We quantify the impact of spatiotemporally correlated Gaussian quantum noise on frequency estimation by Ramsey interferometry. While correlations in a classical noise environment can be exploited to reduce uncertainty relative to the uncorrelated case, we show that quantum noise environments with frequency asymmetric spectra generally introduce additional sources of uncertainty due to uncontrolled entanglement of the sensing system mediated by the bath. For the representative case of collective noise from bosonic sources, and experimentally relevant collective spin observables, we find that the uncertainty can increase exponentially with the number of probes. As a concrete application, we show that correlated quantum noise due to a lattice vibrational mode can preclude superclassical precision scaling in current amplitude sensing experiments with trapped ions.

Nonclassicality of temporal correlations pertaining to noncommutative sequential measurements is defined through the violation of macrorealistic inequalities, known as Leggett-Garg inequalities (LGI). We investigate the energy cost of the process associated with the Leggett-Garg test in the context of noiseless and Markovian noise for arbitrary initial states. We prove that in noiseless and in certain noisy scenarios, the maximal violations of LGI under the energy constraint occurs when the average energy of the process is equal to the negative of the energy of the initial state. Such a dependence of LGI on the choice of the initial state is not seen in the unconstrained case. Moreover, we find that in the presence of a moderate amount of Markovian noise, the amount of violation of LGI remains almost unaltered with a suitable choice of the evolution and dephasing operators in the neighborhood of the maximal violation line, thereby showing the robustness of temporal correlations under environmental effects.

Variational Bayes (VB) inference is one of the most important algorithms in machine learning and is widely used in engineering and industry. However, VB is known to suffer from the problem of local optima. In this paper, we generalize VB by using quantum mechanics and propose an algorithm, which we call quantum annealing variational Bayes (QAVB) inference. We then show that QAVB drastically improves the performance of VB in a clustering problem described by a Gaussian mixture model, which is essentially important from the viewpoint of optimization. Finally, we discuss an intuitive understanding of how QAVB works well.

There has long been a discrepancy between the size distributions of ${\mathrm{Ar}}_n{}^{+}$ clusters measured by different groups regarding whether or not magic numbers appear at sizes corresponding to the closure of icosahedral (sub-)shells. We show that the previously observed magic cluster size distributions are likely the result of an unresolved ${\mathrm{Ar}}_n{\mathrm{H}}^{+}$ component, i.e., from protonated argon clusters. We find that the proton impurity gives cluster geometries that are much closer to those for neutral rare-gas clusters, which are known to form icosahedral structures, than for the pure cationic clusters, explaining why the mass spectra from protonated argon clusters better matches these structural models. Our results thus show that even small impurities, e.g., a single proton, can significantly influence the properties of clusters.

The photon blockade based on weak nonlinearities is called unconventional photon blockade. The studies of the unconventional photon blockade in recent decades are all limited to Markovian approximation. In this paper, we propose a scheme to achieve a strong photon antibunching in non-Markovian reservoir. An exact non-Markovian master equation for the optical cavity coupled with a degenerate optical parametric amplifier (DOPA) is derived. We show that this unconventional photon blockade originates from the destructive interference between two paths which are formed by the DOPA pump and a driving field. Unconventional single-photon blockades that exhibit a transition from the non-Markovian to Markovian regime by controlling environmental spectral width regardless of the weakness of DOPA gain and driving field are found. We analytically derive an optimal condition for strong antibunching, which is in good agreement with that obtained by the full numerical simulation. The presented results then are compared with that given by Markovian approximation in the weak-coupling limit. Our scheme might have paved an avenue towards the investigations of unconventional photon blockades in many other non-Markovian quantum systems in quantum optics.

In a recent paper [Barral et al., Phys. Rev. A 96, 053822 (2017)], we proposed a strategy to generate bipartite and quadripartite continuous-variable entanglement of bright quantum states based on degenerate down-conversion in a pair of evanescently coupled nonlinear ${\chi }^{\left(2\right)}$ waveguides. Here, we show that the resources needed for obtaining these features can be optimized by exploiting the regime of second harmonic generation: the combination of depletion and coupling among pump beams indeed supplies all necessary wavelengths and appropriate phase mismatch along propagation. Our device thus entangles the two fundamental classical input fields without the participation of any harmonic ancilla. Depending on the propagation distance, the generated harmonics are entangled in bright or vacuum modes. We also evidence two-color bipartite and quadripartite entanglement over the interacting modes. The proposed device represents a boost in continuous-variable integrated quantum optics since it enables a broad range of quantum effects in a very simple scheme, which optimizes the resources and can be easily realized with current technology.

The complete dynamic multipole expansion of electromagnetic sources contains more types of multipole terms than is conventionally perceived. The toroidal multipoles are one of the examples of such contributions that have been widely studied in recent years. Here we inspect more closely the other type of commonly overlooked terms known as the mean-square radii. In particular, we discuss both quantitative and qualitative aspects of the mean-square radii and provide a general geometrical framework for their visualization. We also consider the role of the mean-square radii in expanding the family of nontrivial nonradiating electromagnetic sources.

