Dynamical properties of homogeneous Fermi-Fermi mixtures of dipolar and nondipolar atoms are studied at zero temperature, where dipoles are polarized by an external field. We calculate the density-density correlation functions in a ring-diagram approximation and analyze the pole structure to obtain eigenfrequencies of collective excitations. We first determine stability phase diagrams for the mixtures available in experiments:, i.e., ${}^{167}\mathrm{Er}\text{−}{}^{173}\mathrm{Yb}$, ${}^{167}\mathrm{Er}\text{−}{}^6\mathrm{Li}$, ${}^{161}\mathrm{Dy}\text{−}{}^{173}\mathrm{Yb}$, and ${}^{161}\mathrm{Dy}\text{−}{}^6\mathrm{Li}$ systems, and show that the mixtures with larger mass imbalance tend to be more unstable. We then investigate the parameter dependence of an undamped zero sound with an anisotropic real dispersion relation in the stable phase for the ${}^{161}\mathrm{Dy}\text{−}{}^{173}\mathrm{Yb}$ mixture, and the speed of sound exhibits a critical angle of possible propagation with respect to the dipole polarization direction, above which the sound mode disappears in the particle-hole continuum. Since the sound mode is a coherent superposition of density fluctuations of dipolar and nondipolar atoms, the existence of the sound mode, e.g., the value of the critical angle, is significantly affected by the interparticle interaction through the density-density correlation between dipolar and nondipolar atoms. We have also observed such an effect of the interparticle interaction in the study of a linear response of density fluctuations to an external perturbation.

The collective excitation modes in quantum droplets trapped in a two-dimensional harmonic potential in the context of symmetric weakly interacting binary bosonic mixtures are studied. By utilizing the linearization technique, the time-dependent extended Gross–Pitaevskii equation, and a sum-rule approach with a variational approximation, the ground-state properties and collective excitations of such a two-dimensional quantum system are investigated for various system parameters. We present comprehensive analysis and calculations on the effect of the confinement strength and anisotropy of the trapping potential, the number of atoms in the droplet, and the collective excitation modes. The radius of the droplet, as well as the chemical potential, is nonmonotonically related to the number of atoms in the droplet, and the confinement tends to shift the minimum values towards the ideal-gas limit. The excitation frequency peaks, which are prominent in a self-bounded droplet, become less pronounced and smoother when subjected to a strong trapping potential. The sum-rule approach fails to reproduce the breathing mode frequency for a moderate number of atoms in a weak trapping potential, however, works perfectly well in a strong confinement. It was found that the anisotropy in the trap eliminates the degeneracy between the quadrupole and scissors modes that occurs in an isotropic trap, causing the frequencies of these two modes to immediately diverge from each other for any degree of anisotropy. These findings provide valuable insights into the unique characteristics and behavior of quantum droplets, offering potential implications for future research and applications in the dynamic behaviors of intriguing quantum droplets.

We study spin transport in a one-dimensional finite-length wire connected to fermionic leads. The interacting wire is described by the sine-Gordon model while the leads are either noninteracting or interacting Luttinger liquids. We calculate the spin current driven by a spin bias in the nonlinear regime by solving numerically the classical equation of motion, and find that the cosine term in the sine-Gordon model gives rise to an oscillating spin current when the spin bias exceeds its critical value. We discuss the results in connection with transport experiments with ultracold atoms.

Near-electric-field enhancement induced by the nanoscale light-matter interactions has been advancing plasmonics such as plasmon-enhanced spectroscopy, leading to a linear scaling of the observed far-field spectral signals in theory. However, the contributions of an additionally existed chemical effect to the propagated optical signals from near- to far-field are commonly irregular. Here, inspired by the physical origin of surface-enhanced Raman spectroscopy (SERS), we experimentally map the far-field signals on the near-field properties through utilizing the purely electromagnetic coupled plasmon-molecule interactions of particular Raman probe molecules, thereby enabling the precise estimation for the enhanced local electric field in the subwavelength dimension only with the SERS intensity. This work can truly accelerate the translation of SERS into a quantitative analysis tool, but also lays the foundation of an intuitive probing into the plasmonic excited field employing plasmon-enhanced spectroscopic techniques.

We present a work of promoted optical nonreciprocity (ONR) in an asymmetrical cavity containing two asymmetrically arranged two-level atoms with a weak atom-atom interaction. The input-output relation is worked out by using a perturbative approach. Results show that the bistable-monostable-bistable phase transition would exist when the second atom is present, where the optical bistability and nonreciprocity change considerably. Contributions of two types of spatial asymmetries suggest that the ONR originates from the cooperation of the cavity spatial symmetry breaking and the optical nonlinearity, regardless of the atomic spatial symmetry breaking. In addition to the experimentally proved bistable ONR, a type of monostable ONR is proposed, which operates in the monostable phase. Both the ONR optimal regime and the block rate are boosted by adding the other atom in the cavity. Our findings suggest a prospective approach to the generation of a giant ONR by two atoms with unequal atom-cavity coupling strengths.

