By identifying non-Markovianity with nondivisibility, we propose a measure of non-Markovianity for quantum processes. Three examples are presented, and the measure of non-Markovianity is calculated and discussed for these examples. Comparisons with other measures of non-Markovianity are made. The present non-Markovianity measure has the merit that no optimization procedure is required and it is finite for any quantum process, which greatly enhances the practical relevance of the proposed measure.

Different methods have been recently put forward and implemented experimentally to inverse engineer the time-dependent Hamiltonian of a quantum system and accelerate slow adiabatic processes via nonadiabatic shortcuts. In the “transitionless quantum driving” proposed by Berry, shortcut Hamiltonians are designed so that the system follows exactly, in an arbitrarily short time, the approximate adiabatic path defined by a reference Hamiltonian. A different approach is based on first designing a Lewis-Riesenfeld invariant to carry the eigenstates of a Hamiltonian from specified initial to final configurations, again in an arbitrary time, and then constructing from the invariant the transient Hamiltonian that connects these boundary configurations. We show that the two approaches, apparently quite different in form and so far in results, are, in fact, strongly related and potentially equivalent, so that the inverse-engineering operations in one of them can be reinterpreted and understood in terms of the concepts and operations of the other one. We study, as explicit examples, expansions of time-dependent harmonic traps and the state preparation of two-level systems.

Dicke states are an important class of states which exhibit collective behavior in many-body systems. They are interesting because (1) the decay rates of these states can be quite different from a set of independently evolving particles and (2) a particular class of these states are decoherence-free or noiseless with respect to a set of errors. These noiseless states, or more generally subsystems, avoid certain types of errors in quantum-information-processing devices. Here we provide a method for determining a set of transformations of these states which leave the states in their subsystems but still enable them to evolve in particular ways. For subsystems of particles undergoing collective motions, these transformations can be calculated by using essentially the same construction which is used to determine the famous Casimir invariants for quantum systems. Such invariants can be used to determine a complete set of commuting observables for a class of Dicke states as well as to identify possible logical operations for decoherence-free–noiseless subsystems. Our method is quite general and provides results for cases where the constituent particles have more than two internal states.

A theoretical investigation of the radiative capture of an electron into a bound state of heavy, hydrogen-like ion is presented. Special attention is paid to the question of how the linear polarization of the emitted radiation is affected by the interelectronic interaction effects. An analysis of these effects is performed within both, the screening-potential approximation and the perturbation theory that rigorously treats the electron correlations to the first order in the parameter $1/Z$. By making use of these two approaches, detailed calculations are performed for relativistic collisions of hydrogen-like europium Eu${}^{62+}$, bismuth Bi${}^{82+}$, and uranium ${\mathrm{U}}^{91+}$ ions with free electron and low-$Z$ atomic targets. Results of the calculations indicate that the two-electron effects may significantly influence the polarization properties of the recombination x rays; the effect which can be observed by the present-day polarization detectors.

The Bethe-Peierls asymptotic approach which models pairwise short-range forces by contact conditions is introduced in arbitrary representation for spatial dimensions less than or equal to 3. The formalism is applied in various situations and emphasis is put on the momentum representation. In the presence of a transverse harmonic confinement, dimensional reduction toward two-dimensional (2D) or one-dimensional (1D) physics is derived within this formalism. The energy theorem relating the mean energy of an interacting system to the asymptotic behavior of the one-particle density matrix illustrates the method in its second quantized form. Integral equations that encapsulate the Bethe-Peierls contact condition for few-body systems are derived. In three dimensions, for three-body systems supporting Efimov states, a nodal condition is introduced in order to obtain universal results from the Skorniakov–Ter-Martirosian equation and the Thomas collapse is avoided. Four-body bound state eigenequations are derived and the 2D ${}^{\prime }3+1^{\prime }$ bosonic ground state is computed as a function of the mass ratio.

We study how an oscillating mirror affects the electromagnetically induced transparency (EIT) of an atomic ensemble confined in a gas cell, which is placed inside a microcavity with an oscillating mirror in one end. The cavity field acts as a probe of the EIT system and also produces a light pressure on the mirror. The back-action from the mirror to the cavity field results in several (from one to five) steady-states for this atom-assisted optomechanical cavity, producing a complex structure in its EIT. The multiequilibrium positions of the oscillating mirror have been calculated, and then the susceptibility is studied with respect to the different equilibrium positions. We find that the EIT of the atomic ensemble can be significantly changed by the oscillating mirror, and also the various steady states of the mirror have different effects on the EIT.

