Parity-based measurement and control of the spatial wave function of photons

Mohammad Mirhosseini, Jeff S. Lundeen, Robert W. Boyd

Kaveh Gharavi, Darryl Hoving, Jonathan Baugh

We theoretically examine a scheme for projectively reading out the parity state of a pair of Majorana bound states (MBSs) using a tunnel-coupled quantum dot. The dot is coupled to one end of the topological wire but isolated from any reservoir and is capacitively coupled to a charge sensor for measurement. The combined parity of the MBS-dot system is conserved, and charge transfer between the MBS and dot only occurs through resonant tunneling. Resonance is controlled by the dot potential through a local gate and by the MBS energy splitting due to the overlap of the MBS pair wave functions. The latter splitting can be tuned from zero (topologically protected regime) to a finite value by gate-driven shortening of the topological wire. Simulations show that the oscillatory nature of the MBS splitting is not a fundamental obstacle to readout but requires precise gate control of the MBS spatial position and dot potential. With experimentally realistic parameters, we find that high-fidelity parity readout is achievable given nanometer-scale spatial control of the MBS and that there is a trade-off between required precisions of temporal and spatial control. Use of the scheme to measure the MBS splitting versus separation would present a clear signature of topological order and could be used to test the robustness of this order to spatial motion, a key requirement in certain schemes for scalable topological qubits. We show how the scheme can be extended to distinguish valid parity measurements from invalid ones due to gate calibration errors.

Michael-Erik Ronlund

Smith, B J, Killett, B, Raymer, M G +2 more

We present an experimental method to measure the transverse spatial quantum state of an optical field in coordinate space at the single-photon level. The continuous-variable measurements are made with a photon-counting, parity-inverting Sagnac interferometer based on all-reflecting optics. The technique provides a large numerical aperture without distorting the shape of the wave front, does not introduce astigmatism, and allows for characterization of fully or partially coherent optical fields at the single-photon level. Measurements of the transverse spatial Wigner functions for highly attenuated coherent beams are presented and compared to theoretical predictions.

Shengwang Du

Ayman F. Abouraddy, Bahaa E. A. Saleh

We discuss an approach to encoding qubits in the spatial distribution of single photons and entangled-photon pairs based on utilizing the spatial parity of the photon wave fronts. Using simple optical components, that do not require nonlinearities or moving parts, we discuss implementing rotations in the Hilbert space of spatial parity and measurement of the state of parity. Using entangled photon pairs, we use spatial parity to demonstrate quantum nonlocality by violating a Bell inequality using an EPR state. We also discuss generalizations of this scheme that may allow for a larger number of qubits to be encoded per photon.