We develop an efficient numerical approach for simulating the high-power dispersive readout in circuit quantum electrodynamics. In the numerical simulations of the high-power readout, a large-amplitude coherent state induced in a cavity is an obstacle because many Fock states are required to describe such a state. We remove the large-amplitude coherent state from the numerical simulations by simulating the dynamics in a frame where the amplitude of the coherent state is almost absent. Using the developed method, we numerically simulate the high-power dispersive readout of the two-level system and the transmon. Our proposed method succeeds in producing reasonable behaviors of the high-power dispersive readout which can be deduced from the photon-number dependence of the cavity frequency: The high-power dispersive readout works in the two-level-system case while it does not work in the transmon case.

In many problems, the scattering amplitudes of a weak coherent pulse are almost equivalent to the ones of a single propagating photon. We thoroughly compare the scattering of (i) a short microwave coherent pulse from a rf generator and (ii) a vacuum-photon coherent superposition from the two-level emitter, both directed to a single two-level system—the probe. To do that, we use two superconducting qubits to implement emitter and probe, both strongly coupled to the same waveguide. However, with the use of a magnetic circulator we couple the field from the emitter to the probe without reverse backaction, thereby working with a cascaded atomic system implemented in a waveguide-QED setup. By measuring the dynamics of the scattered field, we find a certain discrepancy between two cases, confirmed by analytical and numerical study. Particularly, we find the optimal amplitude ${\mathrm{\Omega }}_{*}$ of classical pulse mimicking the superposition from the emitter, for which the difference becomes very small (but nonvanishing) and is almost unavailable to measure in practice.

The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation between the Riemann curvature tensor of the space described by the metric, and the Berry curvature, by explicit parallel transport of a vector in Hilbert space. Subsequently, we write a generating function from which the complex metric, as well as higher-order geometric tensors (affine connection, Riemann curvature tensor), can be obtained in terms of gauge-invariant cumulants. The generating function explicitly relates the quantities which characterize the geometry of the parameter space to quantum fluctuations. We also show that for a mixed quantum-classical system both real and imaginary parts of the quantum metric contribute to the dynamics, if the mass tensor is Hermitian. A many-operator generalization of the uncertainty principle results from taking the determinant of the complex quantum metric. We also calculate the quantum metric for a number of Lie group coherent states, including several representations of the $\text{SU}(1,1)$ group. In our examples nontrivial complex geometry results for generalized coherent states. A pair of oscillator states corresponding to the $\text{SU}(1,1)$ group gives a double series for its spectrum. The two minimal uncertainty coherent states show trivial geometry, but, again, for generalized coherent states nontrivial geometry results.

Quantum control plays an irreplaceable role in practical use of quantum computers. However, some challenges have to be overcome to find more suitable and diverse control parameters. We propose a promising and generalizable average-fidelity-based machine-learning-inspired method to optimize the control parameters, in which a neural network with periodic feature enhancement is used as an ansatz. In the implementation of a single-qubit gate by cat-state nonadiabatic geometric quantum computation via reverse engineering, compared with the control parameters in the simple form of a trigonometric function, our approach can yield significantly higher-fidelity $(>99.99\%)$ phase gates, such as the $\pi /8$ gate (t gate). Single-qubit gates are robust against systematic noise, additive white Gaussian noise, and decoherence. We numerically demonstrate that the neural network possesses the ability to expand the model space. With the help of our optimization, we provide a feasible way to implement cascaded multiqubit gates with high quality in a bosonic system. Therefore, the machine-learning-inspired method may be feasible in quantum optimal control of nonadiabatic geometric quantum computation.

We measure molecular vibrations with femtometer precision via resonance energy shifts using time-resolved x-ray absorption spectroscopy. For a demonstration, a Raman process excites the $A_{1g}$ mode in gas-phase ${\mathrm{SF}}_6$ molecules with an amplitude of approximately $50\mathrm{fm}$, which is probed by a time-delayed soft-x-ray pulse at the sulfur $L_{2,3}$ edge. Mapping the extremely small measured energy shifts to internuclear distances requires an understanding of the electronic contributions provided by a many-body ab initio simulation. Our study establishes core-level spectroscopy as a precision tool for time-dependent molecular-structure metrology.

