We study the electromagnetic behavior of dense, spherical clusters made of hundreds of plasmonic nanoparticles under illumination by a plane wave. Using high-precision T-matrix numerical calculations, we compute the multipolar response of clusters up to 80 nm in radius and up to 44% in particle volume fraction. We then investigate whether it is possible to obtain an effective-medium description for the clusters, taking into account weak spatial dispersion in a fully consistent way. We find that the average scattered field as well as the average inner field of the spherical cluster can be accurately reproduced by applying an extended Mie theory to an equivalent homogeneous sphere characterized by three effective parameters: an electric permittivity ${\varepsilon }_{\mathrm{eff}}$ and a magnetic permeability ${\mu }_{\mathrm{eff}}$, associated to transverse modes, and a wave vector $k_{\mathrm{L}}$, associated to a longitudinal mode in the sphere. Our results show that artificial magnetism arises from interparticle couplings in the dense cluster, despite inclusions not displaying any individual magnetic dipole. We also find that, although largely overlooked in the literature on metamaterials, the presence of the longitudinal mode is essential to accurately reproduce the fields of the cluster, on par with the role of artificial magnetism. Our paper therefore proves that, even for high concentration in inclusions, it is possible empirically to treat a cluster of plasmonic particles as a sphere made of a spatially dispersive homogeneous medium. This offers a practical solution facilitating the computation of electromagnetic responses of such dense random media in diverse configurations of interest for the design of metamaterials and metasurfaces.

We propose and analyze a scheme for manipulating the propagation of single-photon pulses with two polarization components in a Rydberg atomic gas via double electromagnetically induced transparency. We show that by storing a gate photon in a Rydberg state, a deep and tunable potential for a photon polarization qubit can be achieved based on the strong Rydberg interaction. We also show that the scheme can be used to realize an all-optical switch in the dissipation regime and generate a large phase shift in the dispersion regime for the photon polarization qubit. Moreover, we demonstrate that such a scheme can be utilized to detect weak magnetic fields. The results reported here are not only beneficial for understanding the quantum optical property of Rydberg atomic gases, but also promising for designing devices for quantum information processing.

We propose a fast scheme to generate Schrödinger cat states in a superconducting resonator using a continuously driven qubit without resorting to the dispersive regime, two-photon drives, or engineered two-photon dissipation. We provide analysis for when the qubit is on and off resonance from the drive. We extend our analysis to account for a third level in a weakly anharmonic qutrit. We also discuss the case of a strongly anharmonic qutrit. Throughout the paper, we corroborate our analytical results with numerical simulations in the presence of energy relaxation and dephasing of the qubit and resonator using realistic experimental parameters.

The Zou-Wang-Mandel (ZWM) effect is a remarkable consequence of photon indistinguishability and continuous-variable entanglement in which an optical phase shift is imprinted on photonic modes associated with optical paths that do not pass through the phase-shift source. By bringing the canonical formalism of continuous-variable Gaussian states to bear on the mode structure of the ZWM experiment, we show that the physical consequence of implementing optical path identity is a renormalization of quadrature squeezing which governs the entanglement of four effective optical modes. Nonperturbative expressions for the ZWM interference patterns and normalized first-order coherence function are derived. Generalizations to $\mathcal{H}$-graph states with more than four modes directly follow from the general method used to analyze the minimal example. We show that a ZWM interferometer with a laser-seeded signal mode, which estimates an idler phase shift by detecting photons that did not propagate through the phase shift, exhibits an optimal sensitivity comparable to that of a laser-seeded SU(1,1) interferometer if the path identity is implemented with high fidelity.

A coherent electromagnetic field can be described by its amplitude, frequency, and phase. All these properties can influence the interaction between the field and an atom. Here we demonstrate the phase shaping of microwaves that are scattered by a superconducting artificial atom coupled to the end of a semi-infinite one-dimensional transmission line. In particular, we input a weak exponentially rising pulse with phase modulation to a transmon qubit. We observe that atom-field interaction can be tuned from a nearly full interaction (interaction efficiency, i.e., amount of the field energy interacting with the atom, of 94.5 %) to effectively no interaction (interaction efficiency of 3.5 %).

