We study the dynamical Casimir effect in a double superconducting cavity in a circuit quantum electrodynamics architecture. Parameters in the quantum circuit are chosen in such a way the superconducting cavity can mimic a double cavity, formed by two perfectly conducting outer walls and a dielectric wall, with arbitrary permittivity separating both halves. We undertake a spectral analysis of the cavity, showing that the spectrum varies significantly depending on the values of the susceptibility of the dielectric mirror and the relative lengths of both cavities. We study the creation of photons when the walls oscillate harmonically with a small amplitude. Furthermore, we explore the possibility of entangling two uncoupled cavities, starting from a symmetric double cavity and having both of its halves become uncoupled at a later given instant. We consider both cases: (i) when the field is initially in a vacuum state and (ii) the situation in which photon creation via the dynamical Casimir effect has already taken place. We show that the cavities become entangled in both cases but, in the latter, the quantum correlation between individual modes can be greatly increased at the cost of diminishing the entanglement between most pairs of modes.

We present a theoretical study of the optimal control of a qubit interacting with a structured environment. We consider a model system in which the bath is a bosonic reservoir at zero temperature and the qubit frequency is the only control parameter. Using optimal control techniques, we show the extent to which the qubit population and relaxation effects can be manipulated. The qubit states reachable by a shaped control with a fixed maximum intensity are found numerically. We analyze the role of standard control mechanisms and the structure of the set of reachable states with respect to the coupling strength between the system and the environment. This investigation is used as a starting point to explore the selectivity problem of two uncoupled qubits interacting with their own baths and characterized by a specific coupling strength. We numerically derive the optimal control solution for a wide range of parameters, and we show that the control law is close to a sinusoidal function with a specific frequency in some peculiar cases.

In this article we derive the exact dynamics of a two-qubit (spin $1/2$) system interacting centrally with separate spin baths composed of qubits in a thermal state. Furthermore, each spin of the bath is coupled to every other spin of the same bath. The corresponding dynamical map is constructed. It is used to analyze the non-Markovian nature of the two qubit central spin dynamics. We further observe the evolution of quantum correlations like entanglement and discord under the influence of the environmental interaction. Moreover, we demonstrate the comparison between this exact two-qubit dynamics and the locally acting central spin model in a spin bath. This work is a stepping stone towards the realization of non-Markovian heat engines and other quantum thermal devices.

Estimating causal relations from observed correlations is a central content of science. Although a comprehensive mathematical framework has been developed to identify cause and effect, it is well known that such methods and techniques are not applicable to quantum systems due to Bell's theorem. Generally, the incompatibility between quantum correlation and classical causal theory is illustrated by the violation of Bell inequality. Gachechiladze provides a new method called the violation of lower bound of average causal effect (ACE) to witness the incompatibility. We consider a new lower bound of ACE derived by Cao in multiple measurement settings. We show that there are always pure entangled states and incompatible projective measurements that can generate correlations that violate this new classical lower bound. In Gachechiladze's work, the measurement settings are binary, while the measurement settings in our paper are $K$-ary ($K\ge 2$) and we give more general conclusions. When $K=2$, the same result as in Gachechiladze's work can be obtained.

A linear-optics network is a multimode interferometer system, where indistinguishable photon inputs can create nonclassical interference that cannot be simulated with classical computers. Such nonclassical interference implies the existence of entanglement among its subsystems if we divide its modes into different parties. Entanglement in such systems is naturally encoded in multirail (multimode) quantum registers. For bipartite entanglement, a generation and detection scheme with multirail encoding was theoretically proposed [Wu and Hofmann, New J. Phys. 19, 103032 (2017)] and experimentally realized [Kiyohara et al., Optica 7, 1517 (2020)]. In this paper, we will take a step further to establish a theory for the detection of multirail-encoded discrete-variable genuine multipartite entanglement (GME) in fixed local-photon-number subspaces of linear-optics networks. We also propose a scheme for GME generation with both discrete-variable (single photons) and continuous-variable (squeezed states) light sources. This scheme allows us to reveal the discrete-variable GME in continuous-variable systems. The effect of photon losses is also numerically analyzed for the generation scheme based on continuous-variable inputs.