We calculate repulsive Casimir forces between metallic and magnetic plates and quantitatively probe the magnetic plate's properties as tuning knobs for the repulsion, namely, the plate's thickness and its low-frequency permittivity and permeability. For a thin magnetic plate ($\le 10$ nm), we find that repulsion can exist as long as $\mu \left(0\right)\ge \epsilon \left(0\right)$. We also explore the effect of temperature on the repulsion and transition distance between attractive and repulsive interactions. We show how the parameters can be tuned to allow repulsion in submicron separation regimes, making it potentially accessible to known high-resolution measurement techniques using magnetic van der Waals materials.

In this paper, we bring out several potential signatures of negative mass regimes while investigating an expanding spin-orbit-coupled spinor $F=1$ Bose-Einstein condensate by analyzing the dispersion relation of the single-particle quantum system. In spin-orbit-coupled spinor condensates, a negative-mass parameter generates a wave packet that propagates in the opposite direction of the momentum. We analyze the dynamics of spin waves analytically and present a simple approach to investigate the expansion of spinor condensates. In particular, we examine the dynamics when both masses are negative, which results in the spinor condensates splitting into two counterpropagating self-interfering packets. Using numerical simulations of the coupled Gross-Pitaevskii equations, we demonstrate the density expansion and self-interference patterns with and without magnetization for repulsive and attractive interactions with different coupling parameters. The highlight of our investigation is that we are able to unearth several phenomena observed in experiments, such as self-interfering packets, pileup, modulation instability, slow down, self-trapping, and gap solitons. In particular, the gap soliton exists at the gap created by the intersection of two negative masses.

Atmospheric turbulence is one of the lead disturbance factors for free-space quantum communication. The quantum states of light in such channels are affected by fluctuating losses characterized by the probability distribution of transmittance (PDT). We obtain the PDT for different horizontal links via numerical simulations of light transmission through the atmosphere. The results are compared with analytical models: the truncated log-normal distribution, the beam-wandering model, the elliptic-beam approximation, and the model based on the law of total probability. Their applicability is shown to be strongly dependent on the receiver aperture radius. We introduce an empirical model based on the Beta distribution, which is in good agreement with numerical simulations for a wide range of channel parameters. However, there are still scenarios where none of the above analytical models fits the numerically simulated data. The numerical simulation is then used to analyze the transmission of quadrature-squeezed light through free-space channels.

We study a three-qubit waveguide system in the presence of optical pumping, when the side qubits act as atomlike mirrors, manifesting in a strong light-matter coupling regime. The qubits are modeled as two-level systems, where we account for important saturation effects and quantum nonlinearities. Optically pumping this system into a nonlinear regime is shown to lead to a rich manifold of dressed states that can be seen in the emitted spectrum, and we show two different theoretical solutions using a medium-dependent master-equation model in the Markovian limit, as well as using matrix product states without invoking any Markov approximations. We demonstrate how a rich nonlinear spectrum is obtained by varying the relative decay rates of the mirror qubits as well as their spatial separation and show the limitations of using a Markovian master equation. Our model allows one to directly model giant-atom phenomena, while including important retardation effects and multiphoton nonlinearities. We also show how the excited three-qubit system, in a strong-coupling regime, deviates significantly from a Jaynes-Cummings model when entering the nonlinear regime.

When an electromagnetic field is confined in a cavity of variable length, real photons may be generated from vacuum fluctuations due to highly nonadiabatic boundary conditions. The corresponding effective Hamiltonian is time-dependent and contains infinite intermode interactions. Considering one of the cavity mirrors fixed and the other describing uniform motion (zero acceleration), we show that it is possible to factorize the entire temporal dependency and write its formal solution, i.e., the Hamiltonian becomes a product of a time-dependent function and a time-independent operator. With this factorization, we prove in detail that the photon production is proportional to the Planck factor involving a velocity-dependent effective temperature. This temperature significantly limits photon generation even for ultrarelativistic motion. The time-dependent unitary transformations we introduce to obtain temporal factorization help establish connections with the shortcuts to adiabaticity of quantum thermodynamics and with the quantum Arnold transformation.

The rodeo algorithm has been proposed recently as an efficient method in quantum computing for projection of a given initial state onto a state of fixed energy for systems with discrete spectra. In the initial formulation of the rodeo algorithm, evolution times were chosen randomly via a Gaussian distribution with a fixed standard deviation. In this paper, it is shown that such a random approach for choosing times suffers from exponentially large fluctuations in the suppression of unwanted components: as the number of iterations gets large, the distribution of suppression factors obtained from random selection approaches a log-normal distribution, leading to remarkably large fluctuations. We note that by choosing times intentionally rather than randomly, such fluctuations can be avoided and strict upper bounds on the suppression can be obtained. Moreover, the average suppression using fixed computational cost can be reduced by many orders of magnitude relative to the random algorithm. A key to doing this is to choose times that vary over exponentially many timescales, starting from a modest maximum scale and going down to timescales exponentially smaller.

