Utilizing the fact that the frequency response of a material can be decomposed into the quasinormal modes supported by the system, we present two methods to directly manipulate the complex frequencies of quasinormal modes in the complex plane. We first consider an “eigenpermittivity” approach that allows one to find how to shift the permittivity of the structure everywhere in order to place a single quasinormal mode at a desired complex frequency. Secondly, we then use perturbation theory for quasinormal modes to iteratively change the structure until a given selection of quasinormal modes occurs at desired complex frequencies.

Guided-mode resonant gratings with spatially varying parameters are widely used as linear variable optical filters, and their behavior is often described using the so-called local periodic approximation, in which the structure is locally replaced by a strictly periodic grating with the period coinciding with the “local” period at the considered point. In this work, we investigate the optical properties of guided-mode resonant gratings with the period linearly varying along the periodicity direction. Using full-wave numerical simulations, we show that when the period change rate is relatively high (about 0.5–1 $\mu \mathrm{m}/\mathrm{mm}$ for the considered structures), the local periodic approximation becomes inapplicable, and the linewidth and the line shape of the resonances depend significantly on the period change rate. We qualitatively explain the appearance of an asymmetric non-Fano line shape with secondary maxima by analyzing the local photonic band structure of the studied varying-period gratings. For a more accurate description of such gratings, we develop a spatiotemporal coupled-mode theory, the predictions of which are in good agreement with the rigorous numerical simulation results. The validity of the derived theoretical model is additionally confirmed by a proof-of-concept experiment with a varying-period guided-mode resonant grating. The obtained results may find application in the design of compact linear variable filters based on resonant gratings with spatially varying parameters.

Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave-particle properties of single photons (or single particles in general) showed that a well-defined interferometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with a Bell state. By doing so, we experimentally test the complementarity principle in a scenario in which the setting of the interferometer is not defined at any instance of the experiment, not even in principle. To achieve this goal, we establish the three-photon entangled state, i.e., the entanglement between a single photon and a two-photon Bell state, send the photon of interest $S$ into a quantum Mach-Zehnder interferometer (MZI), in which the output beam splitter of the MZI is controlled by the quantum state of the second photon $C$, which is entangled with a third photon $A$. Therefore, the individual quantum state of photon $C$ is undefined, which implements the undefined settings of the MZI for photon $S$. This is realized by using three cascaded phase-stable interferometers for three photons. There is typically no well-defined setting of the MZI and thus the very formulation of the wave-particle objectivity from local hidden variable models becomes internally inconsistent.

Highly entangled biphoton states, generated by spontaneous parametric processes, find wide applications in many experimental realizations. There is an increasing demand for accurate prediction of their time-dependent detection. Unlike approaches that have emerged so far, this paper presents an approach providing full time-dependent counting statistics in terms of efficiently computable formulas, valid for a wide range of entanglement and arbitrary interaction times. General spatial modes are taken into account to describe free space and fiber propagation. The time intervals that correspond to the statistics are classified according their widths. Apart from large and small widths compared to the temporal correlation width, intermediate interval widths give access to accidental correlations between separated time intervals. Moreover, the approach is easily applicable to a modular array of arbitrary optical components and external influences. This is demonstrated on phase-time coding, where the detuning of the interferometers affecting Franson interference is investigated. An acceptable range for the detuning is estimated, such that the security of the key is not compromised.

Superradiance and subradiance are collective effects that emerge from coherent interactions between quantum emitters. Due to their many-body nature, theoretical studies of extended samples with length larger than the atomic transition wavelength are usually restricted to their early-time behavior or to the few-excitation limit. We use herein a mean-field approach to reduce the complex many-body system to an effective two-atom master equation that includes all correlations up to second order and that can be numerically propagated in time. We find that three-dimensional and two-dimensional inverted atomic arrays sustain superradiance below a critical lattice spacing and quantify the scaling of the superradiant peak for both dimensionalities. Finally, we study the late-time dynamics of the system and demonstrate that a subradiant phase appears before the system finally relaxes.

In a recent publication Bibikov et al. [Phys. Rev. A 105, 022813 (2022)], theoretically investigated the structures of one or two boron atoms binding in endohedral or exohedral positions of ${\mathrm{C}}_{60}$. We found their theoretical methods, i.e., HF/6-31G for structure optimization, may not be reliable, and therefore some of the structures identified as the most stable ones could be incorrect. Our more extensive and systematic calculations on these ${\mathrm{C}}_{60}/\mathrm{B}$ complexes have corrected those deficiencies, and redetermined the most stable structures for those complexes with higher reliability.

