Protection of quantum information from noise is a massive challenge. One avenue people have begun to explore is reducing the number of particles needing to be protected from noise and instead use systems with more states, so-called qudit quantum computers. These systems will require codes which utilize the full computational space. Many prior qudit codes are very restrictive on relations between the parameters of number of qudits, number of logical qudits, distance of the code, and number of bases. In this paper we show that codes for these systems can be derived from already known codes, often relaxing the constraints somewhat, a result which could prove to be very useful for fault-tolerant qudit quantum computers.

We present calculations of electron scattering from ${\mathrm{BeH}}_2$ using the $R$-matrix method. Integral and differential elastic and inelastic cross sections for energies up to 20 eV have been determined and the position and width (when possible) of shape and core-excited resonances is reported. The use of Gaussian, $B$-spline, and mixed bases has been investigated. Results are compared with earlier calculations: it is shown that inclusion of both more target states and higher partial waves affects both the resonant behavior at lower energies and the high-energy behavior of the inelastic cross sections.

The spin-dependent interactions (SDIs), consisted of second-order spin-orbit coupling (SOC) and magnetic dipole-dipole interactions (MDDI), play an important role in ultracold two-body collisions for heavy atoms. We survey the inelastic two-body loss induced by SDIs in ultracold collisions of ${}^{85}\mathrm{Rb}$ in Zeeman sublevel $|2,-2\rangle$ by using time-independent first-order perturbation theory (PT) and close-coupling (CC) approaches. The two-body loss rates from the lowest channel in $M_F=-4$ to outgoing channel $M_F=-3$ at three typical magnetic field ranges are discussed. Our calculations show PT can describe the two-body loss process well by considering the full scattering wave function even though in the region around Feshbach resonances where loss is significantly enhanced. The second-order SOC, which takes the same angular momentum coupling with MDDI, is shown to be important to ${}^{85}\mathrm{Rb}$ two-body loss, while this term was usually omitted in previous PT calculations in some systems. Besides, our numerical results indicate the pronounced dip of two-body loss rate around 571 G mainly comes from the superposition of losses from the two lower outgoing channels in $M_F=-2$ with close minima. We also demonstrated an interesting phenomenon: the interference of two-body loss induced by the second-order SOC and MDDI. It paves an alternative way to suppress inelastic collisions through the interference between different loss causes.

We report an all-optical atomic vector magnetometer using dual Bell-Bloom optical pumping beams in a Rb vapor cell. This vector magnetometer consists of two orthogonal optical pumping beams, with amplitude modulations at ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ Larmor frequencies, respectively. We simultaneously detect atomic signals excited by these two pumping beams using a single probe beam in the third direction, and extract the field orientation information using the phase delays between the modulated atomic signals and the driving beams. By adding a Herriott cavity inside the vapor cell, we improve the magnetometer sensitivity. We study the performance of this vector magnetometer in a magnetic field ranging from 100 mG to 500 mG, and demonstrate a field angle sensitivity better than 10 $\mu \mathrm{rad}/{\mathrm{Hz}}^{1/2}$ above 10 Hz.

We investigate the polarization properties of high harmonics generated from oriented carbon monoxide molecules driven by a linearly polarized laser field combined with a weaker circularly polarized high-frequency assistant laser field (LPCP). The results show that the harmonics with higher ellipticities are obtained close to the cutoff region. Further analysis shows that the results are due to the manipulation of the electron trajectory by the LPCP field and the molecular asymmetric structure. By taking advantage of the properties above, we propose and theoretically demonstrate a method to generate attosecond extreme ultraviolet pulses with large ellipticity. Because of the difference of harmonic ellipticities contributed from the long and short trajectories, an even higher harmonic ellipticity can be obtained by filtering the long trajectory. In addition, by adjusting the relative phase between linearly polarized and circularly polarized fields, the attosecond XUV pulse varies from being left-elliptically polarized to right-elliptically polarized.

We explore the possibility of bicircular high-order harmonic spectroscopy to probe the laser-induced dynamics of molecules in a non-Born-Oppenheimer treatment. The numerical solutions of the time-dependent Schrödinger equation for aligned ${\mathrm{H}}_2$ and its isotopologs in $\omega \text{−}2\omega$ bicircular fields show that the intensity ratio between ${\mathrm{D}}_2$ and ${\mathrm{H}}_2$ for harmonic orders $3q$ is lower than that for orders $3q\pm 1(q\in \mathbb{N})$. Based on the strong-field approximation, we demonstrate that the interplay of vibrational wave-packet motion and dynamical-symmetry breaking leads to the different ratio. In general, the vibrational motion causes the ratio between isotopologs to increase with $q$ for both harmonic orders $3q$ and $3q\pm 1$. On the other hand, the emission of orders $3q$ is possible only because of the alignment-induced breaking of the dynamical symmetry. The faster nuclear motion in ${\mathrm{H}}_2$ enhances the symmetry breaking, resulting in the lower ${\mathrm{D}}_2$/${\mathrm{H}}_2$ ratio for the orders $3q$. Therefore, the harmonic orders $3q$ give access to the attosecond probing of dynamical symmetries in molecules.