In some applications of quantum control, it is necessary to produce very weak excitation of a quantum system. Such an example is presented by the concept of single-photon generation in cold atomic ensembles or doped solids, e.g., by the Duan-Lukin-Cirac-Zoller (DLCZ) protocol, for which a single excitation is shared among thousands and millions of atoms or ions. Another example is the possibility to create a huge Dicke state of $N$ qubits sharing a single or a few excitations. Other examples are using tiny rotations to tune high-fidelity quantum gates, or using these tiny rotations to test high-fidelity quantum process tomography protocols. Ultrasmall excitation of a quantum transition can be generated by either a very weak or far-detuned driving field. However, these two approaches are sensitive to variations in the experimental parameters. Here we propose a different method for generating a well-defined arbitrary preselected very small transition probability—in the range from ${10}^{-2}$ to ${10}^{-8}$—by using composite pulse sequences. Contrary to other methods, it features both high fidelity and robustness to variations in the pulse area and the pulse duration.

High-fidelity two-qubit gates are crucial for the scalability of superconducting quantum processors. While quantum information processing is typically based on qubits, qutrits (or qudits) provide a larger state space for quantum information storage and processing. In this study, we analyze a high-fidelity two-qutrit gate using microwave pulses on fixed-frequency superconducting transmon qutrits and show that a high-fidelity imaginary swap-like ($i$swap-like) gate can be achieved. Perturbation theory is employed to derive an effective interaction Hamiltonian, allowing us to estimate the gate time for the two-qutrit system. Moreover, by employing a microwave-activation scheme, we can realize a high-fidelity $i$swap-like gate on different excited states of the two qutrits. Our numerical results indicate that the proposed scheme can be readily extended to multiqutrit scenarios. Additionally, we investigate the impact of microwave pulse ramp time and qutrit relaxation on gate fidelity. The results demonstrate that, with a longer ramp time and the currently accessible qutrit relaxation time, the gate error remains sufficiently small. This proposed gate scheme enables the implementation of qutrit-qutrit entangling gates, providing a promising approach to realizing superconducting quantum computation.

We prepare ${{\mathrm{N}}_2}^{+}$ mostly in the vibrational ground $X^2{{\mathrm{\Sigma }}_g}^{+}$ state by an ultraviolet 267-nm pulse and create the free induction decay (FID) of the $B{}^2{{\mathrm{\Sigma }}_u}^{+}-X^2{{\mathrm{\Sigma }}_g}^{+}$(0, 0) transition at 391 nm by a resonant excitation pulse. By controlling the phase shift of the FID using a near-IR control pulse through the dynamical Stark effect and rotational coherence, we reveal that the absorption spectrum of this transition, exhibiting a Lorentzian absorption profile, can be changed into a Fano-type profile, and then, a Lorentzian emission profile, resulting in ${{\mathrm{N}}_2}^{+}$ lasing. Our results shed light on the long-term controversy over the mechanism of strong-field-induced ${{\mathrm{N}}_2}^{+}$ lasing and reveal a general route to achieving amplification of light resonantly interacting with molecular ions without population inversion.

We construct two strong-field path integral methods with full Coulomb distortion, in which the quantum pathways are mimicked by interfering electron orbits: the rate-based CQSFA (R-CQSFA) and the hybrid forward-boundary CQSFA (H-CQSFA). The methods have the same starting point as the standard Coulomb quantum-orbit strong-field approximation (CQSFA), but their implementation does not require preknowledge of the orbits' dynamics. These methods are applied to ultrafast photoelectron holography. In the rate-based method, electron orbits are forward propagated and we derive a nonadiabatic ionization rate from the CQSFA, which includes sub-barrier Coulomb corrections and is used to weight the initial orbit ensemble. In the H-CQSFA, the initial ensemble provides initial guesses for a subsequent boundary problem and serves to include or exclude specific momentum regions, but the ionization probabilities associated with individual trajectories are computed from sub-barrier complex integrals. We perform comparisons with the standard CQSFA and ab initio methods, which show that the standard, purely boundary-type implementation of the CQSFA leaves out whole sets of trajectories. We show that the sub-barrier Coulomb corrections broaden the resulting photoelectron momentum distributions (PMDs) and improve the agreement of the R-CQSFA with the H-CQSFA and other approaches. We probe different initial sampling distributions, uniform and otherwise, and their influence on the PMDs. We find that initial biased sampling emphasizes rescattering ridges and interference patterns in high-energy ranges, while an initial uniform sampling guarantees accurate modeling of the holographic patterns near the ionization threshold or polarization axis. Our results are explained using the initial to final momentum mapping for different types of interfering trajectories.

