A theoretical study on the high-order harmonic generation (HHG) in solids by a synthesized driver field is carried out. The vector potential of the driver field is instrumental in determining the Bloch oscillations of the electrons in a periodic crystal, which eventually reflects in the high-order harmonic spectra. To this end, the interaction of the sinc-shaped driver with periodic crystal is studied. It is observed that the emission time of the harmonic cutoff can be controlled by varying the delay parameter introduced in the proposed sinc-shaped driver with a well-defined scaling that depends on the energy bands of the periodic crystal under study. Furthermore, it is also observed that the emission time of the cutoff harmonics and even the harmonic cutoff energy can also be controlled by varying the delay parameter systematically. An optimum delay parameter for maximum harmonic cutoff energy and harmonic yield is also deduced. From the applied perspective, the temporal control of the cutoff harmonics is also demonstrated by the superposition of the subcycle pulsed vector beam.

The frozen mode regime is a unique slow-light scenario in periodic structures, where the flat bands (zero group velocity) are associated with the formation of high-order stationary points (also known as exceptional points). The formation of exceptional points is accompanied by enhancement of various optical properties such as gain, $Q$ factor, and absorption, which are key properties for the realization of a wide variety of devices such as switches, modulators, and lasers. Here we present and study an integrated optical periodic structure consisting of three waveguides coupled via microcavities and a directional coupler. We study this design theoretically, demonstrating that a proper choice of parameters yields a third-order stationary inflection point (SIP). We also show that the structure can be designed to exhibit two almost overlapping SIPs at the center of the Brillouin zone. We study the transmission and reflection of light propagating through realistic devices composed of a finite number of unit cells and investigate their spectral properties in the vicinity of the stationary points. Finally, we analyze the lasing frequencies and threshold level of a finite structure (as a function of the number of unit cells) and show that it outperforms conventional lasers utilizing regular band-edge lasing (such as distributed-feedback lasers).

We propose a scheme for preparing magnon squeezed states in a hybrid cavity-magnon-qubit system. The system consists of a microwave cavity that simultaneously couples to a magnon mode of a macroscopic yttrium-iron-garnet sphere via the magnetic-dipole interaction and to a transmon-type superconducting qubit via the electric-dipole interaction. By far detuning from the magnon-qubit system, the microwave cavity is adiabatically eliminated. The magnon mode and the qubit then get effectively coupled via the mediation of virtual photons of the microwave cavity. We show that by driving the qubit with two microwave fields and by appropriately choosing the drive frequencies and strengths, magnonic parametric amplification can be realized, which leads to magnon quadrature squeezing with the noise below vacuum fluctuation. We provide optimal conditions for achieving magnon squeezing, and moderate squeezing can be obtained using currently available parameters. The generated squeezed states are of a magnon mode involving more than ${10}^{18}$ spins and thus macroscopic quantum states. This work may find promising applications in quantum information processing and high-precision measurements based on magnons and in the study of macroscopic quantum states.

It is a long-standing debate that why quantum mechanics uses complex numbers but not real numbers only. To address this topic, in recent years, the imaginarity theory has been developed in the way of quantum resource theory. However, the existing imaginarity theory mainly focuses on the quantum systems with finite dimensions. Gaussian states are widely used in many fields of quantum physics, but they are in the quantum systems with infinite dimensions. In this paper we establish a resource theory of imaginarity for bosonic Gaussian states. To do so, under the Fock basis, we determine the real Gaussian states and real Gaussian channels in terms of the means and covariance matrices of Gaussian states. Also, we provide two imaginary measures for Gaussian states based on the fidelity.

We investigate a series of two-mode quantum batteries (QBs) which exhibits better performance in both the stored energy and average charging power compared to the two-photon case. In both the model related to coupling strength and Raman cases, we find the QBs can store energy faster and have a higher efficiency than the original case. Among the derived models we have studied, the two-mode Raman QB dependent on coupling strength has the best performance. We also present the relationship between the ergotropy and battery-charger entanglement of incoherent QBs and define the resource utilization efficiency $k\left(t\right)$ and $k^{\mathrm{ins}}\left(t\right)$. We find that entanglement in the energy-extraction stage is a key resource. In addition, we consider a collection of two-level systems embedded in a two-mode microwave cavity with counterrotating terms, which shows that the counterrotating terms lead to a higher stored energy in the ultrastrong-coupling regime.