We investigate an explicitly time-dependent quantum system driven by a secant-pulse external field. By solving the Schrödinger equation exactly, we elucidate exotic properties of the system with respect to its dynamical evolution: On the one hand, the system is shown to be essentially nonadiabatic, which prohibits an adiabatic approximation for its dynamics; on the other hand, the loop evolution of the model can induce a geometric phase which, analogous to the Berry phase of the cyclic adiabatic evolution, is in direct proportion to the solid angle subtended by the path of the state vector. Moreover, we extend the model and show that the described properties coincide in a special family of secant-pulse-driven models.

The conventional notion of elastic, coherent atom-surface scattering originates from the scattering particles acting as a quantum-mechanical matter wave, which coherently interfere to produce distinct Bragg peaks which persist at finite temperature. If we introduce inelastic scattering to this scenario, the result is that the surface particles become displaced by the scattering atoms, resulting in emission or absorption of phonons that shift the final energy and momentum of the scatterer. As the lowest-lying phonons are gapless excitations, the ability to measure these phonons is very difficult and this difficulty is exacerbated by the roughly 1-eV resolution found in high-energy helium scattering experiments. Even though the surface has in effect measured the presence of the scatterer which decoheres the particle, we retain the diffraction spots which are referred to as coherent scattering. How do we reconcile these disparate viewpoints? We propose an experiment to more precisely examine the question of coherence in atom-surface scattering. We begin with an initially coherent superposition of helium particles with equal probabilities of interacting with the surface or not interacting with the surface. The beams are directed so that after the scattering event, the atoms are recombined so that we can observe the resulting interference pattern. The degree to which phonons are excited in the lattice by the scattering process dictates the fringe contrast of the interference pattern of the resulting beams. We use semiclassical techniques to simulate and test the viability of this experiment and show that for a wide range of conditions, despite the massive change in the momentum perpendicular to the surface, we can still expect to have coherent (in the superposition sense) scattering.

Atomic spectra and other properties of superheavy element dubnium (Db, $Z=105$) are calculated using recently developed method combining configuration interaction with perturbation theory [the CIPT method, V. A. Dzuba, J. C. Berengut, C. Harabati, and V. V. Flambaum, Phys. Rev. A 95, 012503 (2017)]. These include energy levels for low-lying states of Db and Db II, electric dipole transition amplitudes between the ground state and low-lying states of opposite parity, isotope shift for these transitions, and the ionization potential of Db. Similar calculations for Ta, which is a lighter analog of Db, are performed to control the accuracy of the calculations.

The elastic scattering of twisted electrons by neutral atoms is studied within the fully relativistic framework. The electron-atom interaction is taken into account in all orders, thus allowing us to explore high-order effects beyond the first Born approximation. To illustrate these effects, detailed calculations of the total and differential cross sections as well as the degree of polarization of scattered electrons are performed. Together with the analysis of the effects beyond the first Born approximation, we discuss the influence of the kinematic parameters of the incident twisted electrons on the angular and polarization properties of the scattered electrons.

We investigate theoretically interference effects between inter- and intraband currents in high-order harmonic generation (HHG) from solids by numerically solving the one-dimensional time-dependent Schrödinger equation (TDSE) for a model crystal and the semiconductor Bloch equation (SBE) for a real material zinc oxide (ZnO). The TDSE method is used to extract the explicit dynamic process of interference. We find that the contribution from constructive interference dominates the harmonic spectrum when the interband current and intraband current have good synchronism. When they lose synchronism, destructive interference counteracts contributions from inter- and intraband currents. The phase differences between intra- and interband harmonics are close to zero and $\pi$ when constructive and destructive interferences occur, respectively. In $k$ space, constructive (destructive) interference occurs near a moment when electrons at most transit to a higher (lower) energy band. Interference effects create fine structures in harmonic spectra and lead to suppression of harmonic signals which can be directly measured in experiments. The interference effect is also investigated by using the SBE method in HHG from ZnO.

In this work, we discuss connections between different theoretical physics communities and their works, all related to systems that act as sources of particles such as photons, phonons, or electrons. Our interest is to understand how a low-dimensional quantum system driven by coherent fields, e.g., a two-level system, a Jaynes-Cummings system, or a photon pair source driven by a laser pulse, emits photons into a waveguide. Of particular relevance to solid-state sources is that we provide a way to include dissipation into the formalism for temporal-mode quantum optics. We will discuss the connections between temporal-mode quantum optics, scattering matrices, quantum stochastic calculus, continuous matrix product states and operators, and very traditional quantum optical concepts such as the Mandel photon counting formula and the Lindblad form of the quantum-optical master equation. We close with an example of how our formalism relates to single-photon sources with dephasing.

