Recently introduced time-dependent renormalized-natural-orbital theory (TDRNOT) is extended towards a multicomponent approach in order to describe ${{\mathrm{H}}_2}^{+}$ beyond the Born-Oppenheimer approximation. Two kinds of natural orbitals, describing the electronic and the nuclear degrees of freedom are introduced, and the exact equations of motion for them are derived. The theory is benchmarked by comparing numerically exact results of the time-dependent Schrödinger equation for an ${{\mathrm{H}}_2}^{+}$ model system with the corresponding TDRNOT predictions. Ground-state properties, linear-response spectra, fragmentation, and high-order harmonic generation are investigated.

We show that, for ultracold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pairwise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two- and three-body interactions for scattering from van der Waals potentials and near Fano-Feshbach resonances. For van der Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pairwise interaction can only be turned off for species with a small negative scattering length, leaving the ${}^{88}\mathrm{Sr}$ isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.

We explore theoretically the driven-dissipative physics of geometrically frustrated lattices of cavity resonators with relatively weak nonlinearities, i.e., a photon-photon interaction smaller than the loss rate. In such systems, photon modes with zero probability at dark sites are present at the single-particle level due to interference effects. In particular, we study the behavior of a cell with three coupled resonators as well as extended Lieb lattices in one and two dimensions. By considering a partial pumping scheme, with the driving field not applied to the dark sites, we predict that even in the presence of relatively weak photon-photon interactions the nominally dark sites achieve a finite photonic population with strong correlations. We show that this is a consequence of biphoton and multiphoton states that in the absence of frustration would not be visible in the observables.

By performing local projective measurements on a two-qubit entangled state one can certify in a device-independent way up to one bit of randomness. We show here that general measurements, defined by positive-operator-valued measures, can certify up to two bits of randomness, which is the optimal amount of randomness that can be certified from an entangled bit. General measurements thus provide an advantage over projective ones for device-independent randomness certification.

We investigate how the combination of nonequilibrium effects and material properties impacts on the Casimir-Polder interaction between an atom and a surface. By addressing systems with temperature inhomogeneities and laser interactions, we show that nonmonotonous energetic landscapes can be produced where barriers and minima appear. Our treatment provides a self-consistent quantum theoretical framework for investigating the properties of a class of nonequilibrium atom-surface interactions.

Singly ionized lutetium has recently been suggested as a potential clock candidate. Here we report a joint experimental and theoretical investigation of ${\mathrm{Lu}}^{+}$. Measurements relevant to practical clock operation are made and compared to atomic structure calculations. Calculations of scalar and tensor polarizabilities for clock states over a range of wavelengths are also given. These results will be useful for future work with this clock candidate.

The nonlocal properties of the $W$ states are investigated under particle loss. By removing all but two particles from an $N$-qubit $W$ state, the resulting two-qubit state is still entangled. Hence, the $W$ state has high persistency of entanglement. We ask an analogous question regarding the persistency of nonlocality [see N. Brunner and T. Vértesi, Phys. Rev. A 86, 042113 (2012)]. Namely, we inquire what is the minimal number of particles that must be removed from the $W$ state so that the resulting state becomes local. We bound this value in function of $N$ qubits by considering Bell nonlocality tests with two alternative settings per site. In particular, we find that this value is between $2N/5$ and $N/2$ for large $N$. We also develop a framework to establish bounds for more than two settings per site.

The relatively low key rate seems to be the major barrier to its practical use for the decoy-state measurement-device-independent quantum key distribution (MDI-QKD). We present a four-intensity protocol for the decoy-state MDI-QKD that hugely raises the key rate, especially in the case in which the total data size is not large. Also, calculations show that our method makes it possible for secure private communication with fresh keys generated from MDI-QKD with a delay time of only a few seconds.

Although quantum key distribution (QKD) is theoretically secure, there is a gap between the theory and practice. In fact, real-life QKD may not be secure because component devices in QKD systems may deviate from the theoretical models assumed in security proofs. To solve this problem, it is necessary to construct the security proof under realistic assumptions on the source and measurement unit. In this paper, we prove the security of a QKD protocol under practical assumptions on the source that accommodate fluctuation of the phase and intensity modulations. As long as our assumptions hold, it does not matter at all how the phase and intensity distribute or whether or not their distributions over different pulses are independently and identically distributed. Our work shows that practical sources can be safely employed in QKD experiments.