There are bipartite quantum nonlocal correlations requiring very low detection efficiency to reach the loophole-free regime but that need too many measurement settings to be practical for actual experiments. This leads to the general problem of what can be concluded about loophole-free Bell nonlocality if only a random subset of these settings is tested. Here we develop a method to address this problem. We show that, in some cases, it is possible to detect loophole-free Bell nonlocality by testing only a small random fraction of the settings. The consequence is a higher detection efficiency. The method allows for the design of loophole-free Bell tests in which, given a quantum correlation that violates a Bell inequality, one can calculate the minimum fraction of contexts needed to reach the detection-loophole-free regime. The results also enforce a different way of thinking about how local realistic models or classical communication can be used to simulate quantum nonlocal correlations, as it shows that the amount of resources that are needed can be made arbitrarily large simply by considering more contexts.

Quantum nonlocality and the uncertainty principle are two fundamental cornerstones of quantum theory, reflecting totally different aspects that distinguish it from classical theory. However, Oppenheim and Wehner introduced fine-grained uncertainty relations (FGURs) to account for the degree of quantum nonlocality. In the simplest Bell scenario, they showed that the quantum nonlocality measured by the maximal violation of some Bell inequality was determined by the FGUR. Along this line of research, we first derive explicit FGURs with general weights about probability distributions of two general projective measurements on local systems. Then we split those joint probabilities of Bell inequalities into a single-party conditional probability and the remaining joint probabilities so that the weighted FGURs can be applied straightforwardly to obtain the maximal violation in various scenarios ranging from bipartite, tripartite, to a complete set of multipartite Bell inequalities. Furthermore, in the bipartite scenario, the exact correlation boundary can be shown to be solely determined by our weighted local FGURs.

A driven quantum system can experience Landau-Zener-Stückelberg-Majorana (LZSM) transitions between its states when the respective energy levels quasicross. If this quasicrossing is traversed repeatedly under periodic driving, the trajectories can interfere either constructively or destructively. In the latter case, known as coherent destruction of tunneling, the transition between the energy states is suppressed. Even for the double-passage case, the accumulated phase difference (also referred to as the Stückelberg phase) can lead to destructive interference, resulting in no transition. In this paper, we discuss a similar process for the single-passage dynamics. We study the LZSM single-passage problem starting from a superposition state. The phase difference of this initial state results in interference. When this results in either a zero or a unit transition probability, such a situation can be called single-passage complete localization in a target state. The phase can be chosen so that the occupation probabilities do not change after the transition, which is analogous to the problem of transitionless driving. We demonstrate how varying the system parameters (driving velocity, initial phase, initial detuning) can be used for quantum coherent control.

Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is corrupted or intact, a step known as syndrome detection is performed. For stabilizer codes, this step consists of measuring a set of stabilizer operators. In this paper, inspired by the QEC approach, and specifically stabilizer codes, we propose a prototype quantum circuit model for classification of classical data. The core quantum circuit can be considered as a quantum perceptron where the classification is based on syndrome detection. In this proposal, a quantum perceptron is realized by one stabilizer as part of a stabilizer code, while a quantum neural network (QNN) layer is realized by a stabilizer code which consists of many stabilizers. The concatenation of stabilizer codes results in complex QNNs. The QNN is trained by performing measurements and optimization of a set of parametrized stabilizers. We demonstrate the concept numerically. In this paper we also consider the first challenge to most applications of quantum computers, including data classification, which is to load data into the memory of the quantum computer. This loading amounts to representing the data as a quantum state, i.e., quantum state preparation. An exact amplitude encoding algorithm requires a circuit of exponential depth. We introduce an alternative recursive algorithm which approximates amplitude encoding with only a polynomial number of elementary gates. We name it the recursive approximate-scheme algorithm.

Supersolids are a phase of matter exhibiting both superfluidity and a periodic density modulation typical of crystals. When formed via quantum phase transition from a superfluid, they require a formation time before their density pattern develops. In this paper protocols and schemes are proposed for experimental applications, building on earlier descriptions of the role roton instability plays in the supersolid formation process and the associated formation time. In particular, two protocols are put forward to shorten the formation time and lessen the excitation produced when crossing the phase transition. As a case study of the impact that mechanical fluctuations (noise) can have on the phase transition when conducting an experiment, the impact of a mechanical kick before the transition is also investigated. The proposed schemes achieve a shortening of the formation process for comparable levels of excitation, in the framework of extended Gross-Pitaevskii theory.

