We study theoretically the effects of dissipation on the performances of a variational quantum algorithm used to approximately solve a combinatorial optimization problem, the maximum independent set, on a platform of neutral atoms. We take a realistic model of dissipation with spontaneous emission, and show numerically that the detrimental effects of these incoherent processes are spontaneously attenuated by the variational nature of the procedure. We furthermore implement an alternative optimization scheme recently proposed, where one uses the expected shortfall of the mean energy as the objective function.

A fully relativistic approach is applied to the evaluation of the nuclear recoil effect on the bound-electron $g$ factor in hydrogenlike ions to first order in the electron-to-nucleus mass ratio $m/M$ and to all orders in $\alpha Z$. The calculations are performed in the range $1\le Z\le 20$ for $g$ factors of the $1s$, $2s$, $2p_{1/2}$, and $2p_{3/2}$ states. The $\alpha Z$ dependence of the nontrivial QED recoil contribution as a function of $Z$ is studied.

We calculate the spectra, electric dipole transition rates, and isotope shifts of the superheavy elements Ds ($Z=110$), Rg ($Z=111$), and Cn ($Z=112$) and their ions. These calculations were performed using a recently developed, efficient version of the ab intio configuration-interaction combined with perturbation theory to treat distant effects. The successive ionization potentials of the three elements are also calculated and compared to lighter analogous elements.

The nuclear recoil effect on the ground-state $g$ factor of highly charged boronlike ions is considered within the relativistic formalism. The interelectronic-interaction contribution is evaluated in the Breit approximation, employing two independent approaches: the second-order perturbation theory and the configuration-interaction Dirac-Fock-Sturm method. The uncertainty of the nuclear recoil $g$-factor contributions is significantly reduced, especially for low- and middle-$Z$ ions.

Coulomb-explosion imaging is a broadly employed technique to reconstruct the geometry of molecules from the direct multibody breakups of its ions. However, we reveal that this technique fails for a large class of systems, such as (${\mathrm{CO})}_2{}^{3+}$ and ${\mathrm{ArCO}}^{3+}$, since the events of the “direct breakup channel” are not the real direct breakups but the rapid sequential breakups with a short-lived and ultrafast-rotational fragment. Using Ar-CO as a prototype, we have investigated theoretically its Coulomb-explosion process. We find that due to the interfield between the metastable ${\mathrm{CO}}^{2+}$ and ${\mathrm{Ar}}^{+}$, ${\mathrm{ArCO}}^{3+}$ changes from its initial T shape into the more stable linear shape within 100 fs; such a rotation of ${\mathrm{CO}}^{2+}$ is hundreds of times faster than the field free case. Further, the advanced three-body surface hopping simulations indicate that the angle ${\angle }_{(\mathrm{Ar},\mathrm{CO})}$ has rotated from an initial ${95}^{\circ }$ to $110.6{}^{\circ }$ on average before the Coulomb explosion, which agrees well with the one (${115}^{\circ }$) detected by Gong et al. [Phys. Rev. A 88, 013422 (2013)]. Furthermore, we point out that correct geometry of ArCO can be obtained from the three-body breakups with high kinetic-energy release ($>20$ eV).

We present a fully relativistic calculation of the bremsstrahlung emitted by twisted electrons propagating in the field of bare heavy nuclei. The electron-nucleus interaction is accounted for to all orders in the nuclear binding strength parameter $\alpha Z$, thus allowing us to investigate the bremsstrahlung in a strong field, where the effects of the “twistedness” are expected to be most pronounced. To explore these effects, we study the angular and polarization properties of the photons emitted in course of the inelastic twisted electrons scattering by the gold target. The influence of the kinematic parameters of the incident electrons on the double-differential cross section and the degree of the linear polarization is also discussed.

We study the dynamics of bosonic atoms on a two-dimensional square lattice, where atomic interactions are long ranged with either a box or soft-core shape. The latter can be realized through laser dressing ground-state atoms to electronically excited Rydberg states. When the range of interactions is equal or larger than the lattice constant, the system is governed by an extended Bose-Hubbard model. We propose a quench process by varying the atomic hopping linearly across phase boundaries of the Mott insulator-supersolid and supersolid-superfluid phases. Starting from a Mott insulating state, the dynamical evolution of the superfluid order parameter exhibits a universal behavior at the early stage, largely independent of interactions. The dynamical evolution is significantly altered by strong, long-range interactions at later times. Particularly, we demonstrate that density wave excitation is important when the quench rate is small. Moreover, we show that the quench dynamics can be analyzed through time-of-flight images, i.e., measuring the momentum distribution and noise correlations.

We investigate a polarization control scheme in two-color two-photon atomic ionization. Experiments employing free-electron laser or high-order harmonic generation sources have shown light polarization dependencies in above threshold ionization of atoms assisted with an IR field. These were mostly performed at relatively high photoelectron energies where the soft-photon approximation remains valid. We use here a perturbation theory approach to show the larger degree of control that can be attained when the short wavelength photon energy is below the ionization threshold. This largely unexplored energy region offers unique possibilities to achieve polarization control of the reaction.