Catalytic coherence transformations allow the otherwise impossible state transformations using only incoherent operations with the aid of an auxiliary system with finite coherence that is not being consumed in any way. Here we find the necessary and sufficient conditions for the deterministic and stochastic catalytic coherence transformations between a pair of pure quantum states. In particular, we show that the simultaneous decrease of a family of Rényi entropies of the diagonal parts of the states under consideration is a necessary and sufficient condition for the deterministic catalytic coherence transformations. Similarly, for stochastic catalytic coherence transformations we find the necessary and sufficient conditions for achieving a higher optimal probability of conversion. We thus completely characterize the coherence transformations among pure quantum states under incoherent operations. We give numerous examples to elaborate our results. We also explore the possibility of the same system acting as a catalyst for itself and find that indeed self-catalysis is possible. Further, for the cases where no catalytic coherence transformation is possible we provide entanglement-assisted coherence transformations and find the necessary and sufficient conditions for such transformations.

Quantum gates in topological quantum computation are performed by braiding non-Abelian anyons. These braiding processes can presumably be performed with very low error rates. However, to make a topological quantum computation architecture truly scalable, even rare errors need to be corrected. Error correction for non-Abelian anyons is complicated by the fact that it needs to be performed on a continuous basis, and further errors may occur while we are correcting existing ones. Here, we prove the feasibility of this task, establishing non-Abelian anyons as a viable platform for scalable quantum computation. We thereby focus on Ising anyons as the most prominent example of non-Abelian anyons and show that for these a finite error rate can indeed be corrected continuously. There is a threshold error rate $p_c>0$ such that for all error rates $p<p_c$ the probability of a logical error per time step can be made exponentially small in the distance of a logical qubit.

Device-independent quantum key distribution (DIQKD) guarantees unconditional security of a secret key without making assumptions about the internal workings of the devices used for distribution. It does so using the loophole-free violation of a Bell's inequality. The primary challenge in realizing DIQKD in practice is the detection loophole problem that is inherent to photonic tests of Bell' s inequalities over lossy channels. We revisit the proposal of Curty and Moroder [Phys. Rev. A 84, 010304(R) (2011)] to use a linear optics-based entanglement-swapping relay (ESR) to counter this problem. We consider realistic models for the entanglement sources and photodetectors: more precisely, (a) polarization-entangled states based on pulsed spontaneous parametric down-conversion sources with infinitely higher-order multiphoton components and multimode spectral structure, and (b) on-off photodetectors with nonunit efficiencies and nonzero dark-count probabilities. We show that the ESR-based scheme is robust against the above imperfections and enables positive key rates at distances much larger than what is possible otherwise.

We investigate a hybrid system of a superconducting charge qubit interacting directly with a single neutral atom via electric dipole coupling. Interfacing of the macroscopic superconducting circuit with the microscopic atomic system is accomplished by varying the gate capacitance of the charge qubit. To achieve a strong interaction, we employ two Rydberg states with an electric-dipole-allowed transition, which alters the polarizability of the dielectric medium of the gate capacitor. Sweeping the gate voltage with different rates leads to a precise control of hybrid quantum states. Furthermore, we show a possible implementation of a universal two-qubit gate.

We have explored the dipole-dipole mediated, resonant energy transfer reaction, $32p_{3/2}+32p_{3/2}\to 32s+33s$, in an ensemble of cold ${}^{85}\mathrm{Rb}$ Rydberg atoms. Stark tuning is employed to measure the population transfer probability as a function of the total electronic energy difference between the initial and final atom-pair states over a range of Rydberg densities, $2\times {10}^8\le \rho \le 3\times {10}^9 {\mathrm{cm}}^{-3}$. The observed line shapes provide information on the role of beyond nearest-neighbor interactions, the range of Rydberg atom separations, and the electric field inhomogeneity in the sample. The widths of the resonance line shapes increase approximately linearly with the Rydberg density and are only a factor of 2 larger than expected for two-body, nearest-neighbor interactions alone. These results are in agreement with the prediction [B. Sun and F. Robicheaux, Phys. Rev. A 78, 040701(R) (2008)] that beyond nearest-neighbor exchange interactions should not influence the population transfer process to the degree once thought. At low densities, Gaussian rather than Lorentzian line shapes are observed due to electric field inhomogeneities, allowing us to set an upper limit for the field variation across the Rydberg sample. At higher densities, non-Lorentzian, cusplike line shapes characterized by sharp central peaks and broad wings reflect the random distribution of interatomic distances within the magneto-optical trap (MOT). These line shapes are well reproduced by an analytic expression derived from a nearest-neighbor interaction model and may serve as a useful fingerprint for characterizing the position correlation function for atoms within the MOT.

