As large-scale multimode Gaussian states begin to become accessible in the laboratory, their representation and analysis become a useful topic of research in their own right. The graphical calculus for Gaussian pure states provides powerful tools for their representation, while this work presents a useful tool for their analysis: passive interferometric (i.e., number-conserving) symmetries. Here we show that these symmetries of multimode Gaussian states simplify calculations in measurement-based quantum computing and provide constructive tools for engineering large-scale harmonic systems with specific physical properties, and we provide a general mathematical framework for deriving them. Such symmetries are generated by linear combinations of operators expressed in the Schwinger representation of $\mathrm{U}\left(2\right)$, called nullifiers because the Gaussian state in question is a zero eigenstate of them. This general framework is shown to have applications in the noise analysis of continuous-various cluster states and is expected to have additional applications in future work with large-scale multimode Gaussian states.

Spontaneous Raman scattering (SRS) in atomic ensembles provides a promising method to generate spin-wave–photon entangled states. In the past experiments, a spin-wave–photon entangled state was produced via SRS from an atomic ensemble. Here, we report a scheme of simultaneously generating two spin-wave–photon (atom-photon) entangled states in a cold Rb ensemble via SRS. Based on joint Bell-state measurements on the two photons coming from the two atom-photon entangled sources, respectively, we projected the two stored spin waves into a Bell state and then mapped the quantum memory into a polarization-entangled photon pair. Such a polarization-entangled photon pair can be released on demand and thus the presented scheme has potential application in the preparation of large-size photonic entangled states.

We present an experimental and theoretical study of the emission and absorption spectra of the ${\mathrm{Ba}}^{+}$ ions and ${\mathrm{Ba}}^{+*}\mathrm{He}$ excimer quasimolecules in the cryogenic Ba-He plasma. We observe several spectral features in the emission spectrum, which we assign to the electronic transitions between bound states of the excimer correlating to the $6{}^2{P}_{3/2}$ and $5{}^2{D}_{3/2,5/2}$ states of ${\mathrm{Ba}}^{+}$. The resulting ${\mathrm{Ba}}^{+}\left(5{}^2{D}_J\right)\text{He}$ is a metastable electronically excited complex with orbital angular momentum $L=2$, thus expanding the family of known metal-helium quasimolecules. It might be suitable for high-resolution spectroscopic studies and for the search for new polyatomic exciplex structures.

We investigate high-order-harmonic generation in inhomogeneous media for reduced dimensionality models. We perform a phase-space analysis, in which we identify specific features caused by the field inhomogeneity. We compute high-order-harmonic spectra using the numerical solution of the time-dependent Schrödinger equation, and provide an interpretation in terms of classical electron trajectories. We show that the dynamics of the system can be described by the interplay of high-frequency and slow-frequency oscillations, which are given by Mathieu's equations. The latter oscillations lead to an increase in the cutoff energy, and, for small values of the inhomogeneity parameter, take place over many driving-field cycles. In this case, the two processes can be decoupled and the oscillations can be described analytically.

Coupled atom-cavity arrays, such as those described by the Jaynes-Cummings-Hubbard model, have the potential to emulate a wide range of condensed-matter phenomena. In particular, the strongly correlated states of the fractional quantum Hall effect can be realized. At some filling fractions, the fraction quantum Hall effect has been shown to possess ground states with non-Abelian excitations. The most well studied of these states is the Pfaffian state of Moore and Read G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991), which is the ground state of a Hall liquid with a three-body interaction. We show how an effective three-body interaction can be generated within the cavity QED framework, and that a Pfaffian-like ground state of these systems exists.

The mechanism of light-shift-related uncertainty in an atom-interferometry gravimeter is investigated systematically, which arises from the inhomogeneous intensity of Raman beams and the Gaussian distribution of an atomic cloud. Experiments using atom interferometry are performed to verify this systematic error by directly modulating the integration time $T$ and the intensity ratio of Raman laser beams. Using our method, the uncertainty of gravity measurements contributed by the single-photon light shift in an atom gravimeter can be corrected to a $\mathrm{sub}-\mu \mathrm{Gal}(1\mu \mathrm{Gal}=1\times {10}^{-8}\mathrm{m}/{\mathrm{s}}^2)$ level.