An unextendible biseparable basis (UBB) is a set of orthogonal pure biseparable states which span a subspace of a given Hilbert space while the complementary subspace contains only genuinely entangled states. These biseparable bases are useful to produce genuinely entangled subspace in a multipartite system. Such a subspace could be more beneficial for information theoretic applications if we were able to extract distillable entanglement across every bipartition from each state of this subspace. In this paper, we have derived a rule for constructing such a class of UBB which exhibits the phenomenon of strong quantum nonlocality. This result positively answers the open problem raised by Agrawal et al. [Agrawal, Halder, and Banik, Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition, Phys. Rev. A 99, 032335 (2019)], that there exists a UBB which can demonstrate the phenomenon of strong quantum nonlocality in the perspective of the local irreducibility paradigm.

We present an implementation of a recently proposed procedure for defining time, based on the description of the evolving system and its clock as noninteracting, entangled systems, according to the Page and Wootters approach. We study how the quantum dynamics transforms into a classical-like behavior when conditions related to macroscopicity are met by the clock alone, or by both the clock and the evolving system. In the description of this emerging behavior finds its place the classical notion of time, as well as that of phase-space and trajectories on it. This allows us to analyze and discuss the relations that must hold between quantities that characterize the system and clock separately, in order for the resulting overall picture to be that of a physical dynamics as we mean it.

Estimating the eigenvalue or energy gap of a Hamiltonian $H$ is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed-matter physics, and nuclear physics investigate the energy gap between two eigenstates. Hence, how to efficiently solve the energy gap becomes an important motive for researching new quantum algorithms. In this work, we propose a hybrid nonvariational quantum algorithm that uses the Monte Carlo method and real-time Hamiltonian simulation to evaluate the energy gap of a general quantum many-body system. Compared to conventional approaches, our algorithm does not require controlled real-time evolution, thus making its implementation much more experimental friendly for near-term quantum devices and early fault-tolerant quantum computers. To verify the efficiency of our algorithm, we conduct numerical simulations for the Heisenberg model and molecule systems on a classical emulator.

Quantum error correction (QEC) exploits redundancy by encoding logical information into multiple physical qubits. In current implementations of QEC, sequences of nonperfect two-qubit entangling gates are used to codify the information redundantly into multipartite entangled states. Also, to extract the error syndrome, a series of two-qubit gates are used to build parity-check readout circuits. In the case of noisy gates, both steps cannot be performed perfectly, and an error model needs to be provided to assess the performance of QEC. We present a detailed microscopic error model to estimate the average gate infidelity of two-qubit light-shift gates used in trapped-ion platforms. We analytically derive leading-error contributions in terms of microscopic parameters and present effective error models that connect the error rates typically used in phenomenological accounts to the microscopic gate infidelities hereby derived. We then apply this realistic error model to quantify the multipartite entanglement generated by circuits that act as QEC building blocks. We do so by using entanglement witnesses, complementing in this way the recent studies in Ref. [Phys. Rev. X 12, 011032 (2022); PRX Quantum 2, 020304 (2021)] by exploring the effects of a more realistic microscopic noise.

We consider the discrimination of bipartite quantum states and establish a relation between a nonlocal quantum state ensemble and quantum data-hiding processing. Using a bound on the optimal local discrimination of bipartite quantum states, we provide a sufficient condition for a bipartite quantum state ensemble to be used to construct a quantum data-hiding scheme. Our results are illustrated with examples in multidimensional bipartite quantum systems.

We bound the time necessary to implement the shift unitary on a one-dimensional ring, both by using local Hamiltonians and those with power-law interactions. This time is constrained by the Frobenius light cone; hence we prove that (for certain power-law exponents) shift unitaries cannot be implemented in the same amount of time needed to prepare long-range Bell pairs. We note an intriguing similarity between the proof of our results and the hardness of preparing symmetry-protected topological states with symmetry-preserving Hamiltonians.

We compare trajectory-surface-hopping (TSH) calculations of the dissociation of quadruply charged formaldehyde molecules with basic classical calculations assuming Coulomb repulsion between singly charged atoms. The TSH calculations show very different dissociation dynamics from the classical Coulomb calculations, illustrating that Coulomb repulsion between point charges does not accurately describe the dissociation dynamics. By comparing the calculations with covariance measurements, we see much better agreement between the experiments and the TSH calculations, and evidence for the production of multiple electronic states of the tetracation via strong-field ionization.