The method of time-resolved measurement with ultrashort laser pulses is vital to the development of attosecond science. Pump-probe measurements using a train of attosecond pulses in combination with a near-infrared (NIR) multicycle driving laser have been successful in capturing the intercycle electron dynamics which repeats every optical cycle and leads to above-threshold ionization (ATI) spectra in the frequency domain. In this work, we study the effect of a carrier-envelope phase (CEP) in a few-cycle ($<6$ fs) NIR laser pulse on the photoelectron momentum distribution (PMD) of a hydrogen atom and show that interference patterns in a PMD change dramatically with CEPs in the few-cycle regime. When the few-cycle driving laser pulse has a sine shape, the double-slit interference with characteristic modulation of ATI peaks dominates the PMD. On the other hand, when the driving pulse has a cosine shape, the holographical interference featured by a spider-like pattern is isolated. Our results suggest that the CEP-stable few-cycle laser pulses can be used to identify different types of intracycle interference structures in a PMD which reveal the underlying subcycle electron dynamics on an attosecond timescale.

We consider the dynamics of a spin-1/2 particle constrained to move in an arbitrary space curve with an external electric and magnetic field applied. With the aid of gauge theory, we successfully decouple the tangential and normal dynamics and derive the effective Hamiltonian. A type of quantum potential called SU(2) Zeeman interaction appears, which is induced by the electric field and couples spin and intrinsic orbital angular momentum. Based on the Hamiltonian, we discuss the spin precession for the zero intrinsic orbital angular momentum case and the energy splitting caused by the SU(2) Zeeman interaction for a helix as examples, showing the combined effect of geometry and external field. The interaction may bring different approaches to manipulate quantum states in spintronics.

We investigate dipole oscillations of ultracold Fermi gases along the BEC-BCS crossover through disordered potentials. We observe a disorder-induced damping of oscillations as well as a change of the fundamental Kohn-mode frequency. The measurement results are compared to numerical density matrix renormalization group calculations as well as to a three-dimensional simulation of noninteracting fermions. Experimentally, we find a disorder-dependent damping, which grows approximately with the second power of the disorder strength. Moreover, we observe experimentally a change of oscillation frequency which deviates from the expected behavior of a damped harmonic oscillator on a percent level. While this behavior is qualitatively expected from the theoretical models used, quantitatively the experimental observations show a significantly stronger effect than predicted by theory. Furthermore, while the frequency shift seems to scale differently with interaction strength in the BEC versus BCS regime, the damping coefficient apparently decreases with the strength of interaction, but not with the sign, which changes for BEC- and BCS-type Fermi gases. This is surprising, as the dominant damping mechanisms are expected to be different in the two regimes.

We propose using ultracold fermionic atoms trapped in a periodically shaken optical lattice as a quantum simulator of the $t\text{−}J$ Hamiltonian, which describes the dynamics in doped antiferromagnets and is thought to be relevant to the problem of high-temperature superconductivity in the cuprates. We show analytically that the effective Hamiltonian describing this system for off-resonant driving is the $t\text{−}J$ model with additional pair hopping terms, whose parameters can all be controlled by the drive. We then demonstrate numerically using tensor network methods for a one-dimensional (1D) lattice that a slow modification of the driving strength allows near-adiabatic transfer of the system from the ground state of the underlying Hubbard model to the ground state of the effective $t\text{−}J$ Hamiltonian. Finally, we report exact diagonalization calculations illustrating the control achievable on the dynamics of spin-singlet pairs in 2D lattices utilizing this technique with current cold-atom quantum-simulation technology. These results open new routes to explore the interplay between density and spin in strongly correlated fermionic systems through their out-of-equilibrium dynamics.

We study separable system-environment evolutions of pure dephasing type in the context of objectivity. We find that it can lead to the natural emergence of spectrum broadcast structures (SBSs), but at discrete time instances. Contrary to the standard way of obtaining SBS states, which requires entanglement, reaching such states here does not require decoherence (no unobserved environments are necessary). Yet the biggest difference is the basis with respect to which the SBS states are formed. Here it is not the pointer basis of the system given by the interaction with the environment, but their equal superposition basis, the so-called mutually unbiased basis. The price to pay is a simple SBS structure with just one environment and its momentary character.

Quantum particles interacting with potential barriers are ubiquitous in physics, and the question of how much time they spend inside classically forbidden regions has attracted interest for many decades. Recent developments of new experimental techniques revived the issue and ignited a debate with often contradictory results. This motivates the present study of an exactly solvable model for quantum tunneling induced by a strong field. We show that the tunneling dynamics can depart significantly from the scenario in which the barrier-traversal time is zero or very small. However, our findings do not support the idea of a well-defined tunneling time either. Our numerically exact results should help in finding a consensus about this fundamental problem.