We theoretically study the orientation dependence of even-order harmonics in biased bilayer graphene (BLG) by numerically solving the semiconductor Bloch equations in the velocity gauge. It is shown that the yield of even-order harmonics has a perfect periodicity of ${60}^{\circ }$ with the rotation of the crystal orientation. The even-harmonic intensity reaches the maximum when the laser field is polarized along with the nearest-neighbor atom. By investigating the crystal orientation dependence for the parallel and perpendicular components of even harmonics, it is found that the Berry curvature plays an insignificant role in the even-harmonic generation of biased BLG. Further analysis reveals that the asymmetric electron density between in-plane adjacent atoms caused by polarization is responsible for the generation of even harmonics in biased BLG. Additionally, we study the ellipticity dependence of even harmonics in biased BLG when the elliptical principal axis of the laser pulse is along with the in-plane nearest-neighbor atoms. As expected, the yield of even harmonics decreases with the ellipticity. Our findings give access to understanding deeply the mechanism of the orientation dependence of even harmonics in biased BLG.

Conditional cooling-by-measurement holds a significant advantage over its unconditional (nonselective) counterpart in the average-population-reduction rate. However, it has a clear weakness with respect to the limited success probability of finding the detector in the measured state. In this work, we propose an optimized architecture to cool down a target resonator, which is initialized as a thermal state, using an interpolation of conditional and unconditional measurement strategies. An optimal measurement-interval ${\tau }_{\mathrm{opt}}^u$ for unconditional measurement is analytically derived, which is inversely proportional to the collective dominant Rabi frequency ${\mathrm{\Omega }}_d$ as a function of the resonator's population in the end of the last round. A cooling algorithm under global optimization by reinforcement learning results in the maximum value for the cooperative cooling performance, an indicator to measure the comprehensive cooling efficiency for arbitrary cooling-by-measurement architecture. In particular, the average population of the target resonator under only 16 rounds of measurements can be reduced by four orders in magnitude with a success probability of about $30\%$.

Previous work on imaging wave-packet dynamics with x-ray scattering revealed that the scattering patterns deviate substantially from the notion of instantaneous momentum density of the wave packet. Here we show that scattering patterns can provide clear insights into the electron wave-packet dynamics if the final state of the scattered electron and the scattered photon momentum are determined simultaneously. The scattering probability is shown to be proportional to the modulus square of the Fourier transform of the instantaneous electronic spatial wave function weighted by the final state of the electron. Several cases for the choice of final state of the electron are explored. First, the case where the final state can be measured up to a given principal quantum number $n$ and orbital angular momentum $l$ are presented. Next, the case where the final states can only be determined up to a given energy is discussed. Finally, the case of an initial wave packet consisting of a large amount of a known stationary state and a small amount of an unknown stationary state is examined. The scattering profile is used to determine the properties of the unknown state in the wave packet.

We study the radiative properties—the Lamb shift, Purcell decay rate, and spontaneous emission dynamics—of an artificial atom coupled to a long, multimode cavity formed by an array of Josephson junctions. Introducing a tunable coupling element between the atom and the array, we demonstrate that such a system can exhibit a crossover from a perturbative to a nonperturbative regime of light-matter interaction as one strengthens the coupling between the atom and the Josephson-junction array. As a consequence, the concept of spontaneous emission as the occupation of the local atomic site being governed by a single complex-valued exponent breaks down. This breakdown, we show, can be interpreted in terms of formation of hybrid atom-resonator modes with radiative losses that are nontrivially related to the effective coupling between individual modes. We develop a singular function expansion approach for the description of the open quantum system dynamics in such a multimode nonperturbative regime. This modal framework generalizes the normal-mode description of quantum fields in a finite volume, incorporating exact radiative losses and incident quantum noise at the delimiting surface. Our results are pertinent to recent experiments with Josephson atoms coupled to high-impedance Josephson-junction arrays.

Building on work by Tsirelson, we present a family of protocols that detect the nonclassicality of suitable states of a single quantum system, under the sole assumption that the measured dynamical observable undergoes a uniform precession. The case of the harmonic oscillator was anticipated in the work by Tsirelson, which we extend. We then apply the protocols to finite-dimensional spins that undergo uniform precession in real space and find a gap between the classical and the quantum expectations for every $j\ge \frac{3}{2}$ (excluding $j=2$).

