Nine decades after Wigner's formulation of quantum rate theory, his celebrated result was recently generalized to the asymmetric barrier using an exact first-order expansion of the transmission probability in terms of ${\hslash }^2$. This paper extends the first-order quantum correction to second-order correction of order ${\hslash }^4$ for the thermally averaged transmission probability through an arbitrary barrier. The derivation employs a systematic expansion of the projection operator onto products and the thermal distribution which involves a Taylor expansion of the potential about the barrier up to eighth order. The resulting exact analytical expression is calibrated with numerical calculations of several model potentials and shows excellent agreement when the ${\hslash }^4$ term is included. In comparison, the semiclassical transition state theory cannot reproduce the correct ${\hslash }^4$ terms when the anharmonicity is treated on the level of VPT-4 (vibrational perturbation theory—fourth order) and will potentially need a VPT-6 expansion. Further analysis of the quartic barrier reveals suppressed transmission due to the dominant role of quantum reflection above the barrier. These results not only provide a conceptual framework but can also be applied to heavy atom tunneling and machine learning.

In a device-independent Bell test, the devices are considered to be black boxes and the dimension of the system remains unspecified. The dichotomic observables involved in such a Bell test can be degenerate and one may invoke a suitable measurement scheme to lift the degeneracy. However, the standard Bell test cannot account for whether or up to what extent the degeneracy is lifted, as the effect of lifting the degeneracy can only be reflected in the postmeasurement states, which the standard Bell tests do not certify. In this work, we demonstrate the device-independent certification of degeneracy-breaking measurement based on the sequential Bell test by multiple observers who perform degeneracy-breaking unsharp measurements characterized by positive-operator-valued measures (POVMs)—the noisy variants of projectors. The optimal quantum violation of Clauser-Horne-Shimony-Holt inequality by multiple sequential observers eventually enables us to certify up to what extent the degeneracy has been lifted. In particular, our protocol certifies the upper bound on the number of POVMs used for performing such measurements along with the entangled state and measurement observables. We use an elegant sum-of-squares approach that powers such certification of degeneracy-breaking measurements.

In this paper, we investigate the critical efficiency of detectors to observe Bell nonlocality using multiple copies of the maximally entangled two-qubit state carried by a single pair of particles, such as hyperentangled states, and the product of Pauli measurements. It is known that in a Clauser-Horne-Shimony-Holt (CHSH) Bell test the symmetric detection efficiency of $82.84\%$ can be tolerated for the two-qubit maximally entangled state. We beat this enigmatic threshold by entangling two particles with multiple degrees of freedom. The obtained upper bounds of the symmetric detection efficiency thresholds are $80.86\%$, $73.99\%$, and $69.29\%$ for two, three, and four copies of the two-qubit maximally entangled state, respectively. The number of measurements and outcomes in the respective cases are 4, 8, and 16. To find the improved thresholds, we use large-scale convex optimization tools, which allows us to significantly go beyond state-of-the-art results. The proof is exact up to three copies, while for four copies it is due to reliable numerical computations. Specifically, we used linear programming to obtain the two-copy threshold and the corresponding Bell inequality, and convex optimization based on Gilbert's algorithm for three and four copies of the two-qubit state. We show analytically that the symmetric detection efficiency threshold decays exponentially with the number of copies of the two-qubit state. Our techniques can also be applied to more general Bell nonlocality scenarios with more than two parties.

In this work we present the general unified description for the unitary time evolution generated by time-dependent non-Hermitian Hamiltonians embedding the bosonic representations of $\mathfrak{su}(1,1)$ and $\mathfrak{su}\left(2\right)$ Lie algebras. We take into account a time-dependent Hermitian Dyson maps written in terms of the elements of those algebras with the relation between non-Hermitian and its Hermitian counterpart being independent of the algebra realization. As a direct consequence, we verify that a time-evolved state of uncoupled modes modulated by a time-dependent complex frequency may exhibits a nonzero entanglement even when the cross operators, typical of the interaction between modes, are absent. This is due the nonlocal nature of the nontrivial dynamical Hilbert space metric encoded in the time-dependent parameters of the general Hermitian Dyson map, which depend on the imaginary part of the complex frequency. We illustrate our approach by setting the $\mathcal{PT}$-symmetric case where the imaginary part of frequency is linear on time for the two-mode bosonic realization of Lie algebras.