We construct the photon-added coherent states of a noncommutative harmonic oscillator associated to a $q$-deformed oscillator algebra. Various nonclassical properties of the corresponding system are explored, first, by studying two different types of higher-order quadrature squeezing, namely, the Hillery type and the Hong-Mandel type, and second, by testing the sub-Poissonian nature of photon statistics in higher order with the help of the correlation function and the Mandel parameter. Also, we compare the behavior of different types of quadrature and photon number squeezing of our system with those of the ordinary harmonic oscillator by considering the same set of parameters.

We present a detailed quantum electrodynamical description of Vavilov-Cherenkov radiation emitted by a relativistic twisted electron in the transparent medium. Simple expressions for the spectral and spectral-angular distributions as well as for the polarization properties of the emitted radiation are obtained. Unlike the plane-wave case, the twisted electron produces radiation within the annular angular region, with enhancement towards its boundaries. Additionally, the emitted photons can have linear polarization not only in the scattering plane but also in the orthogonal direction. We find that the Vavilov-Cherenkov radiation emitted by an electron in a superposition of two vortex states exhibits a strong azimuthal asymmetry. Thus, the Vavilov-Cherenkov radiation offers itself as a convenient diagnostic tool of such electrons and complements the traditional microscopic imaging.

We consider a quantum particle on a one-dimensional lattice subject to weak local measurements and study its stochastic dynamics conditioned on the measurement outcomes. Depending on the measurement strength our analysis of the quantum trajectories reveals dynamical regimes ranging from quasicoherent wave-packet oscillations to a Zeno-type dynamics. We analyze how these dynamical regimes are directly reflected in the spectral properties of the noisy measurement records.

Both simulated quantum annealing and physical quantum annealing have shown the emergence of “heavy tails” in their performance as optimizers: The total time needed to solve a set of random input instances is dominated by a small number of very hard instances. Classical simulated annealing, in contrast, does not show such heavy tails. Here we explore the origin of these heavy tails, which appear for inputs with high local degeneracy—large isoenergetic clusters of states in Hamming space. This category includes the low-precision Chimera-structured problems studied in recent benchmarking work comparing the D-Wave Two quantum annealing processor with simulated annealing. On similar inputs designed to suppress local degeneracy, performance of a quantum annealing processor on hard instances improves by orders of magnitude at the 512-qubit scale, while classical performance remains relatively unchanged. Simulations indicate that perturbative crossings are the primary factor contributing to these heavy tails, while sensitivity to Hamiltonian misspecification error plays a less significant role in this particular setting.

Recent theoretical investigations treat quantum computations as functions, quantum processes which operate on other quantum processes, rather than circuits. Much attention has been given to the $N$-switch function which takes $N$ black-box quantum operators as input, coherently permutes their ordering, and applies the result to a target quantum state. This is something which cannot be equivalently done using a quantum circuit. Here, we propose an all-optical system design which implements coherent operator permutation for an arbitrary number of input operators.

An algorithm is proposed that serves to handle full-rank density matrices when coming from a lower-rank method to compute the convex roof. This is in order to calculate an upper bound for any polynomial SL-invariant multipartite entanglement measure $E$. This study exemplifies how this algorithm works based on a method for calculating convex roofs of rank-2 density matrices. It iteratively considers the decompositions of the density matrix into two states each, exploiting the knowledge for the rank-2 case. The algorithm is therefore quasiexact as far as the rank-2 case is concerned, and it also hints where it should include more states in the decomposition of the density matrix. Focusing on the measure of three-way entanglement of qubits (called three-tangle), I show the results the algorithm gives for two states, one of which is the Greenberger-Horne-Zeilinger–Werner (GHZ-$W$) state, for which the exact convex roof is known. It overestimates the three-tangle in the state, thereby giving insight into the optimal decomposition the GHZ-$W$ state has. As a proof of principle, I have run the algorithm for the three-tangle on the transverse quantum Ising model. I give qualitative and quantitative arguments why the convex roof should be close to the upper bound found here.

The existence of incompatible measurements, epitomized by Heisenberg's uncertainty principle, is one of the distinctive features of quantum theory. So far, quantum incompatibility has been studied for measurements that test the preparation of physical systems. Here we extend the notion to measurements that test dynamical processes, possibly consisting of multiple time steps. Such measurements are known as testers and are implemented by interacting with the tested process through a sequence of state preparations, interactions, and measurements. Our first result is a characterization of the incompatibility of quantum testers, for which we provide necessary and sufficient conditions. Then we propose a quantitative measure of incompatibility. We call this measure the robustness of incompatibility and define it as the minimum amount of noise that has to be added to a set of testers in order to make them compatible. We show that (i) the robustness is lower bounded by the distinguishability of the sequence of interactions used by the tester and (ii) maximum robustness is attained when the interactions are perfectly distinguishable. The general results are illustrated in the concrete example of binary testers probing the time evolution of a single-photon polarization.

