Optimal Pump Shaping for Entanglement Control in Any Countable Basis
Nicholas Bornman, Wagner Tavares Buono, Michael Lovemore, Andrