We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model-based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the earlier proposal by Berry et al. [Phys. Rev. Lett. 114, 090502 (2015)] to evolution generated by explicitly time-dependent Hamiltonians. Two alternative strategies are proposed to implement time ordering while exploiting the superposition principle for sampling the Hamiltonian at different times. The resource cost of our simulation algorithm retains the optimal logarithmic dependence on the inverse of the desired precision.

We report the measurement of the absolute transition frequencies of ${}^{87}\mathrm{Rb}$ atoms to the $n{P}_{1/2}$ ($n=34–52$) and $n{P}_{3/2}$ ($n=34–90$) Rydberg states by performing single-photon Rydberg excitation spectroscopy in a vapor cell. Rydberg transitions were detected by monitoring the transmission of a 780-nm probe beam. Based on the spectroscopic data, we determined the fine-splitting intervals and oscillator-strength ratios of the $nP$ doublets and also extracted the quantum defects and ionization frequency. These results extend the spectroscopic information of the $nP$ Rydberg series, providing basic knowledge for further applications to Rydberg atoms.

Experimentally observed quantum few-body dynamics of neutral atoms excited to a Rydberg state are numerically analyzed. For this, up to five rubidium atoms are trapped with optical tweezers, arranged in various two-dimensional configurations, and excited to the Rydberg $67S$ state in the nearest-neighbor blockade regime. Their coherent evolutions are measured with time-varying ground-state projections and the experimental results are analyzed with a model Lindblad equation with the homogeneous and inhomogeneous dampings determined by systematic and statistical error analysis. The coherent and dissipative dynamics of these entangled systems are successfully reproduced using the given model and external parameters optimally calibrated with the experimental results.

We discuss and numerically test a method for direct and unambiguous measurement of ultrahigh laser intensities exceeding ${10}^{20}\mathrm{W}/{\mathrm{cm}}^2$. The method is based on the use of multiple sequential tunneling ionization of heavy atoms with sufficiently high ionization potentials. We show that, due to a highly nonlinear dependence of tunneling ionization rates on the electromagnetic field strength, an offset in the charge distribution of ions appears sufficiently sensitive to the peak value of intensity in the laser focus. A simple analytic theory is presented which helps in estimating the maximal charge state produced at a given intensity via the tunnel-ionization mechanism. The theory also allows for calculating qualitatively a distribution in charge states generated in different parts of the laser focus. These qualitative predictions are supported by numerical simulations of the tunneling cascades developed in the interaction of a short intense laser pulse with a low-density target consisting of noble gases including argon, krypton, and xenon. Results of these simulations show that, using this technique, intensities in the range ${10}^{20}–{10}^{24}\mathrm{W}/{\mathrm{cm}}^2$ can be measured with sufficient reliability. The method could be extremely useful and of high demand in view of the expected commissioning of several new laser facilities capable of delivering ultrapowerful light pulses in this domain of intensities.

We clarify the optimal conditions for the protocol of Raman sideband cooling (RSC) of a single atom confined with a tightly focused far-off-resonant optical dipole trap (optical tweezers). The protocol ultimately pursues cooling to a three-dimensional ground state of the confining potential. We show that the RSC protocol has to fulfill a set of critical requirements for the parameters of cooling beams and the excitation geometry to be effective in a most general three-dimensional configuration and for an atom having initial temperature between the recoil and the Doppler bounds. We perform a numerical simulation of the Raman passage for an example of an ${}^{85}\mathrm{Rb}$ atom taking into account the full level structure and all possible transition channels.

We consider quantum dynamics of systems with fast spatial modulation of the Hamiltonian. Employing the formalism of supersymmetric quantum mechanics and decoupling fast and slow spatial oscillations we demonstrate that the effective dynamics is governed by a Schrödinger-like equation of motion and obtain the expression of the resulting effective Hamiltonian. In particular, we show that there exists an attractive effective potential even in the case when the oscillating potential averages to zero.

We show that one can quantum simulate the dynamics of a Sachdev-Ye-Kitaev model with $N$ Majorana modes for time $t$ to precision $\epsilon$ with gate complexity $O(N^{7/2}t+N^{5/2}t\mathrm{polylog}(N/\epsilon ))$. In addition to scaling sublinearly in the number of Hamiltonian terms, this gate complexity represents an exponential improvement in $1/\epsilon$ and large polynomial improvement in $N$ and $t$ over prior state-of-the-art algorithms which scale as $O(N^{10}{t}^2/\epsilon )$. Our approach involves a variant of the qubitization technique in which we encode the Hamiltonian $H$ as an asymmetric projection of a signal oracle $U$ onto two different signal states prepared by state oracles, $A|0\rangle \mapsto |A\rangle$ and $B|0\rangle \mapsto |B\rangle$, such that $H=\langle B\left|U\right|A\rangle$. Our strategy for applying this method to the Sachdev-Ye-Kitaev model involves realizing $B$ using only Hadamard gates and realizing $A$ as a random quantum circuit.

