Einstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely, projective measurements. Here we prove that entanglement, one-way steering, two-way steering, and nonlocality are genuinely different considering general measurements, i.e., single round positive-operator-valued measures. Finally, we show that the use of sequences of measurements is relevant for steering tests, as they can be used to reveal “hidden steering.”

We investigate the feasibility of precision frequency metrology with large ion crystals. For clock candidates with a negative differential static polarizability, we show that micromotion effects should not impede the performance of the clock. Using ${\mathrm{Lu}}^{+}$ as a specific example, we show that quadrupole shifts due to the electric fields from neighboring ions do not significantly affect clock performance. We also show that effects from the tensor polarizability can be effectively managed with a compensation laser at least for a small number of ions ($\lesssim {10}^3$). These results provide new possibilities for ion-based atomic clocks, allowing them to achieve stability levels comparable to neutral atoms in optical lattices and a viable path to greater levels of accuracy.

We provide analytical expressions for classical and total trace-norm (Schatten 1-norm) geometric correlations in the case of two-qubit $X$ states. As an application, we consider the open-system dynamical behavior of such correlations under phase and generalized amplitude damping evolutions. Then, we show that geometric classical correlations can characterize the emergence of the pointer basis of an apparatus subject to decoherence in either Markovian or non-Markovian regimes. In particular, as a non-Markovian effect, we obtain a time delay for the information to be retrieved from the apparatus by a classical observer. Moreover, we show that the set of initial $X$ states exhibiting sudden transitions in the geometric classical correlation has nonzero measure.

We present a first-principles theoretical analysis of the entanglement of two superconducting qubits in spatially separated microwave cavities by a sequential (cascaded) probe of the two cavities with a coherent mode, that provides a full characterization of both the continuous measurement induced dynamics and the entanglement generation. We use the SLH formalism to derive the full quantum master equation for the coupled qubits and cavities system, within the rotating wave and dispersive approximations, and conditioned equations for the cavity fields. We then develop effective stochastic master equations for the dynamics of the qubit system in both a polaronic reference frame and a reduced representation within the laboratory frame. We compare simulations with and analyze tradeoffs between these two representations, including the onset of a non-Markovian regime for simulations in the reduced representation. We provide conditions for ensuring persistence of entanglement and show that using shaped pulses enables these conditions to be met at all times under general experimental conditions. The resulting entanglement is shown to be robust with respect to measurement imperfections and loss channels. We also study the effects of qubit driving and relaxation dynamics during a weak measurement, as a prelude to modeling measurement-based feedback control in this cascaded system.

The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process—it is the algorithm which computes the operations needed to correct or compensate for the errors according to the measured syndrome, even when the measurement itself is error prone. Previously decoders based on minimum-weight perfect matching have been studied. However, these are not immediately generalizable from qubit to qudit codes. In this work, we develop a fault-tolerant decoder for the surface code, capable of efficient operation for qubits and qudits of any dimension, generalizing the decoder first introduced by Bravyi and Haah [Phys. Rev. Lett. 111, 200501 (2013)]. We study its performance when both the physical qudits and the syndromes measurements are subject to generalized uncorrelated bit-flip noise (and the higher-dimensional equivalent). We show that, with appropriate enhancements to the decoder and a high enough qudit dimension, a threshold at an error rate of more than $8\%$ can be achieved.

We consider the coupling of a qubit in a pure state to an environment in an arbitrary state and characterize the possibility of qubit-environment-entanglement generation during the evolution of the joint system, that leads to pure dephasing of the qubit. We give a simple necessary and sufficient condition on the initial density matrix of the environment together with the properties of the interaction for the appearance of qubit-environment entanglement. Any entanglement created turns out to be detectable by the Peres-Horodecki criterion. Furthermore, we show that for a large family of initial environmental states, the appearance of nonzero entanglement with the environment is necessarily accompanied by a change in the state of the environment (i.e., by the backaction of the qubit).

