High-precision variational calculations of the operators for the relativistic corrections in the leading $m{\alpha }^4$ order are presented. The rovibrational states in the range of the total orbital angular momentum $L=0–4$ and vibrational quantum number $v=0–10$ for the ${\text{H}}_2{}^{+}$ and ${\text{HD}}^{+}$ molecular ions are considered. We estimate that about 10 significant digits are obtained. This high precision is required for making theoretical predictions for transition frequencies at the level of ${10}^{-12}$ relative uncertainty.

Motivated by recent experimental progresses, we investigate few-body properties of interacting spinless bosons near a $d$-wave resonance. Using the Skorniakov-Ter-Martirosion (STM) equations, we calculate the scattering length between an atom and a $d$-wave dimer, and we find that the atom-dimer scattering length is positive and is much smaller the result from the mean-field approximation. We also reveal unique properties of the three-body recombination rate for a degenerate Bose condensate near the $d$-wave resonance. We find that the total recombination rate is nearly a constant at the quasibound side, in contrast to the behavior of a thermal gas near a high-partial-wave resonance. We also find that the recombination rate monotonically increases across the unitary point toward the bound side, which is due to the largely enhanced coupling between the atom and the $d$-wave dimer with deeper binding energy. This monotonic behavior is also qualitatively different from that of a degenerate gas near an $s$-wave resonance counterpart.

We show that the magnetic field produced by a chiral ferromagnetic film can be applied to control ultracold atoms. The film will act as a magnetic mirror or a reflection grating for ultracold atoms when it is in the helical phase or the skyrmion crystal phase, respectively. By applying a bias magnetic field and a time-dependent magnetic field, one-dimensional or two-dimensional magnetic lattices including honeycomb, Kagome, and triangular types can be created to trap the ultracold atoms. We have also discussed the trapping height, the potential barrier, the trapping frequency, and the Majorana loss rate for each lattice. Our results suggest that the chiral ferromagnetic film can be a platform to develop artificial quantum systems with ultracold atoms based on modern spintronics technologies.

We demonstrate a proof-of-principle of direct Earth gravity-gradient measurement with an atom interferometer-based gravity gradiometer using a single proof mass of cold ${}^{87}\mathrm{Rb}$ atoms. The atomic gradiometer is implemented in the so-called double-loop configuration, hence providing a direct gravity-gradient dependent phase shift insensitive to dc acceleration and constant rotation rate. The atom interferometer (AI) can be either operated as a gravimeter or a gradiometer by simply adding an extra Raman $\pi$ pulse. We demonstrate gravity-gradient measurements first using a vibration isolation platform and second without seismic isolation using the correlation between the AI signal and the vibration signal measured by an auxilliary classical accelerometer allowing one to bypass the absence of common-mode vibration noise rejection in a double-loop geometry. The simplicity of the experimental setup (a single atomic source and unique detection) and the immunity of the AI to rotation-induced contrast loss make it a possible candidate for onboard gravity-gradient measurements.

Using the quantum collapse and revival phenomenon of a Bose–Einstein condensate in three-dimensional optical lattices, the atom number statistics on each lattice site are experimentally investigated. We observe an interaction driven time evolution of on-site number fluctuations in a constant lattice potential with the collapse and revival time ratio as the figure of merit. Through a shortcut loading procedure, we prepare a three-dimensional array of coherent states with Poissonian number fluctuations. The following dynamics clearly show the interaction effect on the evolution of the number fluctuations from Poissonian to sub-Poissonian. Our method can be used to create squeezed states, which are important in precision measurement.

An experimental proposal is presented in which dark port postselection together with weak measurements are used to enlarge the radiation pressure effect of a single photon on a mechanical oscillator placed in the middle of a Fabry-Pérot cavity and initialized in the ground state. By preparing and postselecting the photon (the system) in two quasiorthogonal states, the weak value of the radiation force operator can lie outside the eigenvalue spectrum, producing a large shift on the wave function of the mechanical oscillator (the measuring device) in the position representation. Consequently, the effect of a single photon on the average position of the oscillator can be amplified as compared to the effect caused by a photon without postselection, i.e., only preselected. The strong measurement scenario is also analyzed. In this case, a higher amplification effect is achieved and the mean position of the oscillator can reach the level of the zero-point fluctuations, but the postselection probabilities are smaller. Finally, the situation in which the oscillator starts in a thermal equilibrium state is studied. In this case, the amplification of the average position remains the same, i.e., proportional to the weak value, but the signal-to-noise ratio is reduced by a factor that depends on the average number of thermal phonons.