A well-known method to prepare ground states of fermionic many-body Hamiltonians is adiabatic state preparation, in which an easy-to-prepare state is time-evolved towards an approximate ground state under a specific time-dependent Hamiltonian. However, which path to take in the evolution is often unclear, and a direct linear interpolation, which is the most common method, may not be optimal. In this work, we explore other types of adiabatic paths based on the spectral decomposition of the two-body projection of the residual Hamiltonian (the difference between the final and initial Hamiltonian). The decomposition defines a set of Hamiltonian terms which may be adiabatically interpolated in a piecewise or combined fashion. We demonstrate the usefulness of partially piecewise interpolation through examples involving Fermi-Hubbard models where, due to symmetries, level crossings occur in direct (fully combined) interpolation. We show that this specific deviation from a direct path appropriately breaks the relevant symmetries, thus avoiding level crossings and enabling an adiabatic passage. On the other hand, we show that a fully piecewise scheme, which interpolates every Hamiltonian term separately, exhibits a worst-case complexity of $O(L^6/{\mathrm{\Delta }}^3)$ as compared to $O(L^4/{\mathrm{\Delta }}^3)$ for direct interpolation, in terms of the number of one-body modes $L$ and the minimal gap $\mathrm{\Delta }$ along the path. This suboptimality result suggests that only those terms which break necessary symmetries should be taken into account for piecewise interpolation, while the rest is treated with direct interpolation.

We explore the opportunities of using electron scattering by the screened Coulomb potential as a tool to retrieve properties of the relativistic vortex beams of electrons, such as their transverse momentum and orbital angular momentum (OAM). We focus on relativistic and ultrarelativistic regimes of the electron energies of at least several MeV and higher, in which the transverse beam momentum is typically much smaller than its longitudinal momentum. Different scattering scenarios for the incident electron beam are considered. In particular, the scattering by a very wide target can be used to probe the electron transverse momentum when its values are larger than 10 keV. The scattering by a target of a width comparable to that of the incident beam allows one to obtain information about the electron OAM. Varying target sizes in the range from couple to hundreds of nanometers, one can in principle distinguish OAM values from several units of $\hslash$ up to thousands and more.

The energy shifts of hyperfine structure levels of the ground rotational level of the metastable ${}^3{\mathrm{\Delta }}_1$ electronic state of ${}^{180}{\mathrm{HfF}}^{+}$ ions are calculated in the presence of variable external electric and magnetic fields. The calculations are required for the analysis of systematic effects in the experiment for the search of the electron electric dipole moment ($e\mathrm{EDM}$). Different perturbations in the molecular spectra important for $e\mathrm{EDM}$ spectroscopy are taken into account.

We develop a quantum-corrected semiclassical approach to study the strong-field ionization of an atom. In this approach, the electron wave packet is propagated using Bohmian trajectories near the center of the Coulomb potential and a Herman-Kluk propagator away from the center of the Coulomb potential. We employ this approach to calculate the photoelectron momentum distributions from tunneling and multiphoton ionization of an atom in strong laser fields. The results agree well with the numerical solutions of the time-dependent Schrödinger equation. By selecting electrons released within one laser cycle, we remove the intercycle interference structure from the photoelectron momentum distributions and study the sub-laser-cycle electron dynamics. We show that the subcycle temporal information of the electron obtained by the quantum-corrected semiclassical approach is consistent with the quasiclassical result in the tunneling ionization regime, while it differs from the quasiclassical result in the multiphoton ionization regime. Furthermore, using a semiclassical backpropagation based on the Herman-Kluk propagator, we obtain the information of the ionized wave packets near the tunnel exit and compare them with the quasiclassical results.

A rapidly rotating Bose gas in the quantum Hall limit is usually associated with a melted vortex lattice. In this work, we report a self-bound and visible triangular vortex lattice without melting for a two-dimensional Bose-Bose droplet rotating in the quantum Hall limit, i.e., with rotation frequency $\mathrm{\Omega }$ approaching the trapping frequency $\omega$. Increasing $\mathrm{\Omega }$ with respect to interaction strength $U$, we find a smooth crossover of the vortex lattice droplet from a needling regime, as featured by small vortex cores and an equilibrium flat-top surface, to the lowest-Landau-level regime with Gaussian-extended cores spreading over the whole surface. The surface density of such a rotating droplet is higher than that of a static one, and their ratio is found to be a universal function of $\mathrm{\Omega }/U$. We have demonstrated these results by both numerical and variational methods. The results pave the way for future experimental exploration of rapidly rotating ultracold droplets into the quantum Hall limit.

We study the critical temperature of the superfluid phase transition of strongly interacting fermions in the crossover regime between a Bardeen-Cooper-Schrieffer superconductor and a Bose-Einstein condensate of dimers. To this end, we employ the technique of unsupervised machine learning using an autoencoder neural network, which we directly apply to time-of-flight images of the fermions. We extract the critical temperature of the phase transition from trend changes in the data distribution revealed in the latent space of the autoencoder bottleneck.

We study single-photon-induced electromagnetically induced transparency (EIT) in many-emitter waveguide quantum electrodynamics (wQED) with linear, nonlinear, and quasilinear waveguide dispersion relations. In the single-emitter problem, in addition to the robustness of the EIT spectral features in the overcoupled regime of wQED, we find that the nonlinear dispersion results in the appearance of a side peak for frequencies smaller than the resonant EIT frequency, which turns into a plateau as the nonlinearity is reduced. The quasilinear case produces a similar spectrum to the purely linear scenario with a small observable difference in the far-detuned regime. Consequently, for many-emitter scenarios, our results indicate the formation of band structure for purely linear cases, which, for smaller values of nonlinearity, leads to a narrow band-gap-like structure compared to the corresponding linear and quasilinear dispersion cases. Long-distance quantum networking aided with quantum memories can serve as one of the targeted applications of this work.