Understanding the non-Markovian mechanisms underlying the revivals of quantum entanglement in the presence of classical environments is central in the theory of quantum information. Tentative interpretations have been given by either the role of the environment as a control device or the concept of hidden entanglement. We address this issue from an information-theoretic point of view. To this aim, we consider a paradigmatic tripartite system, already realized in the laboratory, made of two independent qubits and a random classical field locally interacting with one qubit alone. We study the dynamical relationship between the two-qubit entanglement and the genuine tripartite correlations of the overall system, finding that collapse and revivals of entanglement correspond, respectively, to the rise and fall of the overall tripartite correlations. Interestingly, entanglement dark periods can enable plateaux of nonzero tripartite correlations. We then explain this behavior in terms of information flows among the different parties of the system. Besides showcasing the phenomenon of the freezing of overall correlations, our results provide insights on the origin of retrieval of entanglement within a hybrid quantum-classical system.

We report on a detailed characterization of a three-qubit linear optical quantum Toffoli gate. Our experiment utilizes correlated photon pairs generated in the process of spontaneous parametric down-conversion. Two qubits are encoded into polarization and spatial degrees of freedom of a signal photon, and the third qubit is represented by polarization of an idler photon. The linear optical Toffoli gate is implemented by interference of photons on a partially polarizing beam splitter inserted inside a Mach Zehnder interferometer formed by two calcite beam displacers. We have measured 4032 different two-photon coincidences, which allows us to estimate the fidelity of the gate to be 90%. Although these data are not tomographically complete, we show that they are sufficient for a reliable reconstruction of the quantum process matrix of the gate via the recently proposed maximum likelihood–maximum entropy estimation procedure. To probe the entangling capability of the gate, we have investigated generation of three-qubit GHZ states from fully and partially separable input states and we have performed a full tomography of the output states. We compare the reconstructed states with theoretical predictions obtained with the use of the estimated quantum process matrix and obtain a very good agreement.

An optical scheme to create the simplest heteronuclear metal ultracold LiBe molecule is proposed based on ab initio quantum chemistry calculations. The potential energy curves, dipole moments, and transition dipole moments of $1{}^2\mathrm{\Sigma }^{+}, 2{}^2\mathrm{\Sigma }^{+}, 1{}^2\mathrm{\Pi }$, and $2{}^2\mathrm{\Pi }$ states are calculated using the multireference configuration interaction and large basis sets. The analytical functions deduced from the obtained curves are used to determine the rovibrational energy levels, the Franck-Condon factors, and the Einstein coefficients of the states through solving the Schrödinger equation of nuclear movement. The spectroscopic parameters are deduced with the obtained rovibrational energy levels. The Franck-Condon factors $(f_{00}:0.998, f_{11}:0.986, f_{22}:0.920)$ for the $2{}^2\mathrm{\Sigma }^{+}(v=0)\leftrightarrow 1{}^2\mathrm{\Sigma }^{+}(v^{\prime }=0)$ transition are highly diagonally distributed, and the calculated radiative lifetime (74.87 ns) of the $2{}^2\mathrm{\Sigma }^{+}$ state is found to be short enough for rapid laser cooling. The results demonstrate that LiBe could be a very promising candidate for laser cooling and a three-cycle laser cooling scheme for the molecule has been proposed.

The concept of Berry phase is included in an analysis of the intensity distribution in far wings of pressure-broadened spectral lines emitted or absorbed by atoms placed in an external cone-rotating electric field. Particular attention is focused on frequency regions where rainbow satellite bands appear. A classical-path treatment that employs the time-dependent Schrödinger equation is used to derive an expression for the line shape, and it uses a dipole transition moment calculated with quasimolecular wave functions given by the Berry version of the adiabatic approximation. It is found that in the presence of an external rotating electric field, the intensity distribution in far wings can be expressed in terms of the universal line shape function of the unified Franck-Condon theory once energy shifts due to Stark and Berry effects are taken into account. We show that the influence of Berry phase in the profiles of the far wings can be manifested either in the form of deviations of observed profiles from the quasistatic distribution or the appearance of additional features in the vicinity of the maximum of the rainbow satellite band. As an example, the modification of the rainbow satellite at 162.3 nm in the red wing of the self-broadened Lyman-$\alpha$ line of hydrogen, caused by an external rotating electric field, is considered.

The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); R. Szmytkowski, J. Phys. B 30, 2747(E) (1997)] is exploited to derive a closed-form expression for the magnetizability of the relativistic one-electron atom in an arbitrary discrete state, with a pointlike, spinless, and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric functions ${}_3{F}_2$ of the unit argument. Our general expression agrees with formulas obtained analytically earlier by other authors for some particular states of the atom. We present also numerical values of the magnetizability for some excited states of selected hydrogenlike ions with $1\le Z\le 137$ and compare them with data available in the literature.

