Measurement in quantum simulations provides a means for extracting meaningful information from a complex quantum state, and for quantum computing, reducing the complexity of measurement will be vital for near-term applications. For most quantum simulations, the targeted state will obey several symmetries inherent to the system Hamiltonian. We obtain an alternative symmetry projected basis of measurement that reduces the number of measurements needed by a constant factor. Our scheme can be implemented at no additional cost on a quantum computer, can be implemented under various measurement or tomography schemes, and is reasonably resilient under noise.

Modular mixed-species ion-trap networks are a promising framework for scalable quantum information processing, where one species acts as a memory qubit and another as a communication qubit. This architecture requires high-fidelity mixed-species entangling gates to transfer information from communication to memory qubits through their collective motion. We investigate the character of the motional modes of mixed-species ion chains of various lengths and in various trap potentials for entangling operations and sympathetic cooling. We find that the laser power required for high-fidelity entangling gates based on transverse modes is at least an order of magnitude higher than that for gates based on axial modes for ion species with a large mass ratio. We also find that for even moderate mass differences, the transverse modes are much harder to cool than the axial modes regardless of the ion chain configuration. Therefore, transverse modes conventionally used for operations in single-species ion chains may not be well suited for mixed-species chains with widely different masses.

Spin-orbit interactions (SOIs) are a set of subwavelength optical phenomena in which spin and spatial degrees of freedom of light are intrinsically coupled. One of the unique examples of a SOI, the spin-Hall effect of light (SHEL), has been an area of extensive research with potential applications in spin controlled photonic devices as well as emerging fields of spinoptics and spintronics. Here, we report our experimental study on SHEL due to forward scattering of focused linearly polarized Gaussian and Hermite-Gaussian (${\text{HG}}_{10}$) beams from a silver nanowire (AgNW). Spin-dependent antisymmetric intensity patterns are obtained when the polarization of the scattered light is analyzed. The corresponding spin-Hall signal is obtained by computing the far-field longitudinal spin density ($s_3$). Furthermore, by comparing the $s_3$ distributions, significant enhancement of the spin-Hall signal is found for the ${\text{HG}}_{10}$ beam compared to the Gaussian beam. The investigation of the optical fields at the focal plane of the objective lens reveals the generation of longitudinally spinning fields as the primary reason for the effects. The experimental results are corroborated by three-dimensional numerical simulations. The results lead to a better understanding of SOIs and can have direct implications on chip-scale spin assisted photonic devices.

We demonstrate the formation of periodic waves and envelope solitons in dispersive optical media having a Kerr nonlinear response under the influence of third-order dispersion and self-steepening effect. The stability properties of the bright- and dark-soliton solutions are proved using the stability criterion based on the theory of nonlinear dispersive waves. Regimes for the modulation instability of a continuous wave signal propagating inside the dispersive optical medium are also investigated. The results show that the gain spectrum depends crucially on the self-steepening parameter, while the third-order dispersion has no effect on the modulation instability condition. A similarity transformation is presented to reduce the generalized extended nonlinear Schrödinger equation with distributed coefficients which models the pulse evolution in the presence of the inhomogeneities of media to the related constant-coefficient one. The propagation behaviors of self-similar bright and dark solitons are discussed in a periodic distributed fiber system and an exponential dispersion decreasing fiber.

We propose a Heisenberg-limited quantum interferometer whose input is twin optical beams from which one or more photons have been indistinguishably subtracted. Such an interferometer can yield Heisenberg-limited performance while at the same time giving a direct fringe reading, unlike for the twin-beam input of the Holland-Burnett interferometer. We propose a feasible experimental realization using a photon-number correlated source, such as nondegenerate parametric down-conversion, and perform realistic analyses of performance in the presence of loss and detector inefficiency.

