Nonlocal Electronic Wavefunctions engineered in Superconducting circuits – NEWS

In quantum mechanics, a particle or an ensemble of particles are described by wavefunctions, which can in principle spread over arbitrarily large distances. This nonlocality is a specificity of quantum mechanics that has no equivalent in classical physics. For Einstein and others, nonlocality was an artifact of Quantum Mechanics due to its incompleteness, while for Schrödinger it was ‘magic’ because you could influence an object from a distance, a phenomenon called quantum steering. This means that if a wavefunction is separated in two parts that are sufficiently far from each other, one can act on the system at one point in space and measure the consequences somewhere else.
Nowadays, tremendous progress has been made in the control of nonlocal quantum objects, leading to unimaginable breakthrough for quantum technologies. Splitting the wavefunction of pairs of entangled photons via satellites has allowed to perform secured quantum key distribution and even quantum teleportation over thousands of kilometers. Contrary to what this incredible development might suggest, there is still an important ongoing effort to understand nonlocality on a more fundamental level. The experimental demonstration that a single photon wavepacket separated in the two arms of an interferometer is nonlocal was only achieved recently by testing Einstein’s ‘spooky action at a distance’, i.e. the nonlocal collapse of the photon wavefunction, or by violating Bell’s inequalities.
Most of these experiments have been conducted with photons, and the question of how charged particles, such as electrons, can be nonlocal is still a source of controversy in the scientific community. Beyond the fundamental interest that such questions inevitably raise, the answers will be crucial for the development of new resources for quantum circuits, now that the latter are entering an era of quantum engineering. If we follow the same path as for photons, turning electron nonlocality into a resource will require the ability to emit and detect unique electron excitations propagating over a Fermi Sea, a technical challenge that the field of quantum electron optics is currently trying to meet. I propose an alternative route using hybrid superconducting circuits.
In NEWS, I plan to engineer electronic nonlocal wavefunctions in superconducting circuits following two different but closely related strategies: the Andreev Polyacetylene (AnPoly) and the Kitaev chain (KitC). In both cases, like in a bulk superconductor, the ground state is made of pairs of electrons, the Cooper pairs, which naturally provide electronic coherence and entanglement. My circuits are designed to spatially shape the corresponding electronic wavefunctions by connecting in series superconducting electrodes with a carbon nanotube. Depending on the strategy, the nanotube is either chosen metallic to serve as a well transmitted quantum conductor creating weak links between superconductors (AnPoly), or semiconducting in order for the nanotube to behave as a series of splitters that separate the electrons of Cooper pairs (KitC). This leads to two different types of nonlocal electronic states: one is a Cooper pair that is in a quantum superposition at each extremities of the circuit (AnPoly), while the other is made of two entangled electrons that are spatially separated at each ends of the chain (KitC) in a very wide splitted Cooper pair.
Both these systems are expected to exhibit nonlocal Josephson Effect, which remains essentially unexplored experimentally, but these ambitious nanotube-based architectures should provide the leap forward needed to reach this entirely untouched area of mesoscopic superconductivity. These systems could be used to implement new type of quantum bits with intrinsic protections provided by selection rules specific to these nonlocal wavefunctions. NEWS will also pave the way to perform nonlocal on-chip operations such as electron teleportation in the sense of Liang Fu.