In the paper carried out by Wenjun et al. [Phys. Rev. A 95, 032124 (2017)], a generalization of the James effective dynamics theory based on a first version of the James method was presented. However, we contend that this is not a very rigorous way of deriving the effective third-order expansion for an interaction Hamiltonian with harmonic time-dependence. In fact, here we show that the third-order Hamiltonian obtained by Wenjun et al. is not Hermitian for general situations when we consider time dependence. Its non-Hermitian nature arises from the foundation of the theory itself. In this comment paper, the most general expression of the effective Hamiltonian expanded up to third order is obtained. Our derived effective Hamiltonian is Hermitian even in situations where we have time dependence.

The complex Fourier transform of the two-point correlator of the energy spectrum of a quantum system is known as the spectral form factor (SFF). It constitutes an essential diagnostic tool for phases of matter and quantum chaos. In black hole physics, it describes the survival probability (fidelity) of a thermofield double state under unitary time evolution. However, detailed properties of the SFF of isolated quantum systems with generic spectra are smeared out by large temporal fluctuations, whose minimization requires disorder or time averages. This requirement holds for any system size, that is, the SFF is non-self-averaging. Exploiting the fidelity-based interpretation of this quantity, we prove that using filters and disorder and time averages of the SFF involve unitarity breaking, i.e., open quantum dynamics described by a quantum channel that suppresses quantum noise. Specifically, averaging over Hamiltonian ensembles, time averaging, and frequency filters can be described by the class of mixed-unitary quantum channels in which information loss can be recovered. Frequency filters are associated with a time-continuous master equation generalizing energy dephasing. We also discuss the use of eigenvalue filters. They are linked to non-Hermitian Hamiltonian evolution without quantum jumps, whose long-time behavior is described by a Hamiltonian deformation. We show that frequency and energy filters make the SFF self-averaging at long times.

We present a null witness of the dimension of a quantum system, discriminating real, complex, and classical spaces, based on equality due to linear independence. The witness involves only a single measurement with sufficiently many outcomes and prepared input states. In addition, for intermediate dimensions, the witness bounds saturate for a family of equiangular tight frames including symmetric informationally complete positive operator-valued measures. Such a witness requires a minimum of resources, being robust against many practical imperfections. We also discuss errors due to finite statistics.

The topological properties of a Heisenberg $XY$ spin model on the square lattice in the form of a two-dimensional Su-Schrieffer-Heeger model is investigated through the quench dynamics. Based on the topological edge states or the higher-order topological corner states of the square lattice, we propose a scheme to transmit quantum states with high quality, including single-excitation state and entangled state, on square lattices. For the transmission of the single-excitation state, when the square lattice is in the topological phase, the maximum fidelity at the corner sites of the lattice is much larger than that of bulk sites. In addition, it has been found that, due to the different symmetries of the spin ladder and the square lattice, the maximally entangled state can be generated between two qubits when a qubit at the edge of the spin ladder is excited initially, while it cannot be generated between two qubits at the corners of the square lattice. However, the maximally entangled state of two qubits at the edge of the spin ladder or the corners of the lattice can both be transmitted to the two qubits at the other side of the lattices with high quality.

Indefinite causal order is an evolving field with potential involvement in quantum technologies. Here we propose and study one possible scenario of practical application in quantum communication: a compound entanglement distillation protocol that features two steps of a basic distillation protocol applied in a coherent superposition of two causal orders. This is achieved by using one faulty entangled pair to control-swap two others before a fourth pair is combined with the two swapped ones consecutively. As a result, the protocol distills the four faulty entangled states into one of a higher fidelity. Our protocol has a higher fidelity of distillation and probability of success for some input faulty pairs than conventional concatenations of the basic protocol that follow a definite distillation order. Our proposal shows the advantage of indefinite causal order in an application setting consistent with the requirements of quantum communication.

We introduce a framework for designing Hamiltonian engineering pulse sequences that systematically accounts for the effects of higher-order contributions to the Floquet-Magnus expansion. Our techniques result in simple, intuitive decoupling rules, despite the higher-order contributions naively involving complicated, nonlocal-in-time commutators. We illustrate how these rules can be used to efficiently design improved Hamiltonian engineering pulse sequences for a wide variety of tasks such as dynamical decoupling, quantum sensing, and quantum simulation.

Most of the existing proposals for laboratory tests of a quantum nature of gravity are based on the use of two delocalized masses or harmonically bound masses prepared in pure quantum states with large enough spatial extent. Here a setup is proposed that is based on a single delocalized mass coupled to a harmonically trapped test mass (undergoing first expansion and then compression) that moves under the action of gravity. We investigate the in-principle feasibility of such an experiment, which turns out to crucially depend on the ability to tame Casimir-Polder forces. We thus proceed with a design aimed at achieving this, trying at the same time to take advantage of these forces rather than only fighting them.