PHYSICAL REVIEW B 100, 035308 (2019) Maximal quantum scattering by homogeneous spherical inclusions Constantinos Valagiannopoulos * Department of Physics, Nazarbayev University, 53 Qabanbay Batyr Avenue, KZ-010000, Kazakhstan (Received 23 April 2019; revised manuscript received 27 June 2019; published 18 July 2019) Scattering of matter waves, present at multiple quantum setups, is required to be maximized in several applications from sensing and imaging to quantum switching and memory. The simplest case of a homogeneous spherical scatterer is rigorously solved and optimized with respect to its size, texture, and background by considering the effective quantum properties from a long directory of materials. In this context, several alternative layouts with maximal scattering efficiency are proposed, offering additional degrees of freedom in design without requirements for careful engineering of quantum texture. Many of the reported inclusions exhibit substantial selectivity in their scattering response, admitting them to operate as sharp filters for particle energies or sensitive detectors of electron beams. DOI: 10.1103/PhysRevB.100.035308 I. INTRODUCTION The wave-matter duality constitutes one of the backbone concepts in quantum mechanics, according to which the mo- tion of any particle is not deterministically discoverable and therefore its location is described by the spatial distribution of a probability, defining a matter wave. Interaction of objects with such matter waves is a general and ubiquitous operation, present in several and diverse quantum applications. Sensors [1], with usefulness ranging from traditional high-resolution optical spectroscopy to quantum entanglement, exploit vastly that coupling of elementary particles with background fields to increase their sensitivity and precision. In particular, hybrid spin systems comprising pairs of sensing and memory qubits use quantum manipulation to achieve increased time of phase accumulation [2], while quantum interference gives high- fidelity interpolation allowing efficient detection for single biomolecules [3]. Engagement of electron beams (e-beams) with quantum dots and emitters is also utilized for signal labeling in biological conjugates [4], for designing graphene- based photodetectors [5], and for creating highly localized, optically addressable electronic states in two-dimensional me- dia [6]. The intrinsic scientific interest for the functionality potential of similar quantum engineering systems has been recently accompanied (and fed) by significant research fund- ing initiatives. Indeed, US Army Research Laboratory (ARL), Department of Defense (DoD) and Air Force Office of Sci- entific Research (AFOSR) have recently approved numerous large-scale, multidisciplinary programs on electromagnetic excitation of quantum substance [7], quantum plasmons at the nanoscale [8], and phase transitions for quantum switching [9], all related to suitable pairing of matter waves with scat- terers. To build the necessary configurations employed in these multiple applications, a great variety of quantum materials is available. It is not only the long list of semiconducting elements and compounds being extensively utilized in similar * konstantinos.valagiannopoulos@nu.edu.kz devices, but also all the possible alloys of them with arbitrary doping analogy, which multiply the alternatives [10,11]. Dia- mond is also frequently used in several setups like nanoscale thermometers when hosting nitrogen-vacancy centers [12], magnetic sensors at subcellular levels when conjugated with gold nanorods [13], Fourier nuclear spectroscopes [14], and self-assembled hybrid quantum biodevices [15]. Moreover, heterojunction materials with engineered band gaps via proper regulation of concentration proportions [16] are becoming increasingly popular for quantum applications. The same holds true for two-dimensional crystals such as graphene [17] that treats electrons as massless particles due to its linear dispersion relation. Once defining the structure for a quantum application involving interactions between matter waves and objects made of quantum media as those referred to before, one can de- termine the probabilistic trajectories by handling the formu- lated problem in direct analogy with electrodynamics [18]. Indeed, for the case of a single nonrelativistic particle and by suppressing the harmonic time, (the envelope of) its wave function satisfies a version of the Schrödinger equation (quan- tum mechanics) which is identical to the scalar wave equation (electrodynamics/photonics). Given the fact that electromag- netic theory is complete, maturely developed for centuries, and enriched with sophisticated mathematical toolboxes and techniques, it’s no wonder that numerous quantum effects are interpreted from the photonics point of view and, vice versa, several concepts of electromagnetic fields are carried over to quantum waves. More specifically, it is shown that the paradigm of metamaterials may be successfully translated into the quantum arena [19] by using intentionally inhomoge- neous architectures and tailoring their effective band structure; via this path, exotic effects like dramatic radiation intensity enhancement [20] and anomalous tunneling [21] have been reported. In addition, photonic crystal analogies are utilized under quantum excitation for dissipative quantum state engi- neering [22], while quantum properties of surface plasmons have been also extensively investigated [23,24]. Finally, par- tial wave formalism borrowed from electrodynamics has been 2469-9950/2019/100(3)/035308(10) 035308-1 ©2019 American Physical Society