We establish a lower bound on the quantum coherence of an arbitrary quantum state in arbitrary dimension, using a noncommutativity estimator of an arbitrary observable of subunit norm, where the estimator is the commutator of the observable and its incoherent or classical part. The relation provides a direct method of obtaining an estimate of the quantum coherence of an arbitrary quantum state, without resorting to quantum state tomography or the existing witness operators.

A linear scattering problem for which incoming and outgoing waves are restricted to a finite number of radiation channels can be precisely described by a frequency-dependent scattering matrix. The entries of the scattering matrix, as functions of the frequency, give rise to the transmission and reflection spectra. To find the scattering matrix rigorously, it is necessary to solve numerically the partial differential equations governing the relevant waves. Near a resonance, the temporal coupled-mode theory (TCMT) gives a model for the scattering matrix, and it is often quite accurate. In this paper, we consider resonant structures with an isolated nondegenerate resonant mode of complex frequency ${\omega }_{★}$, and derive an approximation to the exact scattering matrix for real frequencies near ${\omega }_0=\text{Re}\left({\omega }_{★}\right)$. The approximate scattering matrix depends on the exact scattering matrix at ${\omega }_0$, and gives the same approximate transmission and reflection spectra as the TCMT. Numerical examples for diffraction of plane waves by periodic structures are presented to validate our theory.

Resonant dipole-dipole interaction (RDDI) emerges in strong light-matter interacting systems, which leads to many fascinating phenomena such as cooperative light scattering and collective radiation. Here, we theoretically investigate the role of RDDI in electromagnetically induced transparency (EIT). The resonant dipole-dipole interactions manifest themselves in the cooperative spontaneous emission of the probe light transition, which give rise a broadened linewidth and associated collective frequency shift. This cooperative linewidth originates from the nonlocal and long-range RDDI, which can be determined by the atomic density, optical depth, and macroscopic length scales of the atomic ensemble. We present the finding that EIT spectroscopy essentially demonstrates all-order multiple scattering of RDDI. Furthermore, we find that the EIT transparency window becomes narrower as the cooperative linewidth increases, which essentially reduces the storage efficiency of slow light as an EIT-based quantum memory application.

We provide a proof that entanglement of any density matrix which is block diagonal in subspaces which are disjoint in terms of the Hilbert space of one of the two potentially entangled subsystems can simply be calculated as the weighted average of entanglement present within each block. This is especially useful for thermal-equilibrium states which always inherit the symmetries present in the Hamiltonian, since block-diagonal Hamiltonians are common, as are interactions which involve only a single degree of freedom of a greater system. We exemplify our method on a simple Hamiltonian, showing the diversity in possible temperature dependences of Gibbs state entanglement which can emerge in different parameter ranges.

We propose a family of discrete space-time quantum walks capable of propagating on any arbitrary triangulations. Moreover, we also extend and generalize the duality principle introduced by Arrighi et al. [Sci. Rep. 9, 10904 (2019)], linking continuous local deformations of a given triangulation and the inhomogeneity of the local unitaries that guide the quantum walker. We proved that in the formal continuous limit, in both space and time, this family of quantum walks converges to the ($1+2$)D massless Dirac equation on curved manifolds. We believe that this result has relevance in both modeling and simulating quantum transport on discrete curved structures, such as fullerene molecules or dynamical causal triangulation, and in addressing fast and efficient optimization problems in the context of the curved space optimization methods.

We propose a method to sequentially optimize arbitrary single-qubit gates in parametrized quantum circuits for simulating real- and imaginary-time evolution. The method utilizes full degrees of freedom of single-qubit gates and therefore can potentially obtain better performance. Specifically, it simultaneously optimizes both the axis and the angle of a single-qubit gate, while the known methods either optimize the angle with the axis fixed, or vice versa. It generalizes the known methods and utilizes sinusoidal cost functions parametrized by the axis and angle of rotation. Furthermore, we demonstrate how it can be extended to optimize a set of parametrized two-qubit gates with excitation-conservation constraints, which includes the HOP and the reconfigurable beam-splitter gates. We perform numerical experiments showing the power of the proposed method to find ground states of typical Hamiltonians with quantum imaginary-time evolution using parametrized quantum circuits. In addition, we show the method can be applied to real-time evolution and discuss the tradeoff between its simulation accuracy and hardware efficiency.

