In this paper, we propose the $5f_{5/2}\to 5f_{7/2}$ transition in ${}^{229}\mathrm{Th}^{3+}$ as an ionic clock with accuracy of ${10}^{-18}$ level, which can be also used together with the nuclear clock transition for measuring variations of fine-structure constant with common-mode rejection of certain systematic effects. The many-body perturbation theory and Dirac-Fock plus core polarizability method are used to perform theoretical calculations. Calculation results show that several systematic frequency shifts can be suppressed to ${10}^{-18}$ level or even below. Assuming the accuracy of ionic clock frequency can be achieved in ${10}^{-18}$ level, ${}^{229}\mathrm{Th}^{3+}$ potentially offers a precision of drift of fine-structure constant of $\dot{\alpha }/\alpha$ in ${10}^{-21}\text{−}{\mathrm{yr}}^{-1}$ level by measuring the frequency ratio of nuclear clock frequency and ionic clock frequency.

The recent experimental realization of the heteronuclear dipolar mixture of Dy and Er atoms opens fascinating prospects for creating intriguing novel phases in dipolar quantum gases. The experimentally measured value of intraspecies $s$-wave scattering length of ${}^{166}\mathrm{Er}$ condensate in a ${}^{164}\mathrm{Dy}\text{−}{}^{166}\mathrm{Er}$ mixture is larger than its intraspecies dipolar length implies that the ${}^{166}\mathrm{Er}$ condensate itself will not be in a regime of dominated dipole-dipole interaction (DDI). However, we find that the presence of ${}^{164}\mathrm{Dy}$ atoms with high magnetic moment induces droplet nucleation and supersolidity in the ${}^{166}\mathrm{Er}$ condensate via the long-range and anisotropic interspecies DDI. Remarkably, we find that the imbalance in the magnetic dipole moment combined with its strong anisotropic coupling leads to the emergence of unique ground-state phases. The emerging phases include doubly superfluid states, a mixture of insulating droplets and supersolid states, binary supersolids with uniform and alternating domains and a combination of supersolid-superfluid mixed states. We delineate the properties of all these ground-state phases and construct a phase diagram. We also explore the dynamical evolution across these phase boundaries via a linear quench of interspecies scattering length. Although we demonstrate the result for the ${}^{164}\mathrm{Dy}\text{−}{}^{166}\mathrm{Er}$ mixture, our results are generally valid for other dipolar bosonic mixtures of different Dy-Er isotope combinations and may become an important benchmark for future experimental scenarios.

Synthetic-dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a synthetic dimension, where the particles are arranged in real space in optical microtrap arrays and interact via dipole-dipole exchange interaction. Using mean-field theory, we find three ordered phases—two are localized in the synthetic dimension, predicted as zero-temperature ground states by Sundar et al. [Sci. Rep. 8, 3422 (2018); Phys. Rev. A 99, 013624 (2019)], and one is a delocalized phase. We characterize them by identifying the spontaneously broken discrete symmetries of the Hamiltonian. We also compute the phase diagram as a function of temperature and interaction strength for both signs of the interaction. For system sizes with more than six synthetic sites and attractive interactions, we find that the thermal phase transitions can be first or second order, which leads to a tricritical point on the phase boundary. By examining the dependence of the tricritical point and other special points of the phase boundary on the synthetic dimension size, we shed light on the physics for thermodynamically large synthetic dimension.

The static and dynamic properties of vortices in dipolar Bose-Einstein condensates (dBECs) can be considerably modified relative to their nondipolar counterparts by the anisotropic and long-ranged nature of the dipole-dipole interaction. Working in a uniform dBEC, we analyze the structure of single vortices and the dynamics of vortex pairs, investigating the deviations from the nondipolar paradigm. For a straight vortex line, we find that the induced dipolar interaction potential is axially anisotropic when the dipole moments have a nonzero projection orthogonal to the vortex line. This results in a corresponding elongation of the vortex core along this projection as well as an anisotropic superfluid phase and enhanced compressibility in the vicinity of the vortex core. Consequently, the trajectories of like-signed vortex pairs are described by a family of elliptical and oval-like curves rather than the familiar circular orbits. Similarly for opposite-signed vortex pairs their translation speeds along the binormal are found to be dipole-interaction dependent. We expect that these findings will shed light on the underlying mechanisms of many-vortex phenomena in dBECs such as quantum turbulence, vortex reconnections, and vortex lattices.