We investigate the Leggett-Garg inequalities (LGIs) for a boson system whose observables are given by deforming the Pegg-Barnett phase operators. We consider two observables and show that the quantum Fourier transform is useful in the realization of the required measurements. Deriving explicit forms for the LGIs using the coherent state $|\alpha \rangle$ as the initial state, we explore the regimes where they are violated when the time difference between observations of the phase operators is varied. We show that the system remains nonclassical in the large amplitude limit without dissipation; however, with dissipation, our violation diminishes rapidly.

Controlling the dynamics of quantum systems is a crucial task in quantum science and technology. Obtaining the driving field that transforms the quantum systems into its objective is a typical control task. This task is hard, scaling unfavorably with the size of the quantum map. To tackle this issue we employ typicality to assist in finding the control field for such transformation. To demonstrate the method we choose the control task of cooling the fine-structure states of the aluminum monofluoride molecule, at relatively high temperature. As a result high-rotational states are occupied, meaning a high effective Hilbert space. Using quantum typicality, we demonstrate that we can simulate an ensemble of states, enabling a control task addressing simultaneously many states. We employ this method to find a control field for cooling molecules with a large number of internal sates, corresponding to high initial temperatures.

We study purity decay—a measure of bipartite entanglement—in a chain of $n$ qubits under the action of various geometries of nearest-neighbor random two-site unitary gates. We use a Markov chain description of average purity evolution, using further reduction to obtain a transfer matrix of only polynomial dimension in $n$. In most circuits, an exception being the brick-wall configuration, purity decays to its asymptotic value in two stages: the initial thermodynamically relevant decay persisting up to extensive times is $\sim {\lambda }_{\mathrm{eff}}^t$, with ${\lambda }_{\mathrm{eff}}$ not necessarily being in the spectrum of the transfer matrix, while the ultimate asymptotic decay is given by the second largest eigenvalue ${\lambda }_2$ of the transfer matrix. The effective rate ${\lambda }_{\mathrm{eff}}$ depends on the location of bipartition boundaries as well as on the geometry of applied gates.

We report a joint experimental and theoretical study of a three-sideband (3-SB) modification of the reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) setup. The 3-SB RABBIT scheme makes it possible to investigate phases resulting from interference between transitions of different orders in the continuum. Furthermore, the strength of this method is its ability to focus on the atomic phases only, independent of a chirp in the harmonics, by comparing the RABBIT phases extracted from specific SB groups formed by two adjacent harmonics. We verify earlier predictions that the phases and the corresponding time delays in the three SBs extracted from angle-integrated measurements become similar with increasing photoelectron energy. A variation in the angle dependence of the RABBIT phases in the three SBs results from the distinct Wigner and continuum-continuum coupling phases associated with the individual angular-momentum channels. A qualitative explanation of this dependence is attempted by invoking a propensity rule. Comparison between the experimental data and predictions from an $R$ matrix (close-coupling) with time dependence calculation shows qualitative agreement in most of the observed trends.

Rare-earth ions doped into low nuclear-spin density host crystals provide a promising platform for quantum information storage and processing. Calcium tungstate $\left({\mathrm{CaWO}}_4\right)$ is an attractive host crystal because it can be isotopically enriched to provide a nuclear spin free environment. Here, we report a spectroscopic investigation of the optical transitions and hyperfine transitions of praseodymium $\left({}^{141}\mathrm{Pr}^{3+}\right)$ doped in ${\mathrm{CaWO}}_4$ at liquid-helium temperatures. The hyperfine structures of the ${}^3{H}_4$(0) and ${}^1{D}_2$(0) states are determined by spectral hole burning. The results indicate that ${\mathrm{Pr}}^{3+}$:${\mathrm{CaWO}}_4$ is an appealing candidate for quantum memory in quantum information processing.