We present an interrogation scheme for the next generation of quantum clocks to suppress frequency shifts induced by laser probing fields that are themselves based on generalized hyper-Ramsey resonances. Sequences of composite laser pulses with a specific selection of phases, frequency detunings, and durations are combined to generate a very efficient and robust frequency locking signal with an almost perfect elimination of the light shift from off-resonant states and to decouple the unperturbed frequency measurement from the laser's intensity. The frequency lock point generated from synthesized error signals using either $\pi /4$ or $3\pi /4$ laser phase steps during the intermediate pulse is tightly protected against large laser-pulse area variations and errors in potentially applied frequency shift compensations. Quantum clocks based on weakly allowed or completely forbidden optical transitions in atoms, ions, molecules, and nuclei will benefit from these hyperstable laser frequency stabilization schemes to reach relative accuracies below the ${10}^{-18}$ level.

The scalar-pseudoscalar (S-PS) interaction, which has been predicted between the electrons and nuclei of atoms and molecules, violates parity- ($P$-) and time- ($T$-) reversal symmetries. The electric dipole moment of the electron (eEDM) and the S-PS interaction together give rise to an energy shift in paramagnetic polar molecules, which in principle can be measured. The determination of the S-PS interaction constant, $k_{s,A}$, for an atom $A$ could be a sensitive probe of physics beyond the standard model. The upper limit for it can be obtained by combining the results of the measured energy shift mentioned above and the accurate quantum chemical calculation of the S-PS coefficient, $W_{s,A}$. In this work, we use a method based on the four-component relativistic coupled-cluster singles and doubles (RCCSD) method to calculate this coefficient for YbF, one of the most promising candidates for the search of the eEDM and the S-PS interaction. We obtain $W_{s,\mathrm{Yb}}=-40.5\left(\mathrm{kHz}\right)$ with an estimated error of less than 10% for YbF. We also calculate the effective electric field ($E_{\mathrm{eff}}$), the molecular dipole moment, and the parallel component of the hyperfine coupling constant ($A_{\parallel }$) by the RCCSD method. The discrepancies in the results of these calculations with those of accurate measurements are used to estimate the accuracy of our calculation of $W_{s,\mathrm{Yb}}$.

A theory of high-order harmonic generation by arbitrary polyatomic molecules is introduced. A polyatomic molecule is modeled by an $(N+1)$-particle system, which consists of $N$ heavy atomic (ionic) centers and an electron. After the separation of the center-of-mass coordinate, the dynamics of this system is reduced to the relative electronic and nuclear coordinates. Various versions (with or without the dressing of the initial and/or final molecular state) of the molecular strong-field approximation are introduced. For neutral polyatomic molecules the derived expression for the $T$-matrix element takes a simple form. The interference minima in the harmonic spectrum are explained as a multiple-slit type of interference. This is illustrated by numerical examples for the ozone (${\mathrm{O}}_3$) and carbon dioxide (${\mathrm{CO}}_2$) molecules.

We propose a scheme to realize a Heisenberg-scaled magnetometer using dipolar spin-1 condensates. The input state of magnetometer is prepared by slowly sweeping a transverse magnetic field to zero, which yields a highly entangled spin state of $N$ atoms. We show that this process is protected by a parity symmetry such that the state preparation time is within the reach of the current experiment. We also propose a parity measurement with a Stern-Gerlach apparatus which is shown to approach the optimal measurement in the large atom number limit. Finally, we show that the phase estimation sensitivity of the proposed scheme roughly follows the Heisenberg scaling.

An expression is obtained on the basis of phase perturbation theory for the contribution to the mean differential reflection coefficient from the in-plane co-polarized component of the light scattered diffusely from a two-dimensional randomly rough dielectric surface when the latter is illuminated by $s$-polarized light. This result forms the basis for an approach to inverting experimental light-scattering data to obtain the normalized-surface-height autocorrelation function of the surface. Several parametrized forms of this correlation function, and the minimization of a cost function with respect to the parameters defining these representations, are used in the inversion scheme. This approach also yields the rms height of the surface roughness, and the dielectric constant of the dielectric substrate if it is not known in advance. The input data used in validating this inversion consist of computer simulation results for surfaces defined by exponential and Gaussian surface-height correlation functions, without and with the addition of multiplicative noise, for a single or multiple angles of incidence. The reconstructions obtained by this approach are quite accurate for weakly rough surfaces, and the proposed inversion scheme is computationally efficient.