We show that negative refraction in materials can occur at frequencies $\omega$ where the real parts of the permittivity $\varepsilon \left(\omega \right)$ and the permeability $\mu \left(\omega \right)$ have different signs and that light with such frequencies can propagate just as well as light with frequencies where they have equal signs. Therefore, for negative refraction one does not need to be in the “double-negative” regime. We consider negative-refractive-index achiral materials using the Drude-Lorentz model and chiral materials using the Drude-Born-Fedorov model. We find that the time-averaged Poynting vector always points along the wave vector, the time-averaged energy-flux density is always positive, and the time-averaged energy density is positive (negative) when the refractive index is positive (negative). The phase velocity is negative when the real part of the refractive index is negative, and the group velocity generally changes sign several times as a function of frequency near resonance.

Circular swallowtail beams (CSBs) with their remarkable autofocusing capability have garnered significant interest due to their potential applications in optical trapping. This study delves into a comprehensive investigation of the trapping force properties of CSBs. Through a combination of experimental observations and theoretical analyses, we systematically explore the quantitative manipulation of trapping forces by adjusting specific parameters. This detailed investigation provides insights into the trapping force performance and stability of CSBs. In detail, our findings reveal a consistent extension of the focal length as scale factor increases, accompanied by a reduction in the focal peak intensity, intensity contrast, and largest trapping force. Notably, the alteration in trapping force exhibits greater sensitivity compared to that of intensity and intensity contrast. Furthermore, the experimental validation of particle trapping using CSBs underscores their effectiveness, emphasizing their significant potential for optical manipulation and trapping applications.

Topological waveguide arrays, which support robust light propagation through edge modes, offer a promising solution for fault-tolerant photonic chips. However, these arrays commonly require a considerable number of waveguide elements to ensure their topological protection, leading to increased footprint and fabrication costs. Here, we propose a topological waveguide array with only a few cells based on a photonic Aharonov-Bohm (AB) cage. This design is advantageous because the edge modes become compactly localized at the boundary waveguides. We achieve this by utilizing the orbital hybridization of the fundamental mode and first-order orbital angular momentum (OAM) modes to construct the AB cage, where arbitrary flux of artificial gauge fields (AGFs) can be generated and controlled by adjusting the angle between adjacent waveguides. Notably, these edge modes exhibit robustness against disorders of on-site potential and coupling, even within a small lattice. Furthermore, we demonstrate the extension of this mechanism to high-order OAM modes. Our work paves the way for miniaturizing topological devices using the orbital degree of freedom, holding the potential for exploring other AGF-enriched phenomena.

We investigate the single-photon scattering and bound states in a coupled resonator waveguide (CRW) which couples to a topological giant atom (TGA) via two distant sites. Here, the TGA is constructed by a one-dimensional Su-Schrieffer-Heeger chain with a finite length. By modulating the topological phase of the TGA, the incident photon in the CRW can be completely reflected or transmitted, and is therefore beneficial to designing a coherent photonic device. Meanwhile, we also achieve two pairs of bound states locating respectively above and below the continuum. Whether the gap is open or closed depends on the boundary condition of the TGA. Therefore, the combination of topology and interference provides us with an exciting opportunity to manipulate the photonic state in the context of waveguide quantum electrodynamics.

