Single-atom gating of quantum-state superpositions

Abstract

Progress in quantum nanoscience has engendered a physically diverse array of controllable solid-state quantum systems [4][5][6] . The prototypical quantum system consists of two wavefunctions that can be coherently combined into superpositions. In this work, we create and study superpositions of electron wavefunctions in nanoassembled quantum corrals where we can finely tune the geometry. We engineered an elliptical resonator to harbour degenerate wavefunctions whose superpositions could be manipulated. The solutions to the Schrödinger equation in a hard-walled ellipse possess two quantum numbers: n, the number of nodes crossing the minor axis, and l, half the number of nodal intersections along the perimeter (these map to the radial and angular momentum quantum numbers in a circle We assembled our designed resonator using a home-built scanning tunnelling microscope (STM) operating in ultrahigh vacuum. The single-crystal Cu(111) substrate was prepared, cooled to ~4 K, and dosed with ~15 Co atoms per (100 Å) 2 . We individually manipulated 2 44 Co adatoms to bound the corral. With spectroscopy, we verified that modes 41 and 42 occurred within a few mV of one another (Supp. Fig. 1). A constant-current ( I ) topograph of the finished structure is shown in Fig 1c. To confirm that the wavefunctions ψ closely describe this system, we used them to calculate (see Methods) a theoretical topograph ( Fig. 1d) that reproduces the data -4/13 -without any fitting parameters. Figure 1e displays the calculated contributions j c of the significant modes composing the topograph ( ) z r , such thatNext, we added a nanoscopic gate: a single cobalt atom. While moving the adatom across the ellipse-effectively sweeping a local electrostatic potential across the eigenstates-we measured topographs (Fig. 2, first column) and simultaneously acquired / dI dV image maps. By subtracting the / dI dV map of the empty ellipse, we created / dI dV difference maps (Fig. 2, second column). We began by placing the gate atom at one of the maxima of the calculated 2, 7 state. The resultant difference map (Fig. 2e) strongly resembles the 2, 7 state. Surprisingly, however, when the Co atom was moved rightward to one of the strong maxima of the state 4, 4 , the image produced ( Fig. 2g) was manifestly different from either of the two eigenstates.We will show that our / dI dV Δ maps are images of superpositions: phase- Electrons in quantum corrals are well modelled by particle-in-a-box solutions to the Schrödinger equation because the surface state wavelength [30 Å in Cu(111) is much larger than the spacing between the wall atoms 1,3,10,[15][16][17][18] . As a first clue to the underlying physics, the original report of the quantum mirage 3 pointed out the similarity between the solitary eigenfunction closest to E F and the spatial fine structure around the (Fig. 3a) comprise an overall 3-dimensional space; the crossover between planes in this space can be inferred from the structure of the wavefunctions (Fig. 3b-d).To generate arbitrary superpositio...

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