Pulsed laser excitation of a dense ultracold Cs vapor has been used to study the pairwise interactions between Cs atoms excited to $n{p}_{3/2}$ Rydberg states of principal quantum numbers in the range $n=22–36$. Molecular resonances were observed that correspond to excitation of Rydberg-atom-pair states correlated not only to the $n{p}_{3/2}+n{p}_{3/2}$ dissociation asymptotes, but also to $n{s}_{1/2}+(n+1)s_{1/2}, n{s}_{1/2}+n^{\prime }{f}_j$, and $(n-4)f_j+(n-3)f_j(j=5/2,7/2)$ dissociation asymptotes. These pair resonances are interpreted as arising from dipole-dipole and higher-order long-range-interaction terms between the Rydberg atoms on the basis of (i) their spectral positions, (ii) their response to static and pulsed electric fields, and (iii) millimeter-wave spectra between pair states correlated to different pair-dissociation asymptotes. The Rydberg-atom-pair states were found to spontaneously decay by Penning ionization and the dynamics of the ionization process were investigated during the first 15 $\mu \mathrm{s}$ following initial photoexcitation. To interpret the experimental observations, a potential model was derived that is based on the numerical determination of the eigenvalues and eigenfunctions of the long-range interaction Hamiltonian. With this potential model, which does not include adjustable parameters, all experimental observations could be accounted for, and the results demonstrate that long-range-interaction models provide a global and accurate description of interactions in ultracold Rydberg gases and that they correctly account for, and enable the analysis of, phenomena as diverse as the formation of Rydberg macrodimers, Penning ionization in dense Rydberg gases, and Rydberg-excitation-blockade effects.

Doppler-limited, high-precision, molecular spectroscopy in the linear regime of interaction may refine our knowledge of the Boltzmann constant. To this end, the global uncertainty in the retrieval of the Doppler width should be reduced down to 1 part over ${10}^6$, which is a rather challenging target. So far, Doppler-broadening thermometry has been mostly limited by the uncertainty associated to the line shape model that is adopted for the nonlinear least-squares fits of experimental spectra. In this paper, we deeply investigate this issue by using a very realistic and sophisticated model, known as partially correlated speed-dependent Keilson-Storer profile, to reproduce near-infrared water spectra. A global approach has been developed to fit a large number of numerically simulated spectra, testing a variety of simplified line-shape models. It turns out that the most appropriate model is the speed-dependent hard-collision profile. We demonstrate that the Doppler width can be determined with relative precision and accuracy, respectively, of 0.42 and 0.75 part per million.

We apply our recently developed, quantum, nonadiabatic, two-dimensional finite element method [Warehime et al., J. Chem. Phys. 142, 034108 (2015).] to estimate the probability of the nonadiabatic reaction in spin-polarized $\mathrm{Li}{(}^{2}S)+\mathrm{CaH}{(}^2{\mathrm{\Sigma }}^{+})$. This spin-orbit-induced reaction leads to trap loss due to the opening of a barrierless pathway to the $\mathrm{Ca}{(}^{1}S)+\mathrm{LiH}{(}^1{\mathrm{\Sigma }}^{+})$ products. To investigate this reaction we calculate three two-dimensional radial cuts of the potential energy surfaces for the triplet and singlet electronic states. We also calculate the spin-orbit coupling matrix element between these two electronic states. From our nonadiabatic scattering calculations we estimate the spin-flip probability in the sympathetic cooling of the CaH molecule with ultracold Li atoms to be small: on the order of ${10}^{-7}$ and increasing to ${10}^{-4}$ at higher temperatures. We estimate the order of the rate constant in our reduced dimensionality approach for the reaction proceeding on the singlet potential at a temperature of 1 K to be ${10}^{-10}{\mathrm{cm}}^3$/s. This is of the same order as the measured value of $3.6\times {10}^{-10}{\mathrm{cm}}^3/s$ [Singh et al., Phys. Rev. Lett. 108, 203201 (2012)]. This reaction rate is at least seven orders of magnitude larger than our estimated rate of the spin-orbit-induced triplet to singlet reaction. Our nonadiabatic result is encouraging for the experimental prospects for this title system.