In the accompanying letter [Gong et al., Phys. Rev. Lett. 124, 210606 (2020)], we introduced a universal error bound for constrained unitary dynamics within a well-gapped energy band of an isolated quantum system. Here, we provide the full details on the derivation of the bound. In addition, we generalize the result to isolated quantum many-body systems by employing the local Schrieffer-Wolff transformation, obtaining an error bound that grows polynomially in time. We also generalize the result to Markovian open quantum systems and quantitatively explain the quantum Zeno effect.

By modeling quantum chaotic dynamics with ensembles of random operators, we explore how machine learning algorithms can be used to detect pseudorandom behavior in qubit systems. We analyze samples consisting of pieces of correlation functions and find that machine learning algorithms are capable of determining the degree of pseudorandomness which a system is subject to in a precise sense. This is done without computing any correlators explicitly. Interestingly, even samples drawn from two-point functions are found to be sufficient to solve this classification problem. This presents the possibility of using deep learning algorithms to explore late time behavior in chaotic quantum systems which have been inaccessible to simulation.

Bell nonlocality, the fact that local hidden-variable models cannot reproduce the correlations obtained by measurements on entangled states, is a cornerstone in our modern understanding of quantum theory. Apart from its fundamental implications, nonlocality is also at the core of device-independent quantum information processing, the successful implementation of which is achieved without precise knowledge of the physical apparatus. Here we show that a stronger form of Bell nonlocality, for which even some nonlocal hidden-variable models cannot reproduce the quantum predictions, allows us to circumvent possible attacks in the implementation of secret sharing, a paradigmatic communication protocol in which a secret split amid many possibly untrusted parts can be decoded only if they collaborate among themselves.

The charge relaxation of accumulated charge patches in insulating straight capillaries is investigated theoretically. The model assumes that charges accumulate only at the inner and outer insulator-vacuum interface of the capillary but not in the bulk. We give an analytical solution to the coupled equations that describe the surface charge dynamics at both interfaces. We provide a tool to calculate easily the characteristic relaxation times in a straight capillary of any dimension, possibly surrounded by a conducting cylinder. The latter allows for different scenarios found in experimental setups, and is applicable to both nanocapillaries and macrocapillaries. We propose an original experimental technique to monitor the charge relaxation in a straight glass capillary and show how to use the presented model to extract the bulk and surface conductivity of the insulator from the measured data. In the Supplemental Material, we provide a script in mathematica that allows the reader to compute comfortably the decay rates for all straight insulating capillaries the reader is interested in.

The charge-transfer process for collisions of ${\mathrm{C}}^{4+}$ with atomic hydrogen is studied theoretically and experimentally in this work. Our theoretical study is based on an electron-nuclear dynamics approach applied here for the state-to-state and total contributions to the electron-capture cross sections. Our theoretical results are complemented by experimental measurements of the absolute total cross section for collisions of ${\mathrm{C}}^{4+}$ with atomic hydrogen, which were carried out using an ion-atom merged-beams technique at relative collision energies of $0.122–2.756$ keV/u and performed with an improved apparatus at Oak Ridge National Laboratory. We find that the structure observed around a collision energy of 0.5 keV/u in the experimental results is due to the combined contributions of the $3\ell$ capture cross sections, the coupling of the electronic and nuclear dynamics, and the acceptance angle in the experimental configuration. We also report the ${\mathrm{C}}^{4+}$ kinetic energy loss and stopping cross section. We find that the ${\mathrm{C}}^{4+}$ gains energy for relative collision energies between 0.1 and 10 keV/u, with a maximum at $\sim 1$ keV/u. Our theoretical study shows that, to compare to the merged-beams experimental results, one has to account for effects produced by the merged path length of the apparatus.

We investigate theoretically the application of sawtooth-wave adiabatic passage (SWAP) in a one-dimensional (1D) magneto-optical trap (MOT). As opposed to related methods that have been previously discussed, our approach utilizes repeated cycles of stimulated absorption and emission processes to achieve both trapping and cooling, thereby reducing the adverse effects that arise from photon scattering. Specifically, we demonstrate this method's ability to cool, slow, and trap particles with fewer spontaneously emitted photons, with higher forces, and in less time when compared to a traditional MOT scheme that utilizes the same narrow linewidth transition. We calculate the phase-space compression that is achievable and characterize the resulting system equilibrium cloud size and temperature.

We analyze the dynamics of a one-dimensional vertical Fabry-Pérot cavity, where the upper mirror levitates due to intracavity radiation pressure force. A perturbative approach is used based around separation of timescales, which allows us to calculate the physical quantities of interest. Due to the dynamics of the cavity field, we find that the upper mirror's motion will always be unstable for levitation performed using only a single laser. Stability can be achieved for two lasers, where one provides the trapping potential and the other a damping effect, and we locate and characterize all parameter regimes where this can occur. Finally we analyze photothermal effects due to heating of the mirror substrate. We show that this can stabilize the system, even with only a single input laser, if it acts to increase the optical path length of the cavity. This work serves as a foundation for understanding how levitated optical cavity schemes can be used as stable metrological platforms.