In this paper, we present a comprehensive analysis of the one-loop self-energy correction at finite temperature for the bound electron. In this approach, we study the influence of thermal radiation on atomic systems. Along the way, we find well-known effects, including thermal Stark and Zeeman shifts, as well as thermal quadrupole interactions and relativistic corrections to the multipole expansion of photon field operators. We show that the corresponding contributions arise from the decomposition of the fully relativistic expression in terms of the $\alpha Z$ parameter. The presented analysis unambiguously determines the consistency of the quantum electrodynamics theory at finite temperature with the perturbation theory of quantum mechanics. Although our analysis mainly focuses on the hydrogen atom model, potential implications for precision spectroscopic experiments are discussed.

Efficient quantum-state detection is crucial for many precision control experiments, such as the ongoing effort to probe the electron's electric dipole moment using trapped molecular ${}^{232}\mathrm{ThF}^{+}$ ions at JILA. While quantum-state detection through state-selective photodissociation has been successfully implemented on this molecule, progress has been hindered by low dissociation efficiency. In this work, we perform spectroscopy on the molecule to identify excited states that facilitate more efficient photodissociation. For the most favorable transition, we achieve a dissociation efficiency of 57(14)% with quantum-state selectivity. Additionally, we discuss several state detection protocols that leverage favorable excited states that will facilitate simultaneous readout of all EDM relevant states, allowing further improvement of overall statistics.

Attosecond photoionization delays yield time-resolved information about the dynamics of electrons within atoms and molecules. Over the past decade, two pump-probe techniques have become the primary experimental methods for extracting such delays. Both methods use an attosecond XUV pump pulse to initiate the photoionization process, while an infrared laser field is used to modify the photoelectron's final momentum and provide timing information. The initial photoionization step is described by the Wigner delay, which is specific to the ionization target. However, both experimental techniques must account for an additional contribution to the measured delay due to the presence of the infrared field. Such contributions are called the Continuum-Continuum (CC) and Coulomb-Laser-Coupling (CLC) delay for the Reconstruction of Attosecond Beating By Two-photon Transitions and streaking methods, respectively. Here, we compare the various proposed formulas for CLC and CC delays using analytical and numerical methods across a range of wavelengths spanning visible to midinfrared. We show that one of the CC definitions is nearly equal to the CLC delay over a range of photoelectron energies and wavelengths. We furthermore obtain alternate expressions for the CC delays. These expressions are simpler to use and show close correspondence to the CLC delays. Based on this correspondence, we suggest a correction to the CLC delay for low-energy electrons, where the currently used approximation breaks down. Our work provides guidance for when it is valid to treat CC and CLC delays as being equivalent.

Rydberg blockade effect provides a convenient platform for simulating locally constrained many-body systems, such as quantum dimer models and quantum loop models, especially their novel phases like topological orders and gapless quantum spin ice (QSI) phases. To discuss the possible phase diagram containing different QSIs in three-dimensional (3D) Rydberg arrays, we have constructed an extended Rokhsar-Kivelson (RK) Hamiltonian with equal weight superposition ground state in different fillings at the RK point. Therefore, the perfect QSIs with fixed local dimer filling and their monomer-doped states can be simulated directly by Monte Carlo sampling. Using single-mode approximation, the excitations of dimers and monomers have also been explored in different fillings. We find that, in the thermodynamical limit, even doping a small amount of monomers can disrupt the topological structure and lead to the existence of off-diagonal long-range order. However, in a finite size (as in cold-atom experiment), the property of QSI will be kept in a certain region like a crossover after doping. The phase diagram containing different QSIs and off-diagonal order phases is proposed.

We solve the Lindblad master equation for the quantum state of a pumped optomechanical system coupled to a thermal bath. We show that the solution to the state in the linear pumping regime is a beam-split thermal state when pumped on the red sideband of cavity resonance and a two-mode squeezed thermal state when pumped on the blue sideband. The time dependence of each state is fully described by four coupled differential equations. Using this formalism, we describe a process of first cooling the mechanical mode via the red-sideband pump, then entangling that mode using the blue-sideband pump. We find that there is an optimal strength of blue-sideband pumping to drive the correlation variance between the two modes below a desired threshold for a maximum amount of time. This optimal value depends both on the loss rates and equilibrium temperatures of the two modes, and we provide an approximate analytic expression for this relationship. We show that a long entanglement time is achievable, even at relatively high temperatures, as long as the optical loss rate is much higher than the mechanical one.