Calculations of molecular spectral properties, like photodissociation rates and absorption bands, rely on knowledge of the excited state energies of the molecule of interest. Protocols based on the variational quantum eigensolver (VQE) are promising candidates to calculate such energies on emerging noisy intermediate-scale quantum (NISQ) computers. The successful implementation of these protocols on NISQ computers, relies on ansätze that can accurately approximate the molecular states and that can be implemented by shallow quantum circuits. We introduce the excited qubit-excitation-based adaptive (e-QEB-ADAPT)-VQE protocol to calculate molecular-excited-state energies. The e-QEB-ADAPT-VQE constructs efficient problem-tailored ansätze by iteratively appending evolutions of qubit excitation operators. The e-QEB-ADAPT-VQE also improves on previous ADAPT-VQE protocol in that it is designed to be independent on the choice of initial reference state. We perform classical numerical simulations for LiH and ${\mathrm{BeH}}_2$ to benchmark the performance of the e-QEB-ADAPT-VQE. We demonstrate that the e-QEB-ADAPT-VQE can construct highly accurate ansätze that require at least an order of magnitude fewer cnot gates than standard fixed unitary coupled-cluster ansätze, such as the UCCSD and the GUCCSD. We also show that the e-QEB-ADAPT-VQE is more successful in constructing ansätze for excited molecular states than other ADAPT-VQE protocols.

A simple model is proposed to compute electron-diatomic molecule elastic differential cross sections at intermediate energies within the framework of an analytical local optical potential. In a spherical harmonic expansion of the molecular potential we treat the isotropic term with the partial-wave decomposition and apply the independent atom model (IAM) on all higher orders. This model is seen to properly converge to the IAM at high energies, while bringing significant improvement at lower energies. We compare the results with a well-tested program called ELSEPA, tailored for high-energy electron-atom scattering and address its further extension to molecules with the method proposed. The simplicity of the calculations and the encouraging agreement in shape with experimental data could promote attractiveness among plasma physics simulations in need of coherent and well-resolved differential cross sections.

Attosecond dynamics in strong-field tunnel ionization are encoded in intricate holographic patterns in the photoelectron momentum distributions. These patterns show the interference between two or more superposed quantum electron trajectories, which are defined by their ionization times and subsequent evolution in the laser field. We determine the ionization time separation between interfering pairs of electron orbits by performing a differential Fourier analysis on the measured momentum spectrum. We identify electron holograms formed by trajectory pairs whose ionization times are separated by less than a single quarter cycle, between a quarter cycle and half cycle, between a half cycle and three fourths of a cycle, and a full cycle apart. We compare our experimental results to the predictions of the Coulomb quantum orbit strong-field approximation (CQSFA) with significant success. We also time-filter the CQSFA trajectory calculations to demonstrate the validity of the technique on spectra with known time correlations. As a general analysis technique, the filter can be applied to all energy- and angularly resolved data sets to recover time correlations between interfering electron pathways, providing an important tool to analyze any strong-field ionization spectra. Moreover, it is independent of theory and can be applied directly to experiments, without the need of a direct comparison with orbit-based theoretical methods.

The behavior of a twisted electron colliding with a linearly polarized laser pulse is investigated within relativistic quantum mechanics. In order to better fit the real experimental conditions, we introduce a Gaussian spatial profile for the initial electron state as well as an envelope function for the laser pulse, so that both interacting objects have a finite size along the laser propagation direction. For this setup, we analyze the dynamics of various observable quantities regarding the electron state: the probability density, angular momentum, and mean values of the spatial coordinates. It is shown that the motion of a twisted wavepacket can be accurately described by averaging over classical trajectories with various directions of the transverse momentum component. On the other hand, full quantum simulations demonstrate that the ring structure of the wavepacket in the transverse plane can be significantly distorted, leading to large uncertainties in the total angular momentum of the electron. This effect remains after the interaction once the laser pulse has a nonzero electric-field area.

Metal-corroles are macrocycle organic molecules with numerous practical applications. In particular, copper corroles exhibit an interesting saddled geometry, which has attracted significant attention from theoreticians and experimentalists over the years. The present work is dedicated to understand the effect of structural saddling in a copper corrole on potential probe signals via imaging ultrafast coherent electron dynamics. A linearly polarized pulse is used to trigger the electron dynamics and time-resolved x-ray diffraction is employed to image the triggered dynamics. It is found that the symmetry reduction in the time-resolved diffraction signals and electronic flux densities is a signature of the saddling in a copper corrole during ultrafast charge migration. Moreover, analysis of the electronic flux density reveals that the diagonal nitrogen atoms mediate coherent charge migration between them via a central copper atom. Correlation of the flux densities and the diffraction signals indicates that the signature of the charge migration is encoded in time-resolved diffraction signals. A comparison of the static diffraction signals of nonsaddled planar copper porphyrin and saddled nonplanar copper corrole in their ground states is made.

