Fig. 1: Atom-by-atom built QDs coupled to a superconducting substrate.

a, Three-dimensional rendering of the constant-current STM topography of a Ag island with a thickness of 12 nm. The simultaneously measured dI/dV signal is used as the texture of the model. The island grows on top of a pseudomorphic Ag double layer on Nb(110) (sketched profile; see Methods). b, Sketch of the experimental setup with the QD walls laterally confining the surface-state electrons into spin-degenerate QD eigenmodes of energies E_r. The eigenmodes couple to the superconducting substrate (Δ_s) with a strength \(V\propto \sqrt{\varGamma }\). E_r can be pitched by adjusting the width L_x of the QD. c, Constant-current STM image of a rectangular QD with side lengths L_x and L_y consisting of 44 Ag atoms. L_x and L_y are defined as the distance between the Ag atoms in the inner ring. Z, apparent height. d, Constant-current STM image of the same structure with one of the QD walls moved as indicated by the arrow. e, Upper panels, constant-height dI/dV maps at bias voltages indicated in the respective panels measured in the interior of the QD in panel d (area marked by the dashed yellow lines). All panels are 15 × 7.5 nm² in size. Lower panels, simulation of a hard-wall rectangular box with dimensions L_x = 16.4 nm, L_y = 9.1 nm assuming a parabolic dispersion of the quasiparticles with m_eff = 0.58m_e and E₀ = −26.4 meV (see Methods). The quantum numbers [n_x, n_y] of the dominant eigenmodes at the energies of the experimental maps (corrected by an offset of Δ_tip) are given below each map. f, dI/dV line profiles along the dashed orange vertical lines marked in panels c and d. QD eigenmodes with n_y = 1 and n_x as indicated by the arrows at the top are observed. Their respective energy is shifted when the length L_x is altered as illustrated by the black arrows. a.u., arbitrary units.