Skyrmions are topological quasiparticles characterized by nontrivial topological textures. The manipulation of topological textures has attracted plenty of attention in recent years. In this study we demonstrate a geometric-phase-based method for dynamically controlling optical skyrmionic textures. By introducing the Pancharatnam-Berry phase through engineering closed paths of polarization evolution on the Poincaré sphere using waveplate combinations, we achieved the conversion between different skyrmionic topological textures. This geometric-phase-dependent strategy enables flexible manipulation of topological textures, paving the way for understanding topology transformations and engineering optical skyrmions for applications in information processing.

Multiphoton blockade provides an efficient way to achieve entangled photon sources and leads to wide applications in modern quantum technologies. Here, we propose a scheme to realize multiphoton blockade by a multitone drive. Specifically, we demonstrate two-photon and three-photon blockades in a single- mode optical Kerr resonator using a two-tone and a three-tone drive, respectively. In comparison with the single-tone drive, except for the blockade of the $(n+1)\mathrm{th}$ photon excitation due to large detuning, the key mechanism in this scheme is the sequentially resonant excitations of all the $m$-photon states $(m\le n)$ by the $n$-tone drive, which lead to the enhancement of photon generation and the demonstration of multiphoton blockade in the weak driving regime. Moreover, the photon distribution within the system can be adjusted on demand by tuning the relative amplitudes of the driving fields for different frequencies. The scheme can be extended to other bosonic systems and be applied to demonstrate other multiphoton physical effects.

Topological photonics, combining the advantages of topological properties with those of optical systems, is anticipated to be significant for various applications. However, how to leverage its benefits for realizing single-photon blockade (PB) remains rarely studied. Here, we propose schemes to generate single PBs in a dimer chain featuring multiple qubits and a two-photon Jaynes-Cummings interaction. We demonstrate that with specific intracell and intercell hopping amplitudes of the lattice, the quantum level lattices are characterized by the form of a one-dimensional array with topological edge states in both two-excitation and three-excitation spaces, resulting in suppressed two-photon excitations and enhanced single-photon excited states. This further leads to a remarkable single PB effect under the resonance-driven case. Interestingly, single PBs can be observed in the off-resonance scenario under coupling strengths with opposite trends, while satisfying that two-excitation and three-excitation transitions are resonant whereas single-photon transition is detuned. We refer to this as an abnormal mechanism compared to previous regimes. Moreover, we show the superiority of the multiqubit-cavity topological chain by comparing with scenarios with different numbers of qubits. Our study not only sheds light on the generation of the single PB effect based on an abnormal mechanism but also establishes a pathway for realizing quantum blockade in topological optical systems, with potential applications in quantum information processing and quantum communication.

Non-Gaussian quantum states of bosons are a key resource in quantum information science with applications ranging from quantum metrology to fault-tolerant quantum computation. Generation of photonic non-Gaussian resource states, such as Schrödinger's cat and Gottesman-Kitaev-Preskill states, is challenging. In this work, we go beyond existing passive architectures and explore a broad set of adaptive schemes. Our numerical results demonstrate a consistent improvement in the probability of success and fidelity of generating these non-Gaussian quantum states with equivalent resources. We also explore the effect of loss as the primary limiting factor and observe that adaptive schemes lead to more desirable outcomes in terms of overall probability of success and loss tolerance. Our work offers a versatile framework for non-Gaussian resource state generation with the potential to guide future experimental implementations.

In this erratum, we provide new parameters for the Na-O screening function that had an unphysical value at the limit of infinite distance in the original data set.