In this work, we theoretically study the role of the spatial chirped pulse in the Cherenkov second-harmonic generation in one-dimensional nonlinear photonic crystals. We show that the spatial chirped input with narrower spectral peaks but wider angular distribution can be used to cancel the natural dispersion of crystals, fitting the phase-matching condition at wider emission angles. Contrary to popular belief, the phase-matching bandwidth can remain almost unchanged with the growth of interaction length, leading to a substantial increase in the signal strength and bandwidth under long interaction. The improvement ratio of the signal can be as high as needed, if the beam waist and the interaction length are large enough.

Highly reflecting mechanically compliant membranes based on photonic-crystal patterns have recently gained increasing attention within cavity optomechanics due to their prospects of reaching high coupling rates in membrane-in-the-middle experiments. Here, we present an analysis and comparison of four different setups in which highly reflecting membranes can be employed for cavity optomechanics and discuss optimal choices with respect to the figures of merit: cooperativity and efficiency-weighted cooperativity. The analysis encompasses three different types of membrane-in-the-middle setups (membrane at the edge, membrane in the actual middle, and membrane at the back), as well as the simple Fabry-Pérot cavity. Interestingly, we identify and propose the membrane-at-the-back setup as an optimal choice in the limit of negligible membrane parasitic loss, which can reach enormous enhancements of optomechanical cooperativity and, if implemented with a low-loss membrane, would pave the way to nonlinear optomechanics in the quantum regime.

Many novel wave phenomena have been observed in parity-time $\left(\mathcal{P}\mathcal{T}\right)$-symmetric optical waveguides with a balanced gain and loss. These phenomena are highly related to the eigenmodes which are solutions of Maxwell's equation without sources. An eigenmode is associated with a propagation constant and an angular frequency. Most existing studies are concerned with guided modes at a real frequency. In this paper, we analyze various eigenmodes in a $\mathcal{P}\mathcal{T}$-symmetric slab waveguide, including guided modes with a complex frequency or a complex propagation constant, leaky modes, resonant modes, lasing-threshold modes, and perfect-absorption modes. We study the dispersion curves of eigenmodes and focus on the connection between the real and complex eigenmodes. It is observed that as the amplitude of balanced gain and loss is varied, there exist a few transition points where the connections between real and complex eigenmodes exhibit abrupt changes. In particular, there exists a transition point corresponding to the emergence of lasing-threshold and perfect-absorption modes. It is expected that the wave phenomena revealed in this paper are generic and can be found in other $\mathcal{P}\mathcal{T}$-symmetric waveguides. Our work improves theoretical understanding on $\mathcal{P}\mathcal{T}$-symmetric waveguides, and may have potential applications in non-Hermitian photonics.

We show that the Schrödinger equation can be derived assuming the Galilean covariance of a generic wave equation and the validity of the de Broglie's wave-particle duality hypothesis. We also obtain from this set of assumptions the transformation law for the wave function under a Galilean boost and prove that complex wave functions are unavoidable for a consistent description of a physical system. The extension to the relativistic domain of the above analysis is also provided. We show that Lorentz covariance and wave-particle duality are consistent with two different transformation laws for the wave function under a Lorentz boost. This leads to two different wave equations, namely, the Klein-Gordon equation and the Lorentz covariant Schrödinger equation.

The correlation function in quantum systems plays a vital role in decoding their properties and gaining insights into physical phenomena. Its interpretation corresponds to the propagation of particle excitations between space-time, similar in spirit to the idea of quantum weak measurement in terms of recording the system information by interaction. By defining weak-valued correlation function, we propose the basic insights and the universal methods for recording them on the apparatus through weak measurement. To demonstrate the feasibility of our approach, we perform numerical experiments of perturbed quantum harmonic oscillators, addressing the intricate interplay between the coupling strength and the number of ensemble copies. Additionally, we extend our protocol to the domain of quantum field theory, where joint weak values encode crucial information about the correlation function. Hopefully, this comprehensive investigation can advance our understanding of the fundamental nature of the correlation function and weak measurement in quantum theories.

Imaginary-time evolution is a powerful tool in the study of quantum physics. However, existing classical algorithms for simulating imaginary-time evolution suffer from high computational complexity as the dimension of the quantum system increases. In this study we propose a quantum algorithm for implementing imaginary-time evolution using nonunitary quantum circuits with one ancillary qubit. The success probability of our algorithm is a polynomial function of the output error and can be enhanced by reorganizing the terms of the Hamiltonian. To illustrate the practicality of our algorithm on current quantum devices, we conduct a demonstration on superconducting and trapped-ion quantum processors to calculate the ground-state energy and determine the most stable molecular structure of ${\mathrm{H}}_2$. Additionally, we validate the feasibility of our algorithm by numerically simulating the ground-state energies of LiH molecules and the quantum Ising chain. In contrast to existing algorithms, our method provides a systematic approach to construct the required nonunitary circuits using universal quantum gates, making it suitable for experimental implementation. Our algorithm opens up possibilities for exploring other physical phenomena such as finite-temperature properties and non-Hermitian systems.