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Quantum mechanical phase underlies all of quantum theory, but its experimental detection in various forms remains a challenge at the forefront of physics. Access to a normally hidden quantum phase is challenging since observables are typically tied to projections of the state space vector, with internal phase information removed. To what extent can such phase information be mapped and manipulated in matter?
This talk will survey recent experiments in which we are able to extract phase information during the spatial mapping of single electron wavefunctions. In the experiments we exploit engineered quantum degeneracies provided by tuning the underlying quantum geometry of electronic nanostructures. Normally a quantum tunneling experiment measures probability amplitude through the square of the wavefunction magnitude. However, we have been able to extract phase information by reconstructing the full wavefunction—magnitude and phase—using a new technique we developed based on quantum isospectrality and topological degeneracy. For this work we harnessed a result from contemporary mathematics: the discovery of isospectral domains, or drums that are shaped differently but “sound the same.” As such, our experiments for the first time take this longstanding problem of inverse spectral geometry into the quantum regime. The results therefore have broad implications for the uniqueness of physical reality reconstructed from a spectrum of excitations.
These experiments are predicated on the exciting technology of atomic and molecular manipulation: a custom-built scanning tunneling microscope, operating at low temperature in ultrahigh vacuum, is used to assemble nanostructures atom-by-atom to generate near-ideal quantum laboratories existing at the spatial limit of condensed matter.
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