We consider a two-component Bose-condensed mixture characterized by positive $s$-wave scattering lengths. We assume equal densities and intraspecies interactions. By doing the Bogoliubov transformation of an effective Hamiltonian, we obtain the lower energy magnon dispersion incorporating the superfluid entrainment between the components. We argue that $p$-wave pairing of distinct bosons should be accompanied by self-localization of magnons and formation of a magnetoroton. We demonstrate the effect on a model system of particles interacting via step potentials.

Mixed pairing in ultracold Fermi gases can give rise to interesting many-body phases, such as topological nontrivial superfluids that support Majorana zero modes (MZMs) with various spatial configurations. Unfortunately, in ordinary lattice systems, the topological phase and the associated MZMs are suppressed by the dominant $s$-wave pairing. Here we present a proposal for engineering effective Hamiltonians with tunable mixed on- and off-site pairing based on driven optical lattices. The on- and off-site pairing can be changed independently by means of a periodical driving field rather than magnetic Feshbach resonances. It paves the way for suppressing the dominant on-site interaction that frustrates the emergence of topological superfluids and for synthesizing MZMs localized in edges or corners.

We consider an impurity immersed in a Bose-Einstein condensate with tunable boson-impurity interactions. Such a Bose polaron has recently been predicted to exhibit an intriguing energy spectrum at finite temperature, where the ground-state quasiparticle evenly splits into two branches as the temperature is increased from zero [Guenther et al., Phys. Rev. Lett. 120, 050405 (2018)]. To investigate this theoretical prediction, we employ a recently developed variational approach that systematically includes multibody correlations between the impurity and the finite-temperature medium, thus allowing us to go beyond previous finite-temperature methods. Crucially, we find that the number of quasiparticle branches is simply set by the number of hole excitations of the thermal cloud, such that including up to one hole yields one splitting, two holes yields two splittings, and so on. Moreover, this effect is independent of the impurity mass. We thus expect that the exact ground-state quasiparticle will evolve into a single broad peak for temperatures $T>0$, with a broadening that scales as $T^{3/4}$ at low temperatures and sufficiently weak boson-boson interactions. In the zero-temperature limit, we show that our calculated ground-state polaron energy is in excellent agreement with recent quantum Monte Carlo results and with experiments.

We show that the Bose-Hubbard approximation fails due to the emergence of chaos, even when excited modes are far detuned and the standard validity condition is satisfied. This is formally identical to the Melnikov-Arnold analysis of the stochastic pump model. Previous numerical observations of Bose-Hubbard breakdown are precisely reproduced by our simple model and can be attributed to many-body enhancement of chaos.

We study the spin-noise spectrum (SNS) of unpolarized Rb vapor in an evacuated anti-relaxation-coated cell using parametric Faraday rotation of a flat-top probe beam with variable diameter. We identify a distinct structure in the spectrum, called the Ramsey peak. We find that the power of the Ramsey peak is inversely proportional to the total number of atoms in the cell, and the power of the total spin noise is inversely proportional to the number of atoms within the probe beam. We further present a full theoretical analysis of the SNS by comparing three models of spin diffusion: Fickian diffusion, the ballistic flight, and Langevin's diffusion. We find that Fickian diffusion fails, while the ballistic flight is acceptable. However, Langevin's diffusion yields a remarkable agreement with the experimental spectrum.

We present a theoretical scheme and its experimental proof of principle for an open quantum system undergoing Markovian and non-Markovian evolutions. We exhibit these two regimes by diagnosing them with the relative entropy of coherence of two polarization qubits playing the roles of system and ancilla. These are initially prepared in a polarization maximally entangled state of a photon pair produced by spontaneous parametric down-conversion. We induce Markovian and non-Markovian regimes in the system's dynamics with the help of two auxiliary qubits, experimentally implemented by optical paths in a layout of Sagnac and Mach-Zehnder interferometers. We replicate system-environment interactions by means of an amplitude damping channel and a suitably designed inversion of it. In our scheme, one needs only two experimentally accessible parameters to achieve Markovian and non-Markovian regimes.

Spontaneous symmetry breaking can occur in the powers of two optical modes coupled into a ring resonator, described by a pair of coupled Lorentzian equations, and featuring tunable self- and cross-phase modulation terms. Investigated is a wide variety of nonlinear materials by changing the ratio of the self- and cross-phase interaction coefficients. Static and dynamic effects range from the number and stability of stationary states to the onset and nature of oscillations. Minimal conditions to observe symmetry breaking are provided in terms of the ratio of the self- and cross-phase coefficients, detuning, and input power. Different ratios of the nonlinear coefficients also influence the dynamical regime, where they can induce or suppress bifurcations and oscillations. A generalized description on this kind is useful for the development of all-optical components, such as isolators and oscillators, constructed from a wide variety of optical media in ring resonators.