We theoretically investigate the pure dephasing dynamics of two static impurity qubits embedded within a common environment of ultracold fermionic atoms, which are confined to one spatial dimension. Our goal is to understand how bath-mediated interactions between impurities affect their performance as nonequilibrium quantum thermometers. By solving the dynamics exactly using a functional determinant approach, we show that the impurities become correlated via retarded interactions of the Ruderman-Kittel-Kasuya-Yosida type. Moreover, we demonstrate that these correlations can provide a metrological advantage, enhancing the sensitivity of the two-qubit thermometer beyond that of two independent impurities. This enhancement is most prominent in the limit of low temperature and weak collisional coupling between the impurities and the gas. We show that this precision advantage can be exploited using standard Ramsey interferometry, with no need to prepare correlated initial states or to individually manipulate or measure the impurities. We also quantitatively assess the impact of ignoring these correlations when constructing a temperature estimate, finding that acceptable precision can still be achieved in some parameter regimes using a simplified model of independent impurities. Our results demonstrate the rich nonequilibrium physics of impurities dephasing in a common Fermi gas, and may help to provide better temperature estimates at ultralow temperatures.

The eigenstate thermalization hypothesis describes how most isolated many-body quantum systems reach thermal equilibrium. However, the hypothesis is violated by phenomena such as many-body localization and quantum many-body scars. In this work, we study a finite, two-dimensional, disordered model hosting a tower of scar states. This construction is a particular instance of a general framework and we demonstrate its generality by constructing two disordered models hosting a different tower of scar states. At weak disorder, we find numerically that the spectra are nonthermal, and the scar states appear as exact eigenstates with high entropy for certain bipartitions. At strong disorder, the spectra localize and the scar states are identified as inverted scars since the scar states are embedded in a localized background as opposed to a thermal background. We argue that, for the considered type of models, the localization is stronger than what would be naively expected, and we show this explicitly for one of the models. The argument also provides guidelines for obtaining similarly strong localization in other scarred models. We study the transition from the thermal phase to localization by observing the adjacent gap ratio shifting from the Wigner surmise to the Poisson distribution with increasing disorder strength. Moreover, the entanglement entropy transitions from volume-law scaling with system size at weak disorder to area-law scaling at strong disorder. Finally, we demonstrate that localization protects scar revivals for initial states with partial support in the scar subspace.

Atom losses occur naturally during cold atoms experiments. Since this phenomenon is unavoidable, it is important to understand its effect on the remaining atoms. Here we investigate a toy model: a lattice gas of hard-core bosons subject to $K$-body losses (where $K=1,2,3,\cdots ,$ is the number of atoms lost in each loss event) on $K$ neighboring sites. In particular, we investigate the effect of losses on the rapidity distribution $\rho \left(k\right)$ of the atoms. Under the assumption that losses are weak enough so that the system relaxes between two loss events, we are able to determine the loss functional $F\left[\rho \right]\left(k\right)$ encoding the loss process for $K$-body losses. We derive closed expressions for the cases of one- and two-body losses and show their effects on the evolution of the total number of particles. Then we add a harmonic trapping potential and study the evolution of the position-dependent rapidity distribution of this system by solving numerically the evolution equation for one-, two-, and three-body losses.

We explore the spatial features of various orders of Fraunhofer diffraction patterns in a four-level $N$-type atomic system. The system interacts with a weak probe light, a standing wave (SW) coupling field in the $x$ direction, and a cylindrical beam of composite optical vortex type. We derive the first-order linear and third-order cross-Kerr nonlinear parts of the probe susceptibility by expanding the probe susceptibility of the system into the second order of the SW beam. This allows us to solve the integral equation of Fraunhofer diffraction, decoding its varying degrees to specific degrees of Bessel functions containing the nonlinear susceptibility. Notably, the nonlinear susceptibility exhibits dependence on the orbital angular momentum (OAM) of the light beam, leading to spatial variations in the Bessel functions, and consequently, in the different orders of Fraunhofer diffraction. Leveraging the manipulation of OAM, we achieve precise control over the spatial mapping of diverse diffraction orders at various locations. Our research sheds light on the spatial behavior of Fraunhofer diffraction in complex atomic systems. It presents exciting prospects for harnessing the OAM characteristics of light in future optical technologies.