Charge exchange in ${\mathrm{C}}^{6+}\text{-He}$ and ${\text{-H}}_2$ collisions followed by x-ray emission is examined using the two-center basis generator method for low to intermediate projectile energies. Within the independent electron model, we calculate capture cross sections and perform a radiative cascade analysis to obtain Lyman line-emission ratios. Single capture is considered for the ${\mathrm{C}}^{6+}\text{-He}$ system, while both single capture and autoionizing double capture are considered for the ${\mathrm{C}}^{6+}{\text{-H}}_2$ system. Effects of a time-dependent screening potential that models target response on the $l$ distribution of capture cross sections and the line-emission ratios are examined as well. Calculated line-emission ratios based on the no-response approximation are in satisfactory agreement with previous measurements.

We study, numerically and experimentally, the momentum distribution of atoms cooled in optical lattices. Using semiclassical simulations, we show that this distribution is bimodal, made up of a central feature corresponding to “cold,” trapped atoms, with tails of “hot,” untrapped atoms, and that this holds true also for very shallow potentials. Careful analysis of the distribution of high-momentum untrapped atoms, both from simulations and experiments, shows that the tails of the distribution do not follow a normal law, hinting at a power-law distribution and nonergodic behavior. We also revisit the phenomenon leading to the existence of an optimal cooling point, i.e., a potential depth below which the temperature of the atoms starts increasing.

We present a monotonic convergent quantum optimal control method that can be utilized to optimize the control field while exactly enforcing multiple equality constraints for steering quantum systems from an initial state towards desired quantum states. For illustration, special consideration is given to finding optimal control fields with (i) exact zero area and (ii) exact zero area along with constant pulse fluence. The method combined with these two types of constraints is successfully employed to maximize the state-to-state transition probability in a model vibrating diatomic molecule.

We present an exploratory study that suggests that Efimov physics, a leading research theme in few-body quantum physics, can also induce stable many-body ground states whose building blocks are universal clusters. We identify a range of parameters in a mass-and-density-imbalanced two-species fermionic mixture for which the ground state is a gas of Efimov-related universal trimers. An explicit calculation of the trimer-trimer interaction reveals that the trimer phase is an SU(3) Fermi liquid stable against recombination losses. We propose to experimentally observe this phase in a fermionic ${}^6\text{Li}\text{−}{}^{53}\text{Cr}$ mixture.

Bose-Einstein condensates (BECs) offer the potential to examine quantum behavior at large length and time scales, as well as forming promising candidates for quantum technology applications. Thus, the manipulation of BECs using control fields is a topic of prime interest. We consider BECs in the mean-field model of the Gross-Pitaevskii equation (GPE), which contains linear and nonlinear features, both of which are subject to control. In this work we report successful optimal control simulations of a one-dimensional GPE by modulation of the linear and nonlinear terms to stimulate transitions into excited coherent modes. The linear and nonlinear controls are allowed to freely vary over space and time to seek their optimal forms. The determination of the excited coherent modes targeted for optimization is numerically performed through an adaptive imaginary time propagation method. Numerical simulations are performed for optimal control of mode-to-mode transitions between the ground coherent mode and the excited modes of a BEC trapped in a harmonic well. The results show greater than $99\%$ success for nearly all trials utilizing reasonable initial guesses for the controls, and analysis of the optimal controls reveals primarily direct transitions between initial and target modes. The success of using solely the nonlinearity term as a control opens up further research toward exploring novel control mechanisms inaccessible to linear Schrödinger-type systems.

We consider analytically the dynamics of an arbitrary number and configuration of vortices in an annular Bose-Einstein condensate obtaining expressions for the free energy and vortex precession rates to logarithmic accuracy. We also obtain lower bounds for the lifetime of a single vortex in the annulus. Our results enable a closed-form analytic treatment of vortex-vortex interactions in the annulus that is exact in the incompressible limit. The incompressible hydrodynamics that is developed here paves the way for more general analytical treatments of vortex dynamics in non-simply-connected geometries.