We experimentally demonstrate a scheme for the preparation of high-dimensional hyperentangled photon pairs with path degree of freedom (DOF) and orbital-angular-momentum (OAM) DOF using beam displacer (BD) interferometers from a warm atomic ensemble. A strong Gaussian pump beam of fixed frequency passes through the BD to produce a superposition state of two paths. The biphoton state is generated from two parallel spontaneous four-wave mixing processes in the ${}^{85}\mathrm{Rb}$ vapor cell. We successfully detect the path entanglement, two-dimensional OAM entanglement, and three-dimensional OAM entanglement by selecting the appropriate measurement. Due to the advantages of the simplicity of our interaction system and high dimensionality of the narrowband hyperentangled photons we generated, such hyperentangled source from an atomic ensemble can be utilized to realize high-dimensional multiple-DOF quantum memory and quantum communication in the future.

We report experimental measurements of the rates of blackbody-radiation-induced transitions between high-lying ($n>60$) $S$, $P,$ and $D$ Rydberg levels of rubidium atoms in a magneto-optical trap using a hybrid field ionization and state-selective depumping technique [Archimi et al., Phys. Rev. A 100, 030501(R) (2019); Simonelli et al., Phys. Rev. A 96, 043411 (2017)]. Our results reveal significant deviations of the measured transition rates from theory for well-defined ranges of the principal quantum number. We assume that the most likely cause for those deviations is a modified blackbody spectrum inside the glass cell in which the magneto-optical trap is formed, and we test this assumption by installing electrodes to create an additional microwave cavity around the cell. From the results, we conclude that it should be possible to use such external cavities to control and suppress the blackbody-radiation-induced transitions.

The configurations of the ${\left({\mathrm{C}}_6{\mathrm{H}}_6\right)}_2\mathrm{Ar}\left({\mathrm{Bz}}_2\mathrm{Ar}\right)$ complex are identified by femtosecond laser-induced Coulomb explosion, in which the produced three-body coincident ionic momenta $({\mathrm{Bz}}^{+}+{\mathrm{Bz}}^{+}+{\mathrm{Ar}}^{+})$ is measured. The triangular structure is clearly determined by coincident momenta combined with quantum chemistry calculations, arising from classical trajectory simulations of eight promising configurations. Additionally, the bond distances between Ar and two Bz molecules are retrieved from the measured coincident momenta. The good agreement between measurement and computational calculations strongly suggests the laser-induced Coulomb explosion is a powerful approach for imaging configurations of the weakly bound molecular clusters.

We demonstrate the nonlinear magnetoelectric (ME) effect in atomic vapor achieved through the parametric interaction of optical electric and radio-frequency (rf) magnetic fields leading to the generation of new optical electric fields. Density matrix calculations are performed to validate the experimental results. Moreover, the predicted dependence of the generated optical electric field amplitudes on the rf magnetic field strength is experimentally verified to confirm the ME effect. The system provides a technique for precision rf magnetometry based on this phenomenon. We could experimentally achieve an rf magnetic field sensitivity of 70 $\mathrm{fT}/\sqrt{\text{Hz}}$ at 1 kHz to 7.5 $\mathrm{pT}/\sqrt{\text{Hz}}$ at 3 MHz for zero bias field in an unshielded environment. The appealing features of the proposed rf magnetometer using our system include a high dynamic range up to ${10}^{12}$, 6 dB bandwidth of 450 kHz, and arbitrary frequency resolution, which are intrinsic to the nonlinear ME effect in the medium.

Recent studies on supersolidity in a single-component Bose-Einstein condensate (BEC) have relied on the Lee-Huang-Yang (LHY) correction for stabilization of self-bound droplets, which, however, involves a high density inside the droplets, limiting the lifetime of the supersolid. Here we propose a two-component mixture of dipolar and nondipolar BECs, such as an ${}^{166}\mathrm{Er}\text{−}{}^{87}\mathrm{Rb}$ mixture, to create and stabilize a supersolid without the LHY correction, which can suppress the atomic loss and may allow observation of the long-time dynamics of the supersolid. In such a system, supersolidity can be controlled by the difference in the trap centers between the two components.