We extend the recently developed classical theory for the optical response of a single-layer crystal to bilayers. We account for the interaction between the two atomic planes and the multiple reflections inside the crystals. We show how to define a global susceptibility meaningful for the bilayer crystal and how its expression varies compared to the single-layer case. We compute both the local and the macroscopic fields, which allow us to make a direct comparison with experimental data.

We study a single two-level system coupled resonantly to an oscillator mode or a large spin. By adiabatically turning on a linear driving term on the oscillator or the spin, the eigenstates of the system change character and its ground state evolves into squeezed states of the oscillator or the spin. The robust generation of such states is of interest in many experimental systems, with applications for sensing and quantum information processing.

We present a scheme to generate unitarily two-mode and four-mode field squeezing in optical cavities with the near-resonantly dressed three-level atoms in the $\mathrm{\Lambda }$ configuration. The dressing fields open two coherent population trapping (CPT) windows, within which the atoms stay predominantly in the dark state and yield strong nonlinearities for both the dressing fields themselves and the other applied fields. The two-mode squeeze operator is separated from degrees of freedom of atoms in a common CPT window, and the multimode squeeze operator is segregated in different CPT windows. The resulting two-mode and multimode interaction strengths are at least one order higher than in the previous dispersive schemes, where all fields are far off resonant with the atoms. The present near-resonant scheme is robust to spontaneous emission since atoms are nearly trapped in a long-lived superposition state.

We present an algorithm for projecting superoperators onto the set of completely positive, trace-preserving maps. When combined with gradient descent of a cost function, the procedure results in an algorithm for quantum process tomography: finding the quantum process that best fits a set of sufficient observations. We compare the performance of our algorithm to the diluted iterative algorithm as well as second-order solvers interfaced with the popular cvx package for matlab, and find it to be significantly faster and more accurate while guaranteeing a physical estimate.

As one of the most essential properties of quantum mechanics, quantum coherence is also considered a key physical resource which can be used to accomplish certain tasks of quantum information processing. Significant efforts are involved in the quantification of quantum coherence using measures such as the $l_1$-norm and the relative entropy of coherence. The quantum coherence as a physical resource is usually defined with respect to a given basis, which also arouses an issue of interest concerning the variation of quantum coherence for a quantum state in different reference bases. In this paper, using an all optical setup, we experimentally investigate a trade-off relation between the coherence measures quantified by relative entropy of coherence in two noncommuting reference bases. Our result shows that the sum of quantum coherence under these bases is bounded in a region defined by its lower bound and upper bound.

We propose a mechanism of unconventional Rydberg pumping (URP) via simultaneously driving each Rydberg atom by two classical fields with different strengths of Rabi frequencies. This mechanism differs from the general Rydberg blockade or Rydberg antiblockade since it is closely related to the ground states of atoms, i.e., two atoms in the same ground state are stable while two atoms in different ground states are resonantly excited. Furthermore, we find the URP can be employed to simplify some special quantum information processing tasks, such as implementation of a three-qubit controlled-phase gate with only a single Rabi oscillation, preparation of two- and three-dimensional steady-state entanglement with two identical atoms, and realization of the autonomous quantum error correction in a Rydberg-atom-cavity system. The feasibility of the above applications is discussed explicitly by the state-of-the-art technology.

We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an experiment, and develop a third, zero-cost, post-processing protocol which is equivalent to a variant of the quantum subspace expansion. We develop methods for inserting global and local symmetries into quantum algorithms, and for adjusting natural symmetries of the problem to boost the mitigation of errors produced by different noise channels. We demonstrate these techniques on two- and four-qubit simulations of the hydrogen molecule (using a classical density-matrix simulator), finding up to an order of magnitude reduction of the error in obtaining the ground-state dissociation curve.

As one of the key steps to achieve fault-tolerant quantum-information processing, nonadiabatic holonomic quantum computation has so far been realized in a number of physical settings. However, in some physical systems, particularly spin-qubit systems (which are actively considered for the realization of quantum computers), the experimental challenges are undeniable, and the lack of a practically feasible and scalable scheme that supports universal holonomic quantum computation all in a single well-defined setup is still an issue. Here, we propose and discuss a scalable star-shaped architecture with promising feasibility, which may pave the way for the realization of universal (electron-)spin-based nonadiabatic holonomic quantum computation.

A formal derivation of the polarization correlations between the incident electron, the scattered electron, and the emitted bremsstrahlung photon is given. For the sake of demonstration, spin asymmetries pertaining to polarized scattered electrons are determined within the relativistic partial-wave theory. In addition to the sum rule for the polarization correlations relating to an unobserved spin of the scattered electron, three further sum rules are established in coplanar geometry.