Largely motivated by a number of applications, the van der Waals dispersion coefficients $C_3$ of the alkali-metal ions ${\mathrm{Li}}^{+},{\mathrm{Na}}^{+},{\mathrm{K}}^{+}$, and ${\mathrm{Rb}}^{+}$, the alkaline-earth-metal ions ${\mathrm{Ca}}^{+},{\mathrm{Sr}}^{+},{\mathrm{Ba}}^{+}$, and ${\mathrm{Ra}}^{+}$, and the inert-gas atoms He, Ne, Ar, and Kr with a graphene layer are determined precisely within the framework of the Dirac model. For these calculations, we evaluate the dynamic polarizabilities of the above atomic systems very accurately by evaluating the transition matrix elements employing relativistic many-body methods and using the experimental values of the excitation energies. The dispersion coefficients are given as functions of the separation distance of an atomic system from the graphene layer and the ambiance temperature during the interactions. For easy extraction of these coefficients, we give a logistic fit to the functional forms of the dispersion coefficients in terms of the separation distances at room temperature.

Using the time-dependent density-matrix renormalization group, we theoretically study the collision of a one-dimensional gas of interacting bosons with an impurity trapped in a shallow box potential. We study the dynamic response of both the impurity and the bosonic gas, and we find an approximate independence of the sign of the interaction (attractive or repulsive) between the impurity and the bosons. This sign independence breaks down when the interaction energy is of the same order as the box potential depth, leading to resonant pair tunneling. Our predictions can be tested using contemporary techniques with ultracold atoms.

Using the three-dimensional classical ensemble method, we investigate the nonsequential double-ionization (NSDI) process of Mg in few-cycle circularly polarized laser fields. We demonstrate the time evolution of the distribution of the electron energy, the repulsion energy between double-ionized electrons, the distance between the nucleus and double-ionized electrons, and the momentum of double-ionized electrons. By analyzing these theoretical results, we find that a few-cycle pulse would allow a single recollision event. In addition, the correlated momentum distribution, the angular distribution between double-ionized electrons, and the ion momentum distribution with different delay time, which is the time interval between final double ionization and recollision, are also demonstrated and the results show that the delay time plays a key role in electron emission processes.

We introduce ultrabroad-band composite pulses (CPs), which maximize (at the expense of a finite error tolerance $\epsilon$) the pulse area range wherein the population inversion remains above $1-\epsilon$. We present such CPs for error thresholds $\epsilon =0.01$, 0.001, and 0.0001 in two versions: CPs with different pulse areas of the constituent pulses, used as control parameters, and with equal pulse areas. The former CPs naturally outperform the CPs of identical pulses, which in turn outperform conventional broad-band CPs obtained by annulling the population inversion derivatives at a single point. Moreover, we derive double-compensation CPs, which correct errors in both the pulse area and the detuning. They outperform the corresponding conventional CPs as well. By using the same error-tolerance approach, we construct ultranarrow-band CPs, which squeeze the population inversion in as narrow a range as possible while keeping the excitation outside this range below the error threshold $\epsilon$.

Shaken optical lattices permit the coherent modification of tunneling of particles in a controllable manner. We introduce a general relation between the geometry of shaken lattices and their admissible effective dynamics. By using three different examples, we illustrate the symmetries of the emerging tunneling rates. The results provide a clear framework to understand the relation between lattice geometry and accessible dynamics, and a tool to straightforwardly derive truncated effective Hamiltonians on arbitrary geometries.

The extreme ultraviolet absorption spectrum of an atom is strongly modified in the presence of a synchronized intense infrared field. In this work we demonstrate control of the absorption properties of helium atoms dressed by an infrared pulse by changing the relative polarization of the infrared and extreme ultraviolet fields. Light-induced features associated with the dressed $1s2s, 1s3s$, and $1s3d$ states, referred to as $2s^{+}, 3s^{\pm }$, and $3d^{\pm }$ light-induced states, are shown to be strongly modified or even eliminated when the relative polarization is rotated. The experimental results agree well with calculations based on the solution of the time-dependent Schrödinger equation using a restricted excitation model that allows efficient treatment of the three-dimensional problem. We also present an analysis of the light-induced states based on Floquet theory, which allows for a simple explanation of their properties. Our results open a new route to creating controllable superpositions of dipole allowed and nondipole allowed states in atoms and molecules.