We investigate the anomalous energy change of the measurement apparatus when a qubit is measured in bases that do not commute with energy. We model two possible measurement implementations: one is a quantum clock model with a completely time-independent Hamiltonian, while the other is a Jaynes-Cummings model that is time-dependent but conserves the total excitation number. We look at the mean energy change of the measurement apparatus in both models, conditioned on the qubit postselection, and we find that this change can be much greater than the level spacing of the qubit, like an anomalous weak value. In the clock model, the expression for the apparatus energy shift explicitly contains the weak value of the qubit Hamiltonian. However, in our case, no explicit weak measurements are carried out. Our two models give different results, which we explain to be a consequence of the nondegenerate spectrum of the Jaynes-Cummings model. We compare our calculations in the Jaynes-Cummings model with the experimental data of J. Stevens et al., [Phys. Rev. Lett. 129, 110601 (2022)], and we find good agreement when the conditions of our derivation are valid.

A quantum metrology scheme can be decomposed into three quantum tasks: state preparation, parameter encoding, and measurements. Consequently, it is imperative to have access to the technologies which can execute the aforementioned tasks to fully implement a quantum metrology scheme. In the absence of one or more of these technologies, one can proceed by delegating the tasks to a third party. However, doing so has security ramifications: the third party can bias the result or leak information. In this paper, we outline different scenarios where one or more tasks are delegated to an untrusted (and possibly malicious) third party. In each scenario, we outline cryptographic protocols which can be used to circumvent malicious activity. Further, we link the effectiveness of the quantum metrology scheme to the soundness of the cryptographic protocols.

Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space. In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with ${\mathbb{Z}}_N$ and $\text{U}\left(1\right)$ symmetry groups. To this end, we develop a diagrammatic method to incorporate partial transpose within the random matrix theory of symmetric states and formulate a perturbation theory in the inverse of the Hilbert space dimension. We further present entanglement phase diagrams as the subsystem sizes are varied and show that there are qualitative differences between systems with and without symmetries. We also design a quantum circuit to simulate our setup.

Active optical frequency standards provide interesting alternatives to their passive counterparts. Particularly, such a clock alone continuously generates highly stable narrow-line laser radiation. Thus, a local oscillator is not required to keep the optical phase during a dead time between interrogations as in passive clocks, but only to boost the active clock's low output power to practically usable levels with the current state of technology. Here we investigate the spectral properties and the stability of active clocks, including homogeneous and inhomogeneous broadening effects. We find that for short averaging times the stability is limited by photon shot noise from the limited emitted laser power and at long averaging times by phase diffusion of the laser output. Operational parameters for best long-term stability were identified. Using realistic numbers for an active clock with ${}^{87}\mathrm{Sr}$, we find that optimized stability of ${\sigma }_y\left(\tau \right)\approx 4\times {10}^{-18}/\sqrt{\tau \left[\mathrm{s}\right]}$ is achievable.

We provide a number-conserving approach to the backreaction problem of small quantum fluctuations onto a classical background for the exactly soluble dynamical evolution of a quasi-one-dimensional Bose-Einstein condensate, experimentally realizable in the ultracold gas laboratory. A force density exerted on the gas particles, which is of quantum origin, is uniquely identified as the deviation from the classical Eulerian force density. The backreaction equations are then explored for the specific example of a finite-size uniform density condens- ate initially at rest. By assuming that the condensate starts from a noninteracting regime and in its ground state, we fix a well-defined initial vacuum condition, which is driven out of equilibrium by instantaneously turning on the interactions. The assumption of this initial vacuum accounts for the ambiguity in choosing a vacuum state for interacting condensates, which is due to phase diffusion and the ensuing condensate collapse. As a major finding, we reveal that the time evolution of the condensate cloud leads to condensate density corrections that cannot in general be disentangled from the quantum depletion in measurements probing the power spectrum of the total density. Furthermore, while the condensate is initially at rest, quantum fluctuations give rise to a nontrivial condensate flux, from which we demonstrate that the quantum force density attenuates the classical Eulerian force. Finally, the knowledge of the particle density as a function of time for a condensate at rest determines, to order $N^0$ (where $N$ is the total number of particles), the quantum force density, thus offering a viable route for obtaining experimentally accessible quantum backreaction effects.

