Maximal quantum scattering by homogeneous spherical inclusions

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.

Figure 1

(a) The probabilistic spatial trajectory of a quantum particle traveling into a background medium gets maximally distorted by a spherical scatterer of different texture. (b) Combinations of effective electron masses $m/m_e$ and potential energies $V$ for the available elements (IV group) and compounds (between elements of different groups III–V, II–VI) of our database. Diamond ($m=m_e$ and $V\cong 15.3\mathrm{eV}$) is an outlier and thus not shown.

Figure 2

Spatial distribution of the normalized probability ${\left|\mathrm{\Psi }(z,x)\right|}^2/{\mathrm{\Psi }}_{\text{max}}^2$ in dB and probability current arrows $\mathbf{J}(z,x)$ for representative optimal pairs of Table 1: (a) MgTe scatterer in SiC background ($k_{0}a\cong 0.65, 20log{\mathrm{\Psi }}_{\text{max}}\cong 19$ dB) (b) SiC scatterer in MgO background ($k_{0}a\cong 1.24, 20log{\mathrm{\Psi }}_{\text{max}}\cong 14$ dB), (c) SiC scatterer in diamond background ($k_{0}a\cong 0.44, 20log{\mathrm{\Psi }}_{\text{max}}\cong 19$ dB), and (d) CdS scatterer in BP background ($k_{0}a\cong 0.88, 20log{\mathrm{\Psi }}_{\text{max}}\cong 27$ dB). $E=0.1\mathrm{eV}$ and the green circle denotes the boundary of the scatterer.

Figure 3

Same as Fig. 2 but for representative optimal pairs of Table 2: (a) CdO scatterer in BN background ($k_{0}a\cong 0.72, 20log{\mathrm{\Psi }}_{\text{max}}\cong 5$ dB), (b) BAs scatterer in diamond background ($k_{0}a\cong 0.47, 20log{\mathrm{\Psi }}_{\text{max}}\cong 7$ dB).

Figure 4

Scattering efficiency $Q$ as function of the electron energy $E$ from optimal spherical inclusions of Table 1 into (a) boron phosphide (BP) and (b) magnesium oxide (MgO) homogeneous background.

Figure 5

Scattering efficiency $Q$ in dB (the quantity $10logQ$ is represented) as function of the particle's energy $E$ and the inclusion's physical radius $a$ for (a) CdO inclusions in MgO background and (b) InSb inclusions in BN background. The two dashed lines define the permissible zone of optical size $\pi /10<k_{0}a<\pi /2$. The red circles mark the optimal designs.

Figure 6

Sensitivity of scattering efficiency $Q$ with respect to imperfect selection of sphere's radius $a^{\prime }/a$ and maladjustment of potential energy of the scatterer's medium $V^{\prime }/V$ for various optimal designs of Table 1: (a) SiC inclusions in diamond, (b) MgS inclusions in MgO, (c) ZnS inclusions in BP, (d) SiC inclusions in MgO.

Figure 7

Scattering efficiency $Q$ changes as function of imperfect selection of sphere's radius $a^{\prime }/a$ for optimal spherical inclusions of Table 2 into (a) magnesium oxide (MgO) and (b) diamond homogeneous background.

Figure 8

Scattering efficiency $Q$ as function of $k_{0}a$ for dual potential well (thin blue line) and potential barrier (thick red line) setups referring to material combinations of Table 1: (a) MgO/CdO and (b) diamond/SiC. Particle energy: $E=0.1\mathrm{eV}$. The vertical dashed lines define the permissible zone of optical size $\pi /10<k_{0}a<\pi /2$.