The inelastic squared form factors of the valence-shell excitations of ${\mathrm{D}}_2$ were measured by high-energy electron scattering and calculated by the multireference single- and double-excitation configuration interaction method in the present work. It is found that for the $B^1{\mathrm{\Sigma }}_u{}^{+}$ state of ${\mathrm{D}}_2$, the theoretical calculation cannot satisfactorily reproduce the inelastic squared form factors with a higher vibrational quantum number. For the vibronic states of $C^1{\mathrm{\Pi }}_u$ and $E{F}^1{\mathrm{\Sigma }}_g{}^{+}$ of ${\mathrm{D}}_2$, obvious discrepancies between our electron-scattering results and theoretical calculations are found. Similar phenomena observed for ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ may be attributed to electronic-vibrational coupling and the failure of the first Born approximation at an incident electron energy of 1500 eV. Furthermore, the present inelastic squared form factors of ${\mathrm{D}}_2$ are in good agreement with the ones of ${\mathrm{H}}_2$ and HD, which indicates that there is no isotope effect for the electronic matrix elements of ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ in the momentum space.

Ultrafast scattering using x-rays or electrons is an emerging method to obtain structure dynamics at the atomic lengthscales and timescales. However, directly resolving in real-space atomic motions is inherently limited by the finite detector range and the probe energy. As a result, the time-resolved signal interpretation is mostly done in reciprocal space and relies on modeling and simulations of specific structures and processes. Here, we introduce a model-free approach to directly resolve scattering signals in real space, surpassing the diffraction limit, using scattering kernels and signal priors that naturally arise from the measurement constraints. We demonstrate the approach on simulated and experimental data, recover multiple atomic motions at sub-angstrom resolutions, and discuss the recovery accuracy and resolution limits versus signal fidelity. The approach offers a robust path to obtain high-resolution real-space information of atomic-scale structure dynamics using current time-resolved x-ray or electron scattering sources.

A judicious design of gain and loss leads to counterintuitive wave phenomena that are inaccessible by conservative systems. Notably, such designs can give rise to laser-absorber modes and anisotropic transmission resonances. Here, we analyze the emergence of these phenomena in an optical scatterer with sinusoid gain-loss modulation that is subjected to monochromatic oblique waves. We derive an analytical solution to the problem, with which we show how the scatterer parameters, and specifically the modulation phase and incident angle, constitute a real design space for these phenomena.

Photon-phonon interaction is a powerful mechanism for all-optical signal processing, slow (fast) light, microscopy, spectroscopy, microwave photonics, and sensing. Here, we demonstrate a photon-echo-like phenomenon induced by a phonon, whose mechanism is represented by a coherent photon-phonon chain interaction (PPCI) theory referring to the alternating evolution between Stokes scattering and anti-Stokes scattering. An analytical solution, including the impulse response of the coherent PPCI theory, is derived to quantitatively analyze the energy conversion between photon and phonon, showing a damped photoacoustic oscillation. All theoretical analysis, numerical simulation, and experiments confirm that the adjacent order echoes have a phase difference of π, i.e., phase flip, and the echoes generated by using photon and phonon as the initial excitation sources, respectively, are in inverse phase. As a result, the echoes up to the third-order are theoretically analyzed by the proposed coherent PPCI theory and verified by the experiment. This physical mechanism bodes well for a class of photonics applications in telecommunications, optical metrology, and optical computation.

We investigated optical localization and vibration in a synthetic photonic lattice (SPL) with two-phase modulators driven by different periodic voltages. By altering the periods of phase modulation, the induced phase circumfluences, band structure, and transmission behaviors of light in the SPL are studied. A transition from discrete diffraction to weak localization was observed in a small modulation period with equal modulation periodicities. For large modulation periods, the band structure exhibits a density distribution and the optical field delocalizes and vibrates. In contrast, strong localization occurs near the initial incident location with some moiré modulation periods of phases that correspond to a flat-band structure. This study reveals the effect of dual-periodic phase modulation on pulse propagation in discrete systems.