A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a Berry curvature whereas the real part induces a metric tensor on the system's parameter manifold. This results in a unified conceptual framework to understand and explore physical properties of $\mathcal{PT}$-symmetric systems from a geometric perspective. To illustrate the usefulness of the extended QGT, we show how its real part, the metric tensor, can be exploited as a tool to detect quantum phase transitions as well as spontaneous $\mathcal{PT}$ symmetry breaking in $\mathcal{PT}$-symmetric systems.

A two-qubit controlled-not (cnot) gate, realized by a controlled-phase (C-phase) gate combined with single-qubit gates, has been experimentally implemented recently for quantum-dot spin qubits in isotopically enriched silicon, a promising solid-state system for practical quantum computation. In the experiments, the single-qubit gates have been demonstrated with fault-tolerant control fidelity, but the infidelity of the two-qubit C-phase gate is, primarily due to the electrical noise, still higher than the required error threshold for fault-tolerant quantum computation (FTQC). Here, by taking the realistic system parameters and the experimental constraints on the control pulses into account, we construct experimentally realizable high-fidelity cnot gates robust against electrical noise with the experimentally measured $1/f^{1.01}$ noise spectrum and also against the uncertainty in the interdot tunnel coupling amplitude. Our fine-tuned optimal cnot gate has about two orders of magnitude improvement in gate infidelity over the ideal C-phase gate constructed without considering any noise effect. Furthermore, within the same control framework, high-fidelity and robust single-qubit gates can also be constructed, paving the way for large-scale FTQC.

We present a method to calculate an upper bound on the generation of entanglement in any spin system using the Fannes-Audenaert inequality for the von Neumann entropy. Our method not only is useful for efficiently estimating entanglement, but also shows that entanglement generation depends on the distance of the quantum states of the system from corresponding minimum-uncertainty spin-coherent states (SCSs). We illustrate our method using a quantum kicked top model and show that our upper bound is a very good estimator for entanglement generated in both regular and chaotic regions. In a deep quantum regime, the upper bound on entanglement can be high in both regular and chaotic regions, while in the semiclassical regime, the bound is higher in chaotic regions where the quantum states diverge from the corresponding SCSs. Our analysis thus explains previous studies and clarifies the relationship between chaos and entanglement.

We propose a tight lower bound on the Holevo capacity of discrete Weyl channels (DWCs), which gives the exact Holevo capacity of known special cases of DWCs. Furthermore, for a physically available but otherwise unknown (channel parameters) DWC, this bound can be directly estimated by utilizing $d+1$ measurement configurations without entanglement and joint measurements. We show that the performance of directly estimating the proposed bound is comparable with first performing the entanglement-based optimal parameter estimation of the DWC and then computing the proposed lower bound.

Dimers of carbon disulfide (${\mathrm{CS}}_2$) molecules embedded in helium nanodroplets are aligned using a moderately intense, 160-ps, nonresonant, circularly polarized laser pulse. It is shown that the intermolecular carbon-carbon (C-C) axis aligns along the axis perpendicular to the polarization plane of the alignment laser pulse. The degree of alignment, quantified by $\langle {cos}^2{\theta }_{\text{2D}}\rangle$, is determined from the emission directions of recoiling ${\mathrm{CS}}_2^{+}$ fragment ions, created when an intense 40-fs probe laser pulse doubly ionizes the dimers. Here, ${\theta }_{\text{2D}}$ is the projection of the angle between the C-C axis on the two-dimensional (2D) ion detector and the normal to the polarization plane. $\langle {cos}^2{\theta }_{\text{2D}}\rangle$ is measured as a function of the alignment laser intensity and the results agree well with $\langle {cos}^2{\theta }_{\text{2D}}\rangle$ calculated for gas-phase ${\mathrm{CS}}_2$ dimers with a rotational temperature of 0.4 K.

We study the growth of two- and three-body correlations in an ultracold Bose gas quenched to unitarity. This is encoded in the dynamics of the two- and three-body contacts analyzed in this work. Via a set of relations connecting many-body correlation dynamics with few-body models, signatures of the Efimov effect are mapped out as a function of evolution time at unitarity over a range of atomic densities $n$. For the thermal resonantly interacting Bose gas, we find that atom bunching leads to an enhanced growth of few-body correlations. These atom-bunching effects also highlight the interplay between few-body correlations that occurs before genuine many-body effects enter on Fermi timescales.