Deterministically cloning (copying) nonorthogonal states is forbidden in quantum mechanics, but deterministic pseudo-unitary cloning is possible in a nonunitary system. We prove and show that, for any two nonorthogonal qubit states, we can find a linear, invertible Hermitian (metric) operator to make these states mutually orthogonal with respect to the corresponding pseudo-inner product. From this metric operator, we construct a pseudo-Hermitian Hamiltonian and its evolution operator as an ideal, deterministic pseudo-unitary cloner. For applicability, suppose Alice lives in our ordinary universe and Bob lives in a universe that has the desired pseudo-unitary evolution. Alice would send her nonorthogonal states to Bob and Bob would do the cloning deterministically and send back to Alice. The quantum channel will be lossy not due to Bob's universe's properties, but rather due to problems making a channel between the two universes. We experimentally demonstrate deterministic pseudo-unitary two-qubit cloning for a photonic pseudo-unitary two-qubit system. In our universe we have to demonstrate that universe by executing a postselected gate that effects loss-based pseudo-unitary evolution. Furthermore, we introduce an algorithmic method for designing experimental realizations of a generic class of nonunitary operators for pseudo-unitary cloning.

Precise measurements of the displacement of, and force acting on, a mechanical oscillator can be performed by coupling the oscillator to an optical cavity. Brownian thermal forces represent a fundamental limit to measurement sensitivity which impedes the ability to use precise force measurements as a tool of fundamental enquiry, particularly in the context of macroscopic quantum measurements and tabletop gravitational experiments. A torsion pendulum with a low mechanical resonant frequency can be limited by very small thermal forces—from its suspensions—at frequencies above resonance. Here, we report torque sensing of a 10-mg torsion pendulum formed by a bar mirror, using two optical cavities on either edge. The rotational mode was measured by subtracting the two signals from the cavities, while intracavity radiation pressure forces were used to trap the torsional mode with a 1 kHz optical spring. The resulting torque sensitivity of 20 aN m/$\sqrt{\mathrm{Hz}}$ is a record for a milligram-scale torsional oscillator. This allows us to test spontaneous wave-function collapse in a parameter regime that falls in between that tested by space-based experiments, and high-frequency cryogenic cantilevers.

In a previous paper tests for entanglement for two-mode systems involving identical massive bosons were obtained. In the present paper we consider sufficiency tests for Einstein-Podolsky-Rosen (EPR) steering in such systems. We find that spin squeezing in any spin component, a Bloch vector test, the Hillery-Zubairy planar spin variance test, and squeezing in two-mode quadratures all show that the quantum state is EPR steerable. We also find a generalization of the Hillery-Zubairy planar spin variance test for EPR steering. The relation to previous correlation tests is discussed. This paper is based on a detailed classification of quantum states for bipartite systems. States for bipartite composite systems are categorized in quantum theory as either separable or entangled, but the states can also be divided differently into Bell local or Bell nonlocal states in terms of local hidden variable theory (LHVT). For the Bell local states there are three cases depending on whether both, one of or neither of the LHVT probabilities for each subsystem are also given by a quantum probability involving subsystem density operators. Cases where one or both are given by a quantum probability are known as local hidden states (LHSs) and such states are nonsteerable. The steerable states are the Bell local states where there is no LHS, or the Bell nonlocal states. The relationship between the quantum and hidden variable theory classification of states is discussed.

Clustering algorithms are a cornerstone of machine learning applications. Recently, a quantum algorithm for clustering based on the $k$-means algorithm has been proposed by Kerenidis, Landman, Luongo, and Prakash. Based on their work, we propose a quantum expectation-maximization algorithm for Gaussian mixture models (GMMs). The robustness and quantum speedup of the algorithm are shown. We also show numerically the advantage of GMM over $k$-means algorithm for nontrivial cluster data.

The real-time flux dynamics of up to three superconducting quantum interference devices (SQUIDs) are studied by numerically solving the time-dependent Schrödinger equation. The numerical results are used to scrutinize the mapping of the flux degrees of freedom onto two-level systems (the qubits) as well as the performance of the intermediate SQUID as a tunable coupling element. It is shown that the qubit representation yields a good description of the flux dynamics during quantum annealing and the presence of the tunable coupling element does not have negative effects on the overall performance. Additionally, data obtained from a simulation of the dynamics of two-level systems during quantum annealing are compared to experimental data produced by the D-Wave 2000Q quantum annealer. The effects of finite temperature are incorporated in the simulation by coupling the qubit system to a bath of two-level systems. It is shown that an environment modeled as noninteracting two-level systems coupled to the qubits can produce data which matches the experimental data much better than the simulation data of the qubits without coupling to an environment and better than data obtained from a simulation of an environment modeled as interacting two-level systems coupling to the qubits.