Topological quantum optical states in one-dimensional (1D) quasiperiodic cold atomic chains are studied in this work. We propose that by introducing incommensurate modulations on the interatomic distances of 1D periodic atomic chains, the off-diagonal Aubry-André-Harper (AAH) model can be mimicked, although the crucial difference is the existence of long-range dipole-dipole interactions. The discrete band structures with respect to the modulation phase, which plays the role of a dimension extension parameter, are calculated for finite chains beyond the nearest-neighbor approximation. It is found that the present system indeed supports nontrivial topological states localized over the boundaries. Despite the presence of long-range dipole-dipole interactions that leads to an asymmetric band structure, it is demonstrated that this system inherits the topological properties of two-dimensional integer quantum Hall systems. The spectral position, for both real and imaginary frequencies, and number of these topologically protected edge states are still governed by the gap-labeling theorem and characterized by the topological invariant, namely, the (first) Chern number, indicating the validity of bulk-boundary correspondence. Due to the fractal spectrum arising from the quasiperiodicity in a substantially wide range of system parameters, our system provides a large number of topological gaps and optical states readily for practical use. It is also revealed that a substantial proportion of the topological edge states are highly subradiant with extremely low decay rates, which therefore offer an appealing route for controlling the emission of external quantum emitters and achieving high-fidelity quantum state storage.

A method based on spectral Green's functions is presented for the simulation of driven open quantum dynamics that can be described by the Lindblad master equation in Liouville density operator space. The method extends the Hilbert space formalism and provides simple algebraic connections between the driven and nondriven dynamics in the spectral frequency domain. The formalism shows remarkable analogies to the use of Green's functions in quantum field theory, such as the elementary excitation energies and the Dyson self-energy equation. To demonstrate its potential, we apply the method to a coherently driven dissipative ensemble of two-level systems comprising a single “active” subsystem interacting with $N$ “passive” subsystems—a generic model with important applications in quantum optics and dynamic nuclear polarization. The method dramatically reduces the computational cost compared with simulations based on solving the full master equation, thus making it possible to study and optimize many-body correlated states up to the physically realistic limit of an arbitrarily large $N$.

Using the time parameter in the time-dependent Schrödinger equation, we study the time of flight for a particle tunneling through a square barrier potential. Comparing the mean and variance of the energy and the flight time for transmitted and reflected particles, using both density and flux distributions, we find that, when accounting for momentum filtering, the suitably normalized transmitted and reflected distributions are identical in both the density and flux cases. In contrast to previous studies, we demonstrate that these results do not imply a vanishing tunneling time, but rather that the time it takes to tunnel through a square barrier is precisely given by the reflected phase time. For wide barriers, this becomes independent of the barrier width, as predicted independently by MacColl and Hartman. We show that these conclusions can be reached using a variety of arguments, including purely quantum mechanical ones. Analysis of the shapes of the distributions under consideration reveals that wave-packet reshaping is not an explanation for the MacColl-Hartman effect. The results presented here have direct implications for understanding recent experimental results in the study of the barrier crossing of rubidium atoms. The finite width of an incident wave packet significantly “masks” the tunneling time, and induces substantial asymmetry between the flight times of transmitted and reflected atoms.

A correlational dialect is introduced within the quantum theory language to give a unified treatment of finite-dimensional informational and operational quantum theories, infinite-dimensional relativistic quantum theories, and quantum gravity. Theories are written in terms of correlation diagrams which specify correlation types and weights. Grouping similar correlation diagrams leads to generalized Feynman diagrams, which in special cases reduce to the familiar Feynman diagrams from quantum field theories. The correlational formalism is applied in a study of correlation constraints, revealing classes of quantum processes that evade previous characterizations of general quantum processes. The results apply to quantum theories of various kinds, including time-asymmetric theories, time-symmetric theories, theories without predefined time, and theories with indefinite causal structures.

In quantum physics, the theoretical study of unbound many-body systems is typically quite demanding, owing to the combination of their large spatial extension and the so-called curse of dimensionality. Often, such systems are studied on truncated numerical domains—at the cost of information. Here we present methods for calculating differential probabilities for unbound particles which are subject to a complex absorbing potential. In addition to attenuating outgoing waves, the absorber is also used to probe them by projection onto single-particle scattering states, thus rendering the calculation of multiparticle scattering states superfluous. Within formalism based on the Lindblad equation, singly differential spectra from subsequent absorptions are obtained by resolving the dynamics of the remaining particles after the first absorption. While the framework generalizes naturally to any number of particles, explicit, compact, and intuitive expressions for the differential probability distributions are derived for the two-particle case. The applicability of the method is illustrated by numerical examples involving two-particle model-systems. These examples, which address scattering and photoionization, demonstrate how energy distributions of unbound particles may be determined on numerical domains considerably smaller than the actual extension of the system.

