Single-Atom Gating of Quantum State Superpositions Page: 4 of 20
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without any fitting parameters. Figure le displays the calculated contributions e, of the
significant modes composing the topograph z(r), such that z(r) c c, (r)) .
Next, 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 12,7) state. The resultant difference map
(Fig. 2e) strongly resembles the 12,7) state. Surprisingly, however, when the Co atom
was moved rightward to one of the strong maxima of the state 14,4), the image
produced (Fig. 2g) was manifestly different from either of the two eigenstates.
We will show that our AdI/dV maps are images of superpositions: phase-
coherent a . This is in contrast to typical STM measurements, such as the
topograph above, where the sum of tunnelling through independent channels14 yields
signals proportional to phase-insensitive c V ) . To demonstrate this result, we
reproduce the difference maps as linear combinations of the states 4') of the
unperturbed elliptical corral. These coherent superpositions (Fig. 2, third column) are
an excellent match to the mirage data. Any methods neglecting phase interference
cannot reproduce our observations (see Supp. Fig. 2).
Electrons in quantum corrals are well modelled by particle-in-a-box solutions to
the Schrodinger equation because the surface state wavelength [30 A in Cu(111) at EF]
is much larger than the spacing between the wall atomsl- 3,10,15-18. As a first clue to the
underlying physics, the original report of the quantum mirage3 pointed out the similarity
between the solitary eigenfunction closest to EF and the spatial fine structure around the
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Moon, Christopher. Single-Atom Gating of Quantum State Superpositions, article, April 28, 2010; United States. (digital.library.unt.edu/ark:/67531/metadc933082/m1/4/: accessed January 16, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.