By numerically solving the time-dependent Schrödinger equation, we investigate the harmonic emission of ${\mathrm{H}}_2{}^{+}$ with a large internuclear distance in the midinfrared laser field. We find that multiple minima are observed in the high-order harmonic spectra. As the laser wavelength and intensity increase, the harmonic minima gradually shift to the high-energy region, which is different from the position of the minima predicted by the originally studied two-center interference. We modify the formula so that the position of the minimum yield of high-order harmonics generated at large internuclear distances can be accurately interpreted by our modified formula. Consequently, by using the harmonic minimum, it is feasible to determine the parameters of the driving laser and the bond length of the molecule. Additionally, we discuss the impact of nuclear motion and laser pulse duration on the position of harmonic minimum.

We characterize the role of roton instability in the formation of a supersolid state of an elongated dipolar condensate, following a quench of the contact interactions across the superfluid-supersolid transition, as observed in recent experiments. We perform dynamical simulations by means of the extended Gross-Pitaevskii equation including quantum corrections, for different final values of the $s\text{−}\mathrm{wave}$ scattering length. The corresponding excitation spectrum is computed using an effective one-dimensional description, which provides a reasonably accurate prediction for the growth rate of the most unstable mode observed in the simulations. To analyze the behavior of the system, we employ the inverse participation ratio, which conveniently characterizes the different degree of localization in the superfluid and supersolid phases. By means of a suitable effective ansatz for the density, we derive a simple yet effective expression for the formation time of the supersolid. This expression provides valuable insights regarding its scaling behavior with respect to the $s$-wave scattering length.

Polygon and star modes enable unidirectional emission and single-frequency lasing in whispering gallery microcavities. To understand their properties and facilitate design, we have adopted both two-dimensional and three-dimensional full-wave perturbation methods to simulate these modes. Our simulation demonstrates that a tapered optical fiber can be used as a weak perturbation to coherently combine multiple whispering gallery modes into a polygon or star mode. Additionally, our simulation predicts an optical quality factor as high as ${10}^7$ for the polygon modes, which is in good agreement with the experimental results.

Nonlinear strong coupling in the frequency conversion process is an emerging field and has recently become accessible in integrated photonic platforms. Here we study the strong-coupling dynamics of second harmonic generation (SHG) in an optical microresonator. It is revealed that the nonlinear modal superposition, featuring intensity-dependent Rabi oscillation, leads to a clamped maximum SHG conversion efficiency, which can be broken through a self-injection configuration. Moreover, the nonlinear strong-coupling physics is revealed for various phenomena, including bistability, period-doubling bifurcation, and chaos. Additionally, pseudo-Hermitian degeneracy is found, where the synchronized resonances result in enhanced SHG efficiency. This work not only provides guidance for the implementation of high-efficiency photonic devices, but also may enrich the studies of nonlinear dynamics and non-Hermitian physics in optical microresonators.

We analyze theoretically the motional quantum dynamics of a levitated dielectric sphere interacting with the quantum electromagnetic field beyond the point-dipole approximation. To this end, we derive a Hamiltonian describing the fundamental coupling between photons and center-of-mass phonons, including Stokes and anti-Stokes processes, and the coupling rates for a dielectric sphere of arbitrary refractive index and size. We then derive the laser recoil heating rates and the information radiation patterns (the angular distribution of the scattered light that carries information about the center-of-mass motion) and show how to evaluate them efficiently in the presence of a focused laser beam, in either a running- or a standing-wave configuration. This information is crucial to implement active feedback cooling of optically levitated dielectric spheres beyond the point-dipole approximation. Our results predict several experimentally feasible configurations and parameter regimes where optical detection and active feedback can simultaneously cool to the ground state the three-dimensional center-of-mass motion of dielectric spheres in the micrometer regime. Scaling up the mass of the dielectric particles that can be cooled to the center-of-mass ground state is relevant not only for testing quantum mechanics at large scales but also for current experimental efforts that search for new physics (e.g., dark matter) using optically levitated sensors.