We study freely decaying quantum turbulence by performing high-resolution numerical simulations of the Gross-Pitaevskii equation (GPE) in the Taylor-Green geometry. We use resolutions ranging from ${1024}^3$ to ${4096}^3$ grid points. The energy spectrum confirms the presence of both a Kolmogorov scaling range for scales larger than the intervortex scale $\ell$, and a second inertial range for scales smaller than $\ell$. Vortex line visualizations show the existence of substructures formed by a myriad of small-scale knotted vortices. Next, we study finite-temperature effects in decaying quantum turbulence by using the stochastic Ginzburg-Landau equation to generate thermal states, and then by evolving a combination of these thermal states with the Taylor-Green initial conditions under the GPE. We use finite-temperature GPE simulations to extract mean-free path by measuring the spectral broadening in the Bogoliubov dispersion relation that we obtain from the spatiotemporal spectra, and use it to quantify the effective viscosity as a function of the temperature. Finally, we perform low-Reynolds-number simulations of the Navier-Stokes equations, in order to compare the decay of high-temperature quantum flows with their classical counterparts, and to further calibrate the estimations of the effective viscosity (based on the mean-free-path computations).

We are pointing out relevant anisotropic effects, related to spatial separation and miscibility, due to dipole-dipole interactions in rotating binary dipolar Bose-Einstein condensates by considering symmetric (${}^{164}\mathrm{Dy}-{}^{162}\mathrm{Dy}$) and asymmetric (${}^{168}\mathrm{Er}-{}^{164}\mathrm{Dy}, {}^{164}\mathrm{Dy}-{}^{87}\mathrm{Rb}$) dipolar mixtures. The binary mixtures are kept in a strong pancake-shaped trap, with repulsive two-body interactions and fixed rotation, modeled by an effective two-dimensional coupled Gross-Pitaevskii equation. The anisotropy of the dipolar interactions on miscibility and vortex-lattice structures is studied by tuning the dipole-dipole interaction (DDI) from repulsive to attractive by varying the dipole polarization angle. A clear spatial separation is verified in the densities for attractive DDI, when the inter- to intraspecies contact interaction ratio is larger than 1, being angular for symmetric mixtures and radial for asymmetric ones. The signature of hidden vortices is evidenced in the particular dipolar-symmetric case. Another relevant outcome is the observed mass-imbalance sensibility verified by the vortex-pattern binary distributions in symmetric and asymmetric-dipolar mixtures, which requires the use of a relation for nonhomogeneous mixtures to estimate the miscibility of two components.

Using a field-theoretic approach within the Schwinger-Keldysh formalism, we study a Bose-Hubbard model in the presence of a driving field and dissipation due to one-body losses. We recover the bistability diagram from the Gross-Pitaevski equation, and analyze the different phases with respect to their elementary excitations and correlations. We find the low-density solution to be subdivided into a dynamically instable, a gapped, and a gapless regime. The correlations decay exponentially, but a substantial increase of correlation length marks the regime of gapless excitations.

Based on the cavity magnomechanical system, which consists of a microwave cavity and a small ferromagnetic sphere, we propose a scheme to construct a parity-time- $\left(\mathcal{PT}-\right)$ symmetric-like system formed by the active magnon mode and passive cavity mode. The effective gain of the magnon mode is achieved by resonantly driving the yttrium iron garnet (YIG) sphere and can be modulated by the power of the driving field. We show the $\mathcal{PT}$-symmetric phase transition following the variation of magnon-photon coupling strength in microwave regime. We find that the transmission amplitudes and time delays on the first- and second-order sidebands in the $\mathcal{PT}$-symmetric-like system can be enhanced for three to four orders, compared to the magnomechanical system, once the magnon-photon coupling strength is tuned to the critical point in the broken-$\mathcal{PT}$-symmetry regime. Particularly, we also show the switching between different transmission spectra (amplification or magnomechanically induced absorption) and time delay (positive or negative) on the first-order Stokes sideband can be achieved by modulating the power of the control field, cavity-waveguide coupling parameter, and magnon-photon coupling strength. Our study shows that the cavity magnomechanical system is a promising platform for exploring $\mathcal{PT}$-symmetric-like paradigms in microwave field, and a good candidate for the microwave control on both the first- and high-order sidebands simultaneously. Our study may inspire further applications in frequency combs and low-power magnomechanical amplifier.

We study how strong mechanical squeezing (beyond 3 dB) can be achieved through reservoir engineering in an optomechanical system which is far from the resolved-sideband regime. In our proposed setup, the effect of unwanted counter-rotating terms is suppressed by quantum interference from two auxiliary cavities. In the weak coupling regime, we develop an analytical treatment based on the effective master equation approach, which allows us to obtain explicitly the condition of maximum squeezing.

We calculate the relative permittivity of a cold atomic gas under weak probe illumination, up to second order in the density. Within the framework of a diagrammatic representation method, we identify all the second-order diagrams that enter into the description of the relative permittivity for coherent light transmission. These diagrams originate from pairwise position correlation and recurrent scattering. Using coupled dipole equations, we numerically simulate the coherent transmission with scalar and vector waves and find good agreement with the perturbative calculations. We applied this perturbative expansion approach to a classical gas at rest, but the method is extendable to thermal gas with finite atomic motion and to quantum gases where nontrivial pair correlations can be naturally included.