We build a machine learning model to detect correlations in a three-qubit system using a neural network trained in an unsupervised manner on randomly generated states. The network is forced to recognize separable states, and correlated states are detected as anomalies. Quite surprisingly, we find that the proposed detector performs much better at distinguishing a weaker form of quantum correlations, namely, the quantum discord, than entanglement. In fact, it has a tendency to grossly overestimate the set of entangled states even at the optimal threshold for entanglement detection, while it underestimates the set of discordant states to a much lesser extent. In order to illustrate the nature of states classified as quantum correlated, we construct a diagram containing various types of states—entangled, as well as separable, both discordant and nondiscordant. We find that the near-zero value of the recognition loss reproduces the shape of the nondiscordant separable states with high accuracy, especially considering the nontrivial shape of this set on the diagram. The network architecture is designed carefully: it preserves separability, and its output is equivariant with respect to qubit permutations. We show that the choice of architecture is important to get the highest detection accuracy, much better than for a baseline model that just utilizes a partial trace operation.

We consider a spatial analogue of the quantum error correction threshold. Given individual time-independent subsystems in which quantum information is coherent over sufficiently long lengths, we show how the information can be kept coherent for arbitrarily long lengths by forming time-independent composite systems. The subsystem coherence range exhibits threshold behavior. When it exceeds a range ${\xi }_{\mathrm{th}}$, meaningful information can be extracted from the ground state of the composite system. Otherwise, the information is garbled. The threshold transition implies that the parent Hamiltonian of the ground state has gone from gapped to gapless. Ramifications of the construction for projected entangled pair states and for adiabatic quantum computation are considered.

We consider quantum two-block group algebra (2BGA) codes, a family of smallest lifted-product (LP) codes. These codes are related to generalized-bicycle codes, except a cyclic group is replaced with an arbitrary finite group, generally non-Abelian. As special cases, 2BGA codes include a subset of square-matrix LP codes over Abelian groups, including quasicyclic codes, and all square-matrix hypergraph-product codes constructed from a pair of classical group codes. We establish criteria for permutation equivalence of 2BGA codes and give bounds for their parameters, both explicit and in relation to other quantum and classical codes. We also enumerate the optimal parameters of all inequivalent binary connected 2BGA codes with stabilizer generator weights $W\le 8$, of length $n\le 100$ for Abelian groups, and $n\le 200$ for non-Abelian groups.

Quantum computers have the potential for a significant speedup of molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) is intractable on current hardware while variational quantum eigensolvers (VQE) are dependent upon approximate wave functions without guaranteed convergence. In this paper we present an algorithm that yields verifiably exact solutions of the many-electron Schrödinger equation. Rather than solve the Schrödinger equation directly, we solve its contraction over all electrons except two, known as the contracted Schrödinger equation (CSE). The CSE generates a wave-function Ansatz, constructed from an iterative product of nonunitary two-body transformations, whose energy gradient with respect to the two-body operator of the current iteration vanishes if and only if the CSE is satisfied. Because the CSE implies the Schrödinger equation, the two-electron Ansatz provides a verifiably exact Ansatz for solving the many-electron Schrödinger equation. The exactness property contrasts with that of Ansätze built from the product of unitary two-body transformations where the gradient—the residual of the anti-Hermitian part of the CSE (ACSE)—can vanish without implying a solution of the Schrödinger equation. We demonstrate the algorithm on both simulators and noisy quantum computers with ${\mathrm{H}}_2$ dissociation and the rectangle-to-square transition in ${\mathrm{H}}_4$.

By solving the time-dependent Schrödinger equation in momentum space, the photoelectron emission from atoms under the irradiation of 400 nm sinusoidal phase-modulated shaped pulses was investigated. It was found that by controlling the phase and amplitude of the pulses in the frequency domain, in addition to the photoelectron peaks generated by the interference of multiple-cycle ionization, additional resonant peak structures and interference phenomena can be observed in the photoelectron emission spectrum. Through the analysis of photoelectrons from different subpulses within the shaped pulse, it was discovered that these structures arise from the modulation of ionization and excitation processes by multiple subpulses within the shaped pulse. This study demonstrates the significant importance of utilizing shaped pulses for the control of photoelectron emission.