A nonlinear model for the stopping power of cluster ions based on partial-wave analysis is developed through the generalization of the induced density approach (IDA) model for the interaction of homo- and heteronuclear molecular ions with a free-electron gas (IDAMol). We apply IDAMol to the energy loss of ${{\mathrm{H}}_2}^{+}$ dimers in ${\mathrm{SiO}}_2$ and ${\mathrm{Al}}_2{\mathrm{O}}_3$, where we find that the results are consistent with established linear (dielectric) models at higher speeds, as expected for small perturbations (small values of the projectile charge or high velocities). Specifically at low projectile energies, however, it is important that IDAMol goes beyond perturbation theory. This feature appears to be central for a good description of negative and positive vicinage effects, a measure of the deviation from the independent-atom model. The focus of this work, however, is the investigation of enhanced nonlinear effects. Here we present experimental results for a heteronuclear cluster ion namely ${\mathrm{HeH}}^{+}$ on ${\mathrm{Al}}_2{\mathrm{O}}_3$, in the energy range of few tens of keV/u using the medium energy ion scattering technique. The IDAMol results are corroborated by the experimental data and time-dependent density-functional calculations for this case. Strong nonlinearities are observed for the energy loss of the fragment ${\mathrm{H}}^{+}$ due to the higher charge of its He companion.

Using the analytic time-dependent effective range theory, we study two-color high-order harmonic generation (HHG) involving a weak extreme ultraviolet (XUV) pulse and an intense infrared laser field. Our analysis shows that XUV-assisted HHG spectra contain multiple additional plateau structures originating from absorption of one or more XUV photons at the photorecombination step of HHG. We show also that the HHG rate corresponding to the $n\mathrm{th}$ plateau can be presented in a factorized form involving the XUV-assisted (multiphoton) photorecombination cross section (PRCS) corresponding to absorption of $n$ XUV photons of energy $\mathrm{\Omega }$ and emission of a harmonic of energy ${\mathrm{\Omega }}_h$. This factorization allows one to extract the PRCS from the HHG spectrum and to retrieve the cross section of the inverse process: the photoionization cross section involving absorption of a single photon of energy ${\mathrm{\Omega }}_h$ and emission of $n$ XUV photons of frequency $\mathrm{\Omega }$. The analytic HHG results are in excellent agreement with numerical solutions of the three-dimensional time-dependent Schrödinger equation.

Delayed electron detachment yields of ${{\mathrm{C}}_4}^{-}$ and ${{\mathrm{C}}_6}^{-}$ induced by photoexcitation in an electrostatic ion storage ring were measured as functions of excitation energies and laser firing times, allowing for a mapping of their radiative cooling in a wide energy range. The energy window concept and discrimination of one- and two-photon absorption are critical in understanding the obtained results. The experimentally obtained electronic and vibrational cooling rates were consistent with a simulation based on detailed-balance theory. The even-odd alternation of vibrational cooling rates, predicted from IR intensities, was also examined. We found that the larger anion cools faster, with no indication of an even-odd alternation.

The efficiency of an ensemble-based optical quantum memory depends critically on the strength of the atom-light coupling. An optical cavity is an effective method to enhance atom-light coupling strength, with the drawback that cavities can be difficult to integrate into a memory setup. In this work we show coherent enhancement of atom-light coupling via an interference effect. The light to be absorbed into the atomic ensemble is split and used to drive the atoms from opposite ends of the ensemble. We compare this method theoretically to a cavity-enhanced scheme and present experimental results for our coherent enhancement in cold ${}^{87}\mathrm{Rb}$ atoms that show an efficiency of $72\pm 5\%$ and a storage lifetime of $110\pm 10\mu \text{s}$.

Topological matter exhibits exotic properties yet phases characterized by large topological invariants are difficult to implement, despite rapid experimental progress. A promising route toward higher topological invariants is via engineered Floquet systems, particularly in photonics, where flexible control holds the potential of extending the study of conventional topological matter to novel regimes. Here we implement a one-dimensional photonic quantum walk to explore large winding numbers. By introducing partial measurements and hence loss into the system, we detect winding numbers of three and four in multistep nonunitary quantum walks, which agree well with theoretical predictions. Moreover, by probing statistical moments of the walker, we identify locations of topological phase transitions in the system and reveal the breaking of pseudounitary near topological phase boundaries. As the winding numbers are associated with nonunitary time evolution, our investigation enriches understanding of topological phenomena in nonunitary settings.