Optical lattices have been used as a versatile toolbox to control Bose-Einstein condensates (BECs) in recent years, and a wealth of emergent nonlinear phenomena have been found, including bright gap solitons and dark ones, among which the former has been realized in experiments. The latter, however, has only theoretical results and its fundamental properties are still not well understood. Here we theoretically and numerically explore an open issue of creating stable matter-wave dark gap solitons in a one-dimensional optical lattice, onto which the BECs with self-defocusing quintic nonlinearity are loaded. Using linear-stability analysis and direct simulations, the formation, structures, and properties of dark gap solitons in quintic nonlinearity have been compared to those upheld by cubic Kerr nonlinearity. In particular, we uncover that the dark gap solitons and soliton clusters are robustly stable in the first finite band gap of the underlying linear spectrum, and are hard to be stabilized in the second gap. The predicted dark gap solitons are observable in current experiments on dense ultracold atoms, using an optical lattice technique, and in the optics domain for nonlinear light propagation in periodic optical media with quintic nonlinearity.

A significant problem in laser cooling of molecules is the presence of the dark Zeeman sublevels. Herein, a detailed theoretical and experimental study of destabilizing the dark states is reported in magnesium monofluoride molecules. By applying an external magnetic field, the Zeeman sublevels are made to be time dependent and nondegenerate, forcing the dark states to Larmor precess into the bright states. It is found that the laser induced fluorescence signal depends on the angle and the magnitude of the magnetic field. Theoretical calculations are performed by solving the density matrix equations for the multiple-level system, which shows good agreement with experimental data. This study may provide a useful perspective for continuous efforts toward laser cooling of MgF molecules.

It is shown analytically and numerically that the finite-temperature many-body perturbation theory in the grand canonical ensemble has zero radius of convergence at zero temperature when the energy ordering or degree of degeneracy for the ground state changes with the perturbation strength. When the degeneracy of the reference state is partially or fully lifted at the first-order Hirschfelder-Certain degenerate perturbation theory, the second-order grand potential and internal energy diverge as $T\to 0$. Contrary to earlier suggestions of renormalizability by the chemical potential $\mu$, this nonconvergence, first suspected by Kohn and Luttinger, is caused by the nonanalytic nature of the Boltzmann factor $e^{-E/k_{\text{B}}T}$ at $T=0$, also plaguing the canonical ensemble, which does not involve $\mu$. The finding reveals a fundamental flaw in perturbation theory, which is deeply rooted in the mathematical limitation of power-series expansions and is unlikely to be removed within its framework.

The Kibble-Zurek (KZ) mechanism is a universal framework that can in principle describe nonequilibrium phase transition phenomena in any system with the required symmetry properties. However, a conflicting phenomenon termed anti-KZ behavior has been reported in the study of ferroelectric phase transitions, in which slower driving results in more topological defects [S. M. Griffin et al., Phys. Rev. X 2, 041022 (2012)]. Although this finding is significant, related experimental work remains scarce. In this work, we experimentally demonstrate anti-KZ behavior under a noisy control field in three different quantum phase transition protocols using a single trapped ${}^{171}{\mathrm{Yb}}^{+}$ ion. The density of defects is studied as a function of the quench time and the noise intensity. We experimentally verify that the optimal quench time to minimize excitations scales as a universal power law of the noise intensity. Our work provides an experimental verification of anti-KZ behavior in a two-level system.

We use a gradient-based optimization scheme to find single-qubit rotations to be interwoven between time steps of a noisy logical two-qubit entangling gate in order to suppress the effects of arbitrary logical and leakage noise in the two-qubit gate. We show how the sequence fidelity is affected by imperfections in the single-qubit operations, as well as by various relative strengths of the logical and leakage noise. Our approach is completely general and system-independent, allowing for application to any two-qubit system regardless of the experimental implementation details.