The accurate evaluation of the second-order Doppler frequency shift (SODFS) of trapped ions in a linear Paul trap has been studied with experiments and molecular dynamics (MD) simulations. The motion of trapped ions in the trap has three contributions, and we focus on the ion excess micromotion, which is rarely discussed when evaluating the SODFS of ions. Based on the hypothesis that the ion density is uniformly distributed in the radial direction, we propose a model to accurately evaluate the total SODFS for an ion ensemble with temperature less than 100 mK, which consists of three contributions of ion motion. The effectiveness of the model has been verified by MD simulation, and the experimental results of the excess micromotion of trapped ions are consistent with the theory. We believe that our model offers advantages in accurately evaluating the SODFS for the ion trap, especially those of laser-cooled ion microwave clocks based on large ion clouds.

In this paper, we apply the Monte Carlo wave packet method to study the ultrafast nuclear dynamics following inner-shell photoionization of ${\mathrm{N}}_2$ exposed to an ultrashort intense x-ray pulse. The intermediate states in ${\mathrm{N}}_2{}^{+}$ are highly excited so that autoionization takes place from these states to the quasibound or dissociative electronic states in ${\mathrm{N}}_2{}^{++}$. The nuclear kinetic energy release (KER) spectra following double ionization of ${\mathrm{N}}_2$ are obtained by using the spectral methods. The very sharp peaks in the nuclear KER spectra, which were, however, absent from many relevant experiments due to a limited vibrational resolution, can be ascribed to the long-lived vibrational resonances supported by the quasibound states in ${\mathrm{N}}_2{}^{++}$. The origins for the other main characteristic structures appearing in the nuclear KER spectra are also identified. To control the fragmentation dynamics of doubly ionized ${\mathrm{N}}_2$, the x-ray-pump–infrared-probe setting is employed. It is found that the laser-induced one-photon resonant transitions between the dissociative $1^1{\mathrm{\Pi }}_g$ state and the quasibound $1^1{\mathrm{\Pi }}_u$ state at around $R=3$ a.u. are responsible for suppression or enhancement of the signals at different energy regions in the nuclear KER spectra. In addition, the delay-dependent nuclear KER distributions are constructed to achieve time-resolved imaging and controlling of the ultrafast nuclear dynamics that takes place following inner-shell photoionization of ${\mathrm{N}}_2$.

We present the analysis of the structure of fermionic vortices with the spin-polarized core from a weak coupling limit to the unitary regime. We show the mechanism for the generation of the reversed circulation in the vortex core induced by an excess of majority spin particles. We introduce the classification of the polarized vortices based on the number of Fermi circles where the minigap vanishes. This provides a unique description of the vortex as one cannot smoothly map wave functions into one another corresponding to vortices differing by the number of Fermi circles. The effective mass of quasiparticles along the vortex core is analyzed and its role in the propagation of spin-polarization along the vortex line is discussed.

The $t-J$ Hamiltonian of the spinful hard-core bosonic ring in the Nagaoka limit is solved. The energy spectrum becomes quantized due to presence of spin, where each energy level corresponds to a cyclic permutation state of the spin chains. The ground state is true ferromagnetic when the ring contains $N=2$ and 3 spinful hard-core bosons; for all other $N$ it is a mixture of the ferromagnetic and nonferromagnetic states. This behavior is different from the fermionic ring, where ground state is true ferromagnetic only for $N=3$. It is shown that the intrinsic spin-generated gauge fields are analogous to the synthetic gauge fields generated by rotation of either the condensate or the confining potential. It is argued that the low-lying excited levels of the spin-flipped states intrinsically support the superfluidity. Possible ways to experimentally verify these results are also discussed.

The interaction between the quantum emitter and topological photonic system makes both the emitter and the photon behave in exotic ways. We here study a system where a giant atom is coupled to two points of a one-dimensional topological waveguide formed by the Su-Schrieffer-Heeger (SSH) chain. The topological nature of the hybrid system is studied. We find that the giant atom can act as an effective boundary and induce the chiral zero-energy modes for the waveguide under the periodical boundary. The properties of these modes are similar to those in the SSH model with open boundary. Meanwhile, the SSH waveguide, as a structured environment, induces the retarded effect and the non-Markovian dissipation of the giant atom. Our work may promote more studies on the interaction between matter and topological environment. Experimental demonstration for our study using superconducting quantum circuits is very possible within current technology.