Quantum walks exhibit properties without classical analogues. One of those is the phenomenon of asymptotic trapping—there can be nonzero probability of the quantum walker being localized in a finite part of the underlying graph indefinitely even though locally all directions of movement are assigned nonzero amplitudes at each step. We study quantum walks with the flip-flop shift operator and the Grover coin, where this effect has been identified previously. For the version of the walk further modified by a random dynamical disruption of the graph (percolated quantum walks) we provide a recipe for the construction of a complete basis of the subspace of trapped states allowing to determine the asymptotic probability of trapping for arbitrary finite connected simple graphs, thus significantly generalizing the previously known result restricted to planar 3-regular graphs. We show how the position of the source and sink together with the graph geometry and its modifications affect the excitation transport. This gives us a deep insight into processes where elongation or addition of dead-end subgraphs may surprisingly result in enhanced transport and we design graphs exhibiting this pronounced behavior. In some cases this even provides closed-form formulas for the asymptotic transport probability in dependence on some structure parameters of the graphs.

Entanglement purification is the distilling of high-quality entanglement from low-quality entanglement and is a key element in the quantum repeater. As a new branch of entanglement purification, the measurement-based entanglement purification protocol (MBEPP) only requires one to perform the Bell state measurement to couple resource states with noisy pairs, and it tolerates more local noise than the conventional purification protocols. Existing MBEPPs usually focus on physical qubit entanglement. In this paper, we propose a measurement-based logical qubit entanglement purification protocol (MBLEPP) with quantum nondemolition detection (QND), where the qubit is encoded in the quantum parity code. The results show that this MBLEPP can also work with photon loss under the conditions that each block of the logical Bell state measurement contains at least one physical qubit, that at least one of the blocks is intact, and that the entanglement exists between all blocks. Moreover, we also consider the MBLEPP with imperfect QND. We show that below a certain QND error threshold, this MBLEPP can still work. In this way, this MBLEPP not only obtains high-fidelity entanglement but also tolerates photon loss and the error from imperfect QND. This MBLEPP combines the benefits of the MBEPP and quantum error correction code and may have potential application in long-distance quantum communication.

Quantum gates constructed by geometric phase are naturally robust to control errors due to the global nature of the geometric evolution path. Therefore, how to cope with the inevitable decoherence errors is worthy of serious attention for geometric quantum computation. Different from conventional nonadiabatic geometric quantum computation (NGQC), which needs the same evolution time for any geometric rotation angle, we have proposed and experimentally demonstrated nonadiabatic noncyclic geometric quantum computation (NNGQC) without the requirement of the cyclic evolution condition, which thus reduces decoherence errors due to shortened evolution time [J. W. Zhang et al., Phys. Rev. Lett. 127, 030502 (2021)]. In addition, the use of decoherence-free subspaces (DFS) is another effective strategy to protect quantum gates from dephasing error and has been studied in nonadiabatic holonomic quantum computation [G. F. Xu et al., Phys. Rev. Lett. 109, 170501 (2012)]. Motivated by previous studies, we propose a one-step scheme to implement single-qubit NNGQC operation in DFS constructed by two Rydberg atoms, and then generalize the scheme to the two-logical-qubit case in one step. The numerical results show that our scheme is robust against decoherence in contrast to the NGQC counterparts. The present scheme combines the features of NNGQC and DFS and can further reduce the impact of decoherence on gate infidelity, which may provide an option for the realization of Rydberg-atom-based quantum computation in the future.