Microwave cavities with high quality factors enable coherent coupling of distant quantum systems. Virtual photons lead to a transverse interaction between qubits when they are nonresonant with the cavity but resonant with each other. We experimentally investigate the inverse scaling of the interqubit coupling with the detuning from a cavity mode and its proportionality to the qubit-cavity interaction strength. We demonstrate that the enhanced coupling at higher frequencies is mediated by multiple higher-harmonic cavity modes. Moreover, we observe dark states of the coupled qubit-qubit system and analyze their relation to the symmetry of the applied driving field at different frequencies.

We analyze the role of quantum interference effects induced by an embedded two-level system on the photon transport properties in waveguiding structures that exhibit cutoffs (band edges) in their dispersion relation. In particular, we demonstrate that these systems invariably exhibit single-particle photon-atom bound states and strong effective nonlinear responses on the few-photon level. Based on this, we find that the properties of these photon-atom bound states may be tuned via the underlying dispersion relation and that their occupation can be controlled via multiparticle scattering processes. This opens an interesting route for controlling photon transport properties in a number of solid-state-based quantum optical systems and the realization of corresponding functional elements and devices.

We numerically investigate the interplay between Kerr self-focusing (SF) and transient stimulated Brillouin scattering (SBS) for nanosecond pulses in bulk silica. The influences of the input power, phase, or amplitude modulations in the pump pulse together with the incident beam shape on the filamentation dynamics are discussed. We show that appropriate amplitude modulations dividing nanosecond laser pumps into picosecond-long pulse trains inhibit SBS at any power. In contrast, phase-modulated pulses with comparable spectral width undergo multiple filamentation and earlier beam collapse due to modulational instabilities. We demonstrate, however, the existence of a critical pump bandwidth above which SBS can be efficiently suppressed by phase modulations even at high powers. This observation also holds for squared beam shapes with much broader spatial spectra, which decay more easily into multiple filaments over short distances. Intensity profiles of the reflected Stokes waves for such broad pumps are finally discussed.

Stroboscopic spin flips have already been shown to prolong the coherence times of quantum systems under noisy environments. Uhrig’s dynamical decoupling scheme provides an optimal sequence for a quantum system interacting with a dephasing bath. Several experimental demonstrations have already verified the efficiency of such dynamical decoupling schemes in preserving single-qubit coherences. In this work we describe the experimental study of Uhrig’s dynamical decoupling in preserving two-qubit entangled states using an ensemble of spin-1/2 nuclear pairs in solution state. We find that the performance of odd-order Uhrig sequences in preserving entanglement is superior to both even-order Uhrig sequences and periodic spin-flip sequences. We also find that there exists an optimal order of the Uhrig sequence in which a singlet state can be stored at high correlation for about 30 seconds.

We examine the role of the exact-exchange (EXX) Kohn-Sham potential in curing the problem of fractional molecular dissociation. This is achieved by performing EXX calculations for the illustrative case of the LiF molecule. We show that by choosing the lowest-energy electronic configuration for each interatomic distance, a qualitatively correct binding energy curve, reflecting integer dissociation, is obtained. Surprisingly, for LiF this comes at the cost of violating the Aufbau principle, a phenomenon we discuss at length. Furthermore, we numerically confirm that in the EXX potential of the diatomic molecule, one of the atomic potentials is shifted by a constant while the other one is not, depending on where the highest occupied molecular orbital is localized. This changes the relative positions of the energies of each atom and enforces the integer configuration by preventing spurious charge transfer. The size of the constant shift becomes increasingly unstable numerically the larger the interatomic separation is, reflecting the increasing absence of coupling between the atoms.