This paper introduces an innovative approach for representing Gaussian fermionic states, pivotal in quantum spin systems and fermionic models, within a range of alternative quantum bases. We focus on transitioning these states from the conventional computational ${\sigma }^z$ basis to more complex bases, such as $(\varphi ,\frac{\pi }{2},\alpha )$, which are essential for accurately calculating critical quantities like formation probabilities and Shannon entropy. Our methodology can be advantageous in quantum quench studies and quantum tomography, where alternative basis representations significantly enhance optimization processes. We present an algorithm that not only simplifies the basis transformation, but also reduces computational complexity, making it feasible to calculate amplitudes of large systems efficiently. Our key contribution is a technique that translates amplitude calculations into the Pfaffian computation of submatrices from an antisymmetric matrix, a process facilitated by understanding domain wall relationships across different bases. As an application, we will determine the formation probabilities for various bases and configurations within the critical transverse field Ising chain, considering both periodic and open boundary conditions. We aim to categorize the configurations and bases by examining the universal constant term that characterizes the scaling of the logarithm of the formation probability in the periodic system, as well as the coefficient of the logarithmic term in the case of open systems. In the open system scenario, this coefficient is influenced by the central charge and the conformal weight of the boundary condition-changing operator. This work is set to expand the toolkit available for researchers in quantum information theory and many-body physics, providing a more efficient and elegant solution for exploring Gaussian fermionic states in nonstandard quantum bases.

Neural network quantum states such as ansatz wave functions have shown a great deal of promise for finding the ground state of spin models. Recently, work has focused on extending this idea to mixed states for simulating the dynamics of open systems. Most approaches so far have used a purification ansatz where a copy of the system Hilbert space is added, which when traced out gives the correct density matrix. Here we instead present an extension of the restricted Boltzmann machine which directly represents the density matrix in Liouville space. This allows the compact representation of states which appear in mean-field theory. We benchmark our approach on two different versions of the dissipative transverse-field Ising model, which show our ansatz is able to compete with other state-of-the-art approaches.

This article focuses on the development of scalable and qubit-efficient algorithms for computing power functions of random quantum states. Two algorithms, based on the Hadamard Test and Gate Set Tomography, are proposed. We provide a comparative analysis of their computational outcomes, accompanied by a meticulous evaluation of inherent errors in the Gate Set Tomography approach. The second algorithm exhibits a significant reduction in the utilization of two-qubit gates compared to the first. Consequently, the second algorithm exhibits reduced susceptibility to noise. As an illustration, we apply both methods to compute the von Neumann entropy of randomly generated quantum states. We evaluate the performance of two algorithms by applying noise obtained from actual superconducting systems. The numerical simulation indicates that, in the majority of scenarios, the second algorithm outperforms the first.

This study investigates the thermal properties of the repulsive Fermi-Hubbard model with chemical potential using variational quantum algorithms, crucial in comprehending particle behavior within lattices at high temperatures in condensed matter systems. Conventional computational methods encounter challenges, especially in managing chemical potential, prompting exploration into Hamiltonian approaches. Despite the promise of quantum algorithms, their efficacy is hampered by coherence limitations when simulating extended imaginary time evolution sequences. To overcome such constraints, this research focuses on optimizing variational quantum algorithms to probe the thermal properties of the Fermi-Hubbard model. Physics-inspired circuit designs are tailored to alleviate coherence constraints, facilitating a more comprehensive exploration of materials at elevated temperatures. Our study demonstrates the potential of variational algorithms in simulating the thermal properties of the Fermi-Hubbard model while acknowledging limitations stemming from error sources in quantum devices and encountering barren plateaus.

Quantum computing devices require exceptional control of their experimental parameters to prepare quantum states and simulate other quantum systems. Classical optimization procedures used to find such optimal control parameters have further been shown in idealized settings to exhibit different regimes of learning. Of interest in this work is the overparametrization regime, where for systems with a sufficient number of parameters, global optima for prepared state and compiled unitary fidelities may potentially be reached exponentially quickly. Here, we study the robustness of overparametrization phenomena in the presence of experimental constraints on the controls, such as bounding or sharing parameters across operators, as well as in the presence of noise inherent to experimental setups. We observe that overparametrization phenomena are resilient in these realistic settings at short times, however fidelities decay to zero past a critical simulation duration due to accumulation of either quantum or classical noise. This critical depth is found to be logarithmic in the scale of noise, and optimal fidelities initially increase exponentially with depth, before decreasing polynomially with depth, and with noise. Our results demonstrate that parametrized Ansätze can mitigate entropic effects from their environment, offering tantalizing opportunities for their application and experimental realization in near-term quantum devices.