We establish a general framework for studying the bound states and the photon-emission dynamics of quantum emitters coupled to structured nanophotonic lattices with engineered dissipation (loss). In the single-excitation sector, the system can be described exactly by a non-Hermitian formalism. We have pointed out in the accompanying letter [Gong et al., Phys. Rev. Lett. 129, 223601 (2022)] that a single emitter coupled to a one-dimensional non-Hermitian lattice may already exhibit anomalous behaviors without Hermitian counterparts. Here we provide further details on these observations. We also present several additional examples on cases with multiple quantum emitters or in higher dimensions. Our work unveils the tip of the iceberg of rich non-Hermitian phenomena in dissipative nanophotonic systems.

Chiral coupling at the single-quantum level promises to be a remarkable potential for quantum information processing. Here we propose to achieve a chiral interaction between a magnon mode in a ferromagnetic sphere and a superconducting qubit mediated by a one-dimensional coupled-cavity array. When the qubit is coupled to two lattice sites of the array and each one is encoded with a tunable phase, we can acquire a directional qubit-magnon interaction via the quantum interference effect. This work opens up an alternative route to construct chiral devices, which are expected to become a building block in quantum magnonic networks.

A gauge-invariant Wigner quantum mechanical theory is obtained by applying the Weyl-Stratonovich transform to the von Neumann equation for the density matrix. The transform reduces to the Weyl transform in the electrostatic limit, when the vector potential and thus the magnetic field are zero. Both cases involve a center-of-mass transform followed by a Fourier integral on the relative coordinate introducing the momentum variable. The latter is continuous if the limits of the integral are infinite or, equivalently, the coherence length is infinite. However, the quantum theory involves Fourier transforms of the electromagnetic field components, which imposes conditions on their behavior at infinity. Conversely, quantum systems are bounded and often very small, as is, for instance, the case in modern nanoelectronics. This implies a finite coherence length, which avoids the need to regularize nonconverging Fourier integrals. Accordingly, the momentum space becomes discrete, giving rise to momentum quantization and to a semidiscrete gauge-invariant Wigner equation. To gain insights into the peculiarities of this theory one needs to analyze the equation for specific electromagnetic conditions. We derive the evolution equation for the linear electromagnetic case and show that it significantly simplifies for a limit dictated by the long coherence length behavior, which involves momentum derivatives. In the discrete momentum picture these derivatives are presented by finite difference quantities which, together with further approximations, allow to develop a computationally feasible model that offers physical insights into the involved quantum processes. In particular, a Fredholm integral equation of the second kind is obtained, where the “power” of the kernel components, measuring their rate of modification of the quantum evolution, can be evaluated.

We study the effects of entanglement and control parameters on the symmetry of the energy landscape and optimization performance of the variational quantum circuit. Through a systematic analysis of the Hessian spectrum, we characterize the local geometry of the energy landscape at a random point and along an optimization trajectory. We argue that decreasing the entangling capability and increasing the number of circuit parameters have the same qualitative effect on the Hessian eigenspectrum. Both the low-entangling capability and the abundance of control parameters increase the curvature of nonflat directions, contributing to the efficient search of area-law entangled ground states as to the optimization accuracy and the convergence speed.

The quantum long-range extended Ising model possesses several striking features which cannot be observed in the corresponding short-range model. We report that the pattern obtained from the entanglement between any two arbitrary sites of the long-range model can be mimicked by the model having a finite range of interactions provided the interaction strength is moderate. On the other hand, we illustrate that when the interactions are strong, the entanglement distribution in the long-range model does not match the class of a model with a few interactions. We also show that the monogamy score of entanglement is in good agreement with the behavior of pairwise entanglement. Specifically, it saturates when the entanglement in the finite-range Hamiltonian behaves similarly to the long-range model, while it decays algebraically otherwise.

Topology identification comprises reconstructing the Hamiltonian, and thus the corresponding interaction terms, by properly processing measurements of its density operator within a fixed time interval. It finds application in several quantum technology contexts, ranging from quantum communication to quantum computing or sensing. In this paper we provide analytical conditions for the solvability of the topology identification problem for autonomous quantum dynamical networks (i.e., as in our case, not explicitly depending on time via the use of an external drive). The solvability condition is then converted in an algorithm for quantum network reconstruction that is easily implementable on standard computer facilities. The obtained algorithm is tested for Hamiltonian reconstruction on numerical examples based on the quantum walks formalism.

We study optimal quantum control robust against pulse inhomogeneities for various partial population transfers and single-qubit gates by inverse optimization. We show that the pulse is constant for time or energy minimization and we provide the analytic form of the detuning as Jacobi elliptic cosines. The performance of composite pulse techniques, which we optimize for the case of complete population transfer, is compared to this optimal bound.