Theoretical calculations have been made for the dielectronic recombination (DR) rate coefficients of Sn${}^{12+}$ ion using a relativistic flexible atomic code with configuration interaction. Comparison of the rate coefficients for $4s$, $4p$, and $4d$ subshell excitation shows that while the $4p$ subshell excitation dominates over the whole temperature region, $4d$ subshell excitation at low temperature and $4s$ subshell excitation at high temperature cannot be neglected. In order to facilitate simple applications, the calculated DR rate coefficients are fitted to an empirical formula. The total DR rate coefficient is greater than either the radiative recombination or three-body recombination coefficients for electron temperatures greater than 1 eV. Therefore, DR can strongly influence the ionization balance of laser-produced tin plasmas.

The single-center convergent close-coupling method has been applied to positron-magnesium scattering at incident energies from 0.01 to 100 eV. Cross sections are presented for elastic scattering and excitation of $3\hspace{0.5em}{}^{1}P$, as well as for the total ionization and total scattering processes. We also provide an estimate of the positronium formation cross section. The results agree very well with the measurements of the total cross section by Stein et al. [Nucl. Instrum. Methods Phys. Res. Sect. B 143, 68 (1998)], and consistent with the positronium formation measurements of Surdutovich et al. [Phys. Rev. A 68, 022709 (2003)] for positron energies above the ionization threshold. For energies below the positronium formation threshold (0.8 eV) we find a large $P$-wave resonance at 0.17 eV. A similar resonance behavior was found by Mitroy and Bromley [Phys. Rev. Lett. 98, 173001 (2007)] at an energy of 0.1 eV.

The dissipative dynamics of a pointlike Josephson junction in binary Bose-Einstein-condensed mixtures is analyzed within the framework of the model of a tunneling Hamiltonian. The transmission of unlike particles across a junction is described by the different transmission amplitudes. The effective action that describes the dynamics of the phase differences across the junction for each of two condensed components is derived by employing the functional integration method. In the low-frequency limit the dynamics of a Josephson junction can be described by two coupled equations in terms of the potential energy and dissipative Rayleigh function using a mechanical analogy. The interplay between mass currents of each mixture component appears in the second-order term in the tunneling amplitudes due to the interspecies hybridizing interaction. The asymmetric case of the binary mixtures with different concentrations and order parameters is considered as well.

This paper shows that transient alignment of linear molecules in a dense collisional environment can result from the formation of trapped aligned “dark” states in a laser field constituting either a comb of resonant short pulses or a sinusoidally frequency-modulated wave with a continuous flux. Simulation of the laser-induced dynamics of CO molecules reveals that the latter approach is effective at room temperature and requires three orders of magnitude less laser intensity compared to known alignment techniques.

The optimal-phase estimation strategy is derived when partial a priori knowledge on the estimated phase is available. The solution is found with the help of the most famous result from the entanglement theory: the positive partial transpose criterion. The structure of the optimal measurements, estimators, and the optimal probe states is analyzed. This Rapid Communication provides a unified framework bridging the gap in the literature on the subject which until now dealt almost exclusively with two extreme cases: almost perfect knowledge (local approach based on Fisher information) and no a priori knowledge (global approach based on covariant measurements). Special attention is paid to a natural a priori probability distribution arising from a diffusion process.

We calculate the properties of a biphoton source based on resonant backward-wave spontaneous parametric down conversion. We show that the biphotons are generated in a single longitudinal mode having a subnatural linewidth and a Glauber correlation time exceeding 65 ns.

Nonlocality can be quantified by the violation of a Bell inequality. Since this violation may be amplified by local operations, an alternative measure has been proposed—distillable nonlocality. The alternative measure is difficult to calculate exactly due to the double exponential growth of the parameter space. In this paper, we give a way to bound the distillable nonlocality of a resource by the solutions to a related optimization problem. Our upper bounds are exponentially easier to compute than the exact value and are shown to be meaningful in general and tight in some cases.

This paper deals with the problem of estimating the coupling constant $\theta$ of a mixing quantum Markov chain. For a repeated measurement on the chain’s output we show that the outcomes’ time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of $\theta$ whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolute bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of $\theta =0$ we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.

We introduce an intuitive measure of genuine multipartite entanglement, which is based on the well-known concurrence. We show how lower bounds on this measure can be derived and also meet important characteristics of an entanglement measure. These lower bounds are experimentally implementable in a feasible way enabling quantification of multipartite entanglement in a broad variety of cases.