We propose a variational quantum algorithm named variational open quantum eigensolver (VOQE) for solving steady states of open quantum systems described by either Lindblad master equations or non-Hermitian Hamiltonians. In VOQE, density matrices of mixed states are represented by pure states in doubled Hilbert space. We give a framework for building a circuit ansatz which we call the Hermitian-preserving ansatz to restrict the searching space. We also give a method to efficiently measure the operators' expectation values by postselection measurements. We show the workflow of VOQE on solving steady states of the Lindblad master equations of the driven XXZ model and implement VOQE to solve the spectrum of the non-Hermitian Hamiltonians of the Ising spin chain in an imaginary field.

An important practical problem in the field of quantum metrology and sensors is to find the optimal sequences of controls for the quantum probe that realize optimal adaptive estimation. In Belliardo et al. [arXiv:2312.16985], we solved this problem in general by introducing a procedure capable of optimizing a wide range of tasks in quantum metrology and estimation by combining model-aware reinforcement learning with Bayesian inference. We take a model-based approach to the optimization where the physics describing the system is explicitly taken into account in the training through automatic differentiation. In this follow-up paper we present some applications of the framework. The first family of examples concerns the estimation of magnetic fields, hyperfine interactions, and decoherence times for electronic spins in diamond. For these examples, we perform multiple Ramsey measurements on the spin. The second family of applications concerns the estimation of phases and coherent states on photonic circuits, without squeezing elements, where the bosonic lines are measured by photon counters. This exposition showcases the broad applicability of the method, which has been implemented in the qsensoropt library released on PyPI, which can be installed with pip.

We report measurements of the ratio of the scalar polarizability $\alpha$ to the vector polarizability $\beta$ for the $6s{}^{2}S_{1/2}\to 7s{}^{2}S_{1/2}$ transition in atomic cesium. These measurements are motivated by a discrepancy between the values of the vector transition polarizability as determined using two separate methods. In the present measurement, we use a two-pathway, coherent-control technique in which we observe the interference between a two-photon interaction driven by infrared light at 1079 nm and a linear Stark-induced interaction driven by the mutually coherent second harmonic of this infrared beam at 540 nm. The result of our measurements is $\alpha /\beta =-9.902\left(9\right)$, in good agreement with the previous determination of this ratio. This measurement, critical to the study of atomic parity violation in cesium, does not reduce the discrepancy between the two methods for the determination of the vector polarizability $\beta$ for this transition.

We show that the frequency of a Raman laser is highly correlated or anticorrelated with the frequency of the Raman pump laser, depending on whether the dispersion experienced by the Raman laser is positive or negative. For a subluminal laser, corresponding to a positive dispersion with a group index that is much larger than unity, the shift in its frequency is approximately the same as that in the Raman pump laser. In contrast, for a superluminal laser, corresponding to a negative dispersion with a group index that is close to zero, its frequency shifts in the direction opposite to that of the Raman pump lasers and has an amplitude that is larger by a factor approximately equaling the inverse of the group index. These findings would play a critical role in determining the maximum achievable sensitivity of sensors employing such lasers, especially under conditions where the pump laser linewidth is broadened significantly beyond the Schawlow-Townes linewidth due to classical fluctuations.

A recently introduced theoretical framework for modeling the dynamics of x-ray amplified spontaneous emission is based on stochastic sampling of the density matrix of quantum emitters and the radiation field, similarly to other phase-space sampling techniques. While based on first principles and providing valuable theoretical insights, the original stochastic differential equations exhibit divergences and numerical instabilities. Here, we resolve this issue by accounting the stochastic components perturbatively. The refined formalism accurately reproduces the properties of spontaneous emission and proves universally applicable for describing all stages of collective x-ray emission in paraxial geometry, including spontaneous emission, amplified spontaneous emission, and the nonlinear regime. Through numerical examples, we analyze key features of superfluorescence in a one-dimensional approximation. Importantly, single realizations of the underlying stochastic equations can be fully interpreted as individual experimental observations of superfluorescence.