splitting of the second excited level of atomic hydrogen (with principal quantum number $n=3$) has been measured by pulsed laser spectroscopy in order to determine small electric fields by optical means. Doppler-free excitation with two counterpropagating laser beams at $205\mathrm{nm}$ allows us to measure the $n=3$ Stark spectra either by an optogalvanic signal after ionization by a third laser photon or by detection of the Balmer-$\alpha$ fluorescence photons emitted by the excited atoms. Three different cases of laser polarization have been investigated in order to evaluate the possibilities and limitations of this one-step laser excitation method for electric field determination, especially at field strengths below $200\mathrm{V}∕\mathrm{cm}$. The method provides the best field sensitivity achieved with lower excited levels that can be reached directly by two-photon absorption from the ground state (in contrast to the more sensitive Rydberg levels). For this purpose, an advanced tunable pulsed uv laser with narrow bandwidth almost at the Fourier limit has been used. The high spectral resolution allowed us to deduce electric field strengths as small as $50\mathrm{V}∕\mathrm{cm}$ from the frequency shift between two selected isolated Stark components. As a main advantage, this simple analysis of the measured spectra does not rely on knowledge of the line intensities which may be strongly affected by the measuring conditions.

The ionization-detected multiresonant absorption spectrum of the high Rydberg states of ${}^{11}\mathrm{B}\mathrm{H}$ shows evidence of a valence electronic excitation of the $X{}^2\Sigma ^{+}{}^{11}\mathrm{B}\mathrm{H}^{+}$ core in which the principal and azimuthal quantum numbers of a bound Rydberg electron are conserved. This phenomenon, known as isolated core excitation (ICE), has been previously reported with Rydberg quantum state specificity only for atoms. In the present triple-resonant photoexcitation experiment, the third laser frequency happens to scan an energy interval of coincidental fourth-photon resonance with transitions in the $A{}^2\Pi \text{−}X{}^2\Sigma ^{+}$ system of the ${}^{11}\mathrm{B}\mathrm{H}^{+}$ ion core. For a certain range of principal quantum number $n$, we find that the initially prepared Rydberg electron remains unaffected while the core undergoes an adventitious, strongly allowed valence electron transition, taking the system from a Rydberg level that converges to the $X{}^2\Sigma ^{+}$ state of ${}^{11}\mathrm{B}\mathrm{H}^{+}$ to a corresponding level converging to excited ${}^{11}\mathrm{B}\mathrm{H}^{+}$ $A{}^2\Pi$. We denote this absorption as $\mid A{}^2\Pi ⟩\mid nl⟩\leftarrow \mid X{}^2\Sigma ^{+}⟩\mid nl⟩$. Using a simple mathematical model for which only transitions vertical in $n$ and $l$ are allowed, we show that the interval of principal quantum number over which the rate of adventitious ICE exceeds that of ${}^{11}\mathrm{B}\mathrm{H}^{*}$ dissociation depends on the finite linewidths and positions of $\mid A{}^2\Pi ⟩\mid nl⟩$ features and on the $n$-dependent predissociative lifetimes of ${}^{11}\mathrm{B}\mathrm{H}^{*}$ Rydberg molecules.

The effects of a background state, or states, on stimulated Raman adiabatic passage (STIRAP) processes are investigated. The study is based on a realistic model of the laser-assisted $\mathrm{HCN}\to \mathrm{HNC}$ isomerization process. While the high density of states in the energy regime above the isomerization barrier plays an important role, the strong variation of the transition dipole moments connecting these states with the localized HCN and HNC states is shown to be more significant in determining the success or failure of the STIRAP process. Therefore, care must be taken when proposing the use of STIRAP-based schemes to control molecular excitation especially when control is justified via few-level models.

A remarkable feature of standard quantum mechanics is its analogy with classical fluid dynamics. This has motivated in the past efforts to formulate phase-space techniques based on various statistical models of quantum hydrodynamic equations. In this work an inverse kinetic theory for the Schrödinger equation has been constructed in order to formally describe the standard quantum dynamics by means of a classical dynamical system (to be denoted as phase-space Schrödinger dynamical system). It is shown that the inverse kinetic theory can be (non)uniquely determined under suitable mathematical prescriptions. In particular, when the quantum linear momentum is identified with a suitable linear kinetic momentum, it follows that the fluctuations of the position vector and the kinetic linear momentum satisfy identically the Heisenberg theorem.