We propose a scheme to dissipatively produce steady-state entanglement in a two-qubit system, via an interaction with a bosonic mode. The system is driven into a stationary entangled state, while we compensate the mode dissipation by injecting energy via a coherent pump field. We also present a scheme which allows us to adiabatically transfer all the population to the desired entangled state. The dynamics leading to the entangled state in these schemes can be understood in analogy with electromagnetically induced transparency and stimulated Raman adiabatic passage, respectively.

We discuss the short-time perturbative expansion of the linear entropy for finite-dimensional quantum systems whose dynamics can be effectively described by a non-Hermitian Hamiltonian. We derive a timescale for the degree of mixedness for an input state undergoing non-Hermitian dynamics and specialize these results in the case of a driven-dissipative two-level system. Next, we derive a timescale for the growth of mixedness for bipartite quantum systems that depends on the effective non-Hermitian Hamiltonian. In the Hermitian limit, this result recovers the perturbative expansion for coherence loss in Hermitian systems, while it provides an entanglement timescale for initial pure and uncorrelated states. To illustrate these findings, we consider the many-body transverse-field XY Hamiltonian coupled to an imaginary all-to-all Ising model. We find that the non-Hermitian Hamiltonian enhances the short-time dynamics of the linear entropy for the considered input states. Overall, each timescale depends on minimal ingredients such as the probe state and the non-Hermitian Hamiltonian of the system, and its evaluation requires low computational cost. Our results find applications to non-Hermitian quantum sensing, quantum thermodynamics of non-Hermitian systems, and $\mathcal{PT}$-symmetric quantum field theory.

Quantum machine learning is a growing research field that aims to perform machine learning tasks assisted by a quantum computer. Kernel-based quantum machine learning models are paradigmatic examples where the kernel involves quantum states, and the Gram matrix is calculated from the overlap between these states. With the kernel at hand, a regular machine learning model is used for the learning process. In this paper we investigate the quantum support vector machine and quantum kernel ridge models to predict the degree of non-Markovianity of a quantum system. We perform digital quantum simulation of amplitude damping and phase damping channels to create our quantum data set. We elaborate on different kernel functions to map the data and kernel circuits to compute the overlap between quantum states. We show that our models deliver accurate predictions that are comparable with the fully classical models.

Quantum metrology is supposed to significantly improve the precision of parameter estimation by utilizing suitable quantum resources. However, the predicted precision can be severely distorted by realistic noises. Here, we propose a control-enhanced quantum metrology scheme to defend against these noises to improve the metrology performance. Our scheme can automatically alter the parameter-encoding dynamics with adjustable controls, thus leading to optimal resultant states that are less sensitive to the noises under consideration. As a demonstration, we numerically apply it to the problem of frequency estimation under several typical Markovian noise channels. By comparing our control-enhanced scheme with the standard scheme and the ancilla-assisted scheme, we show that our scheme performs better and can improve the estimation precision up to around one order of magnitude. Furthermore, we conduct a proof-of-principle experiment in a nuclear magnetic resonance system to verify the effectiveness of the proposed scheme. The research here is helpful for current quantum platforms to harness the power of quantum metrology in realistic noise environments.

Nuclear-spin memories of divalent neutral atoms can allow spin-preserving resolved-sideband cooling in a strong magnetic field [I. Reichenbach and I. H. Deutsch, Phys. Rev. Lett. 99, 123001 (2007)]. We present a theory for cooling ${}^{87}\mathrm{Sr}$ nuclear-spin qubits in a weak magnetic field. The theory depends on laser excitation of $5s5p{}^{3}P_1$ to a nearby state which results in $m_J$-dependent AC Stark shifts large compared to the hyperfine interaction. This effectively suppresses the nuclear-spin mixing due to the hyperfine interaction. Sideband cooling via the clock state quenched by the AC Stark-shifted ${}^{3}P_1$ state leads to nuclear-spin-preserving spontaneous emission back to the ground state. More than being compatible with low magnetic fields, the theory is applicable when the nuclear-spin qubits are defined by the two lowest Zeeman substates.