Collective coherent (CC) errors are inevitable, as every physical qubit undergoes free evolution under its kinetic Hamiltonian. These errors can be more damaging than stochastic Pauli errors because they affect all qubits coherently, resulting in high-weight errors that standard quantum error-correcting (QEC) codes struggle to correct. In quantum memories and communication systems, especially when storage durations are long, CC errors often dominate over stochastic noise. Trapped-ion platforms, for example, exhibit strong CC errors with minimal stochastic Pauli components. In this work, we address the regime where immunity to CC errors, high code rate (due to limited qubit availability), and moderate distance (sufficient for correcting low-weight errors) are all essential. We construct a family of constant-excitation stabilizer codes with parameters $\left[[2^{r+1},2^r-(r+1),4]\right]$. The smallest instance, the [[8,1,4]] code, improves the code rate and error threshold of the best previously known CE code by factors of approximately two and four, respectively.

Large-scale quantum networks have been employed to overcome practical constraints on transmission and storage for single entangled systems. The deterministic preparation of entangled states is one of the key factors for the realization of quantum networks. There is no efficient method to verify whether single multipartite entanglement can be prepared by multisource quantum networks. Here, we theoretically analyze under what conditions entangled states can be prepared in three kinds of basic Gaussian quantum networks, named triangle networks, star-shaped networks, and chain-type networks. Some necessary criteria are derived for all preparable entangled Gaussian states in such networks. They show that the network structure imposes strong constraints on the set of preparable entangled Gaussian states, which is fundamentally different from standard single multipartite entanglement. This study takes the first step towards understanding the network mechanism for preparing entangled Gaussian states.

We demonstrate a method for superresolving signals encoded as finite mixtures of bosonic modes using collective measurements that exploit permutation symmetry. Specifically, we use multiple copies of the state $\rho$ of the finite mixture to extract an estimate for the purity of $\rho$ via a spectrum measurement, the weak Schur-sampling measurement. Depending on the outcome, we then further fine-grain the measurement to optimally extract an estimate of the relative intensity between the two incoherent mixtures. Our protocol furnishes simultaneous estimates for both the relative intensity and the separation of incoherent signals saturating the multiparameter Cramér-Rao bound and is robust against misalignment errors. We also provide viable experimental avenues for implementing such collective measurements in different setups.

We report experimental single-electron-capture cross sections for ${\mathrm{Sn}}^{3+}$ ions impacting on ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ molecules at low projectile energies, ranging from 0.8 to 153 eV/u. The data were obtained in a crossed-beam-type experiment with a decelerated ${\mathrm{Sn}}^{3+}$ ion beam and a ${\mathrm{H}}_2$ $\left({\mathrm{D}}_2\right)$ gas target. Charge-state resolved Sn ion currents are measured with a retarding field analyzer. After an extensive description of the setup and measurement procedure, we present and discuss the results in comparison to model calculations. Ab initio calculations of potential energy curves, including spin-orbit interactions, are performed and used to fit a four-state diabatic model. The experimental and theoretical single-electron-capture cross sections show good agreement and are found to have values in the range of 20–$45\times {10}^{-16}{\mathrm{cm}}^2$ with a shallow maximum around 10 eV/u. We do not observe a significant difference between the cross sections for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$, as hinted at in our previous work at energies of 80–400 eV/u.

The introduction of disorder in the extended Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass and disordered solid phases. In this work, we present a rich phase diagram of interacting bosons in a disordered two-dimensional optical lattice, modeled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean-field theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the disordered solid and Bose-glass phases. We have investigated this transition in greater detail using cluster Gutzwiller mean-field theory to study the effect of intersite correlations which is absent in the single-site Gutzwiller mean-field theory. We have also studied this phase transition from the perspective of percolation theory.

The quantum speed limit (QSL) is a fundamental concept in quantum mechanics, providing a lower bound on the evolution time. The attainability of the QSL, which greatly depends on the understanding of the QSL, is a long-standing open problem, especially for high-dimensional systems. In this paper, we solve this problem by establishing a QSL suitable and attainable for both open and closed quantum systems based on a new proposed state distance. It is shown that, given any initial state in a certain finite dimension, unitary and nonunitary dynamics can always be found to attain our QSL bound in the corresponding dimension, and for any given Hamiltonian for a unitary evolution a pair of states always exists, attaining the bound. As applications, we demonstrate the QSL time attained by various physical settings. This paper will shed light on the QSL problems.