Gray solitons are a one-parameter family of solutions to the one-dimensional nonlinear Schrödinger equation (NLSE) with positive cubic nonlinearity, as found in repulsively interacting dilute Bose-Einstein condensates or electromagnetic waves in the visible spectrum in waveguides described by Gross-Pitaevskii mean-field theory. In two dimensions, these solutions to the NLSE appear as a line or plane of depressed condensate density or light intensity, but numerical solutions show that this line is dynamically unstable to “snaking”: the initially straight line of density or intensity minimum undulates with exponentially growing amplitude. To assist future studies of quantum mechanical instability beyond mean-field theory, we here pursue an approximate analytical description of the snake instability within Bogoliubov–de Gennes perturbation theory. Within this linear approximation the two-dimensional result applies trivially to three dimensions as well, describing buckling modes of the low-density plane. We extend the analytical results of Kuznetsov and Turitsyn [Sov. Phys. JETP 67, 1583 (1988)] to shorter wavelengths of the snake modulation and show to what extent the snake mode can be described accurately as a parametric instability, in which the position and grayness parameter of the initial soliton simply become dependent on the transverse dimension(s). We find that the parametric picture remains accurate up to second order in the snaking wave number, if the snaking soliton is also dressed by an outward-propagating sound wave, but that beyond second order in the snaking wave number the parametric description breaks down.

We examine the dynamics of electron beams that, in free space, are self-accelerating, in the presence of an additional magnetic field. We focus our attention on the case of Airy beams that follow parabolic trajectories and in generalized classes of beams associated with power-law trajectories. We study the interplay between beam self-acceleration and the circular motion caused by the magnetic field. In the case of Airy beams, using an integral representation, we find closed-form solutions for the electron wave function. We also derive asymptotic formulas for the beam trajectories, both for Airy beams and for self-accelerating power-law beams. A ray optics description is rather useful for the interpretation of the beam dynamics. Our results are in excellent agreement with direct numerical simulations.

As is well known, light arising from Raman scattering on molecules shows nonclassical mutual correlations between the Stokes and anti-Stokes components. However, the practical use of nonclassical Raman light is limited, due to its low intensity. The Raman signal can be enhanced in surface-enhanced Raman scattering (SERS) experiments by placing Raman active molecules near a plasmonic nanoantenna, due to the Purcell effect. Since the main contribution to emission in SERS experiments is re-emitted light from the plasmonic nanoantenna with no nonclassical correlations, the question arises as to whether it is possible to simultaneously amplify the Raman signal and preserve the nonclassical correlations. In this work, we give a positive answer to this question. We show that plasmonic nanoantennas can be used to enhance the nonclassical light intensity. We demonstrate that the main factor causing deterioration of the cross correlations of SERS light is the fluorescent background of the plasmonic nanoantenna. We analyze the way in which the geometry of a plasmonic nanoantenna affects the nonclassical cross correlations of the Raman light, and show that there is an optimal size of plasmonic nanoantenna that both increases the Raman signal and preserves the nonclassical correlations of the light at the level of a single molecule. The obtained results pave the way for the creation of sources with controlled intensity and a degree of nonclassicality.

We study the dynamics of a quantum walker simultaneously subjected to time-independent and -dependent phases. Such dynamics emulates a charged quantum particle in a lattice subjected to a superposition of static and harmonic electric fields. With proper settings, we investigate the possibility to induce Bloch-like superoscillations, resulting from a close tuning of the frequency of the harmonic phase $\omega$ and that associated with the regular Bloch-like oscillations ${\omega }_B$. By exploring the frequency spectra of the wave-packet centroid, we are able to distinguish the regimes on which regular and super-Bloch oscillations are predominant. Furthermore, we show that under exact resonant conditions $\omega ={\omega }_B$ unidirectional motion is established with the wave-packet average velocity being a function of the quantum coin operator parameter, the relative strengths of the static and harmonic terms, as well as the own phase of the harmonic field. We show that the average drift velocity can be well described within a continuous-time analogous model.