Optical phase spaces represent fields of any spatial coherence and are typically measured through phase-retrieval methods involving a computational inversion, optical interference, or a resolution-limiting lenslet array. Recently, a weak-values technique demonstrated that a beam's Dirac phase space is proportional to the measurable complex weak value, regardless of coherence. These direct measurements require raster scanning through all position-polarization couplings, limiting their dimensionality to less than 100 000 [C. Bamber and J. S. Lundeen, Phys. Rev. Lett. 112, 070405 (2014)]. We circumvent these limitations using compressive sensing, a numerical protocol that allows us to undersample, yet efficiently measure, high-dimensional phase spaces. We also propose an improved technique that allows us to directly measure phase spaces with high spatial resolution with scalable frequency resolution. With this method, we are able to easily and rapidly measure a 1.07-billion-dimensional phase space. The distributions are numerically propagated to an object in the beam path, with excellent agreement for coherent and partially coherent sources. This protocol has broad implications in quantum research, signal processing, and imaging, including the recovery of Fourier amplitudes in any dimension with linear algorithmic solutions and ultra-high-dimensional phase-space imaging.

We derive a Magnus expansion for a frequency chirped quantum two-level system. We obtain a time-independent effective Hamiltonian which generates a stroboscopic time evolution. At lowest order the according dynamics is identical to results from using a rotating wave approximation. We determine, furthermore, also the next higher-order corrections within our expansion scheme in correspondence to the Bloch-Siegert shifts for harmonically driven systems. Importantly, our scheme can be extended to more complicated systems, i.e., even many-body systems.

Two overlapping bipartite binary Bell inequalities cannot be simultaneously violated as this would contradict the usual no-signaling principle. This property is known as monogamy of Bell inequality violations and generally Bell monogamy relations refer to trade-offs between simultaneous violations of multiple inequalities. It turns out that multipartite Bell inequalities admit weaker forms of monogamies that allow for violations of a few inequalities at once. Here we systematically study monogamy relations between correlation Bell inequalities both within quantum theory and under the sole assumption of no signaling. We first investigate the trade-offs in Bell violations arising from the uncertainty relation for complementary binary observables, and exhibit several network configurations in which a tight trade-off arises in this fashion. We then derive a tight trade-off relation which cannot be obtained from the uncertainty relation showing that it does not capture monogamy entirely. The results are extended to Bell inequalities involving different numbers of parties and find applications in device-independent secret sharing and device-independent randomness extraction. Although two multipartite Bell inequalities may be violated simultaneously, we show that genuine multiparty nonlocality, as evidenced by a generalized Svetlichny inequality, does exhibit monogamy property. Finally, using the relations derived we reveal the existence of flat regions in the set of quantum correlations.

A metastable quantum state coupled to a continuum undergoes an exponential decay in the Weisskopf-Wigner (Markovian) approximation. However, quantum theory strictly predicts deviations from an exponential decay law both at small and long time scales. In multilevel systems, even in the Markovian approximation strong deviations from an exponential decay can be observed in the intermediate time scale owing to interference of overlapping resonances. Such interference effects are simply described by an effective non-Hermitian Hamiltonian and are known to explain, for example, the existence of dark states and fractional decay. Here we show that the wide variety of anomalous behaviors observed in multilevel quantum decay are rooted in the non-normal nature of the effective non-Hermitian Hamiltonian, revealing strong similarities between anomalous quantum mechanical decay and non-normal dynamics found in hydrodynamic flows. Major signatures of non-normal dynamics include delayed decay, accelerated decay, and exponential-power-law decay at an exceptional point. Such signatures are exemplified by suggesting simple tight-binding lattice realizations of multilevel quantum decay, which could be emulated in integrated photonic experiments. Finally, it is shown that for noninteracting particles with fermionic statistics the usual exponential decay law is restored, i.e., all anomalous decay effects arising from single-particle non-normal dynamics are washed out.

Numerous works have shown that under mild assumptions, unitary dynamics inevitably leads to equilibration of physical expectation values if many energy eigenstates contribute to the initial state. Here, we consider systems driven by arbitrary time-dependent Hamiltonians as a protocol to prepare systems that do not equilibrate. We introduce a measure of the resilience against equilibration of such states, and we show, under natural assumptions, that in order to increase the resilience against equilibration of a given system, one needs to possess a resource system that itself has a large resilience. In this way, we establish a link between the theory of equilibration and resource theories by quantifying the resilience against equilibration and the resources that are needed to produce it. We connect these findings with insights into local quantum quenches, and we investigate the (im)possibility of formulating a second law of equilibration by studying how resilience can be either only redistributed among subsystems, if these remain completely uncorrelated, or in turn created in a catalytic process if subsystems are allowed to build up some correlations.

We show that the decoherence, which in the long run destroys quantum features of a system, can be used to reveal the entanglement in a two-qubit system. To this end, we consider a criterion that formally resembles the Clauser-Horne-Shimony-Holt (CHSH) inequality. In our case the local observables are set by the coupling of each qubit to the environmental noise, controlled with the dynamical decoupling method. We demonstrate that the constructed inequality is an entanglement criterion—it can only be violated by nonseparable initial two-qubit states, provided that the local noises are correlated. We also show that, for a given initial state, this entanglement criterion can be repurposed as a method of discriminating between Gaussian and non-Gaussian noise generated by the environment of the qubits. The latter application is important for ongoing research on using qubits to characterize the dynamics of environment that perturbs them and causes their decoherence.