In this paper we investigate the quantum information theoretical limits to several tasks related to lifetime estimation and discrimination of a two-level spontaneous optical emitter. We focus, in particular, on the model problem of resolving two mutually incoherent exponential decays with highly overlapping temporal probability profiles. Mirroring recent work on quantum-inspired super-resolution of point emitters, we find that direct lifetime measurement suffers from an analog of “Rayleigh's curse” when the time constants of the two decay channels approach one another. We propose alternative measurement schemes that circumvent this limit and demonstrate superiority to direct measurement for a related binary hypothesis test. Our findings add to a growing list of examples in which a quantum analysis uncovers significant information gains for certain tasks in optomolecular metrology that do not rely on multiphoton interference but evidently do benefit from a more thorough exploitation of the coherence properties of single photons.

We use density-matrix simulations to study the performance of three distance three quantum error correction (QEC) codes in the context of the rare-earth (RE) ion-doped crystal platform for quantum computing. We analyze pseudothresholds for these codes when parallel operations are not available, and examine the behavior both with and without resting errors. In RE systems, resting errors can be mitigated by extending the system's ground-state coherence time. For the codes we study, we find that if the ground-state coherence time is roughly 100 times larger than the excited-state coherence time, resting errors become small enough to be negligible compared to other error sources. This leads us to the conclusion that beneficial QEC could be achieved in the RE system with the expected gate fidelities available in the noisy intermediate-scale quantum regime. However, for codes using more qubits and operations, a factor of more than 100 would be required. Furthermore, we investigate how often QEC should be performed in a circuit. We find that for early experiments in RE systems, the minimal $[[5,1,3]]$ would be most suitable as it has a high threshold error and uses few qubits. However, when more qubits are available the $[[9,1,3]]$ surface code might be a better option due to its higher circuit performance. Our findings are important for steering experiments to an efficient path for realizing beneficial quantum error correcting codes in early RE systems where resources are limited.

We investigate the attosecond response of the electronic cloud of a molecular system to an outer-valence ionization. The time needed for the remaining electrons to respond to a sudden perturbation in the electronic structure of the molecule is a measure of the degree of electron correlation. Using the ab initio multielectron wave-packet propagation method, we analyze the ultrafast many-body dynamics following the removal of different outer-valence electrons of two tautomers of the uracil molecule and show that this response time can be sensitive to the molecular structure and the symmetry of the ionized molecular orbital.

Sensitivity of the frequencies of 22 atomic transitions to the variation of the fine-structure constant $\alpha$ is calculated. The findings are to be used in a search for possible variations of $\alpha$ across our galaxy using high-quality spectroscopic data for stars similar to our sun.

We consider the three-body problem in a generic multiband lattice, and analyze the dispersion of the trimer states that are made of two spin-$\uparrow$ fermions and a spin-$\downarrow$ fermion due to an on-site attraction in between. Based on a variational approach, we first obtain the exact solution in the form of a set of coupled integral equations, and then reduce it to an eigenvalue problem. As an illustration we apply our theory to the sawtooth lattice, and numerically show that energetically stable trimers are allowed in a two-band setting, which is in sharp contrast with the single-band linear-chain model. In particular, we also reveal that the trimers have a nearly flat dispersion when formed in a flat band, which is unlike the highly dispersive spectrum of its dimers.

We present a theoretical framework for homonuclear, ground-state ion-atom collisions wherein the indistinguishability of direct elastic and resonant charge exchange (RCE) scattering channels is discussed. The discussion in terms of the total cross section(${\sigma }_{\text{tot}}$) is motivated and derived. The standard cross-section expressions for direct elastic(${\tilde{\sigma }}_{\text{el}}$) and RCE (${\tilde{\sigma }}_{\text{ce}}$) channels are obtained as high-energy approximations to ${\sigma }_{\text{tot}}$. We show that the total cross section resolves the inconsistency, at low energies, between the diffusion cross section (${\sigma }_D$) and the high-energy approximation to the total cross section (${\tilde{\sigma }}_{\text{tot}}$). The validity of the equivalence relation between the ${\sigma }_D$ and $2\times {\tilde{\sigma }}_{\text{ce}}$ is also discussed. The differences which result in cross sections which are frequently used in the description of ion-atom collision is illustrated with specific calculations for an ${\mathrm{Li}}^{+}-\mathrm{Li}$ system. The use of ${\sigma }_{\text{tot}}$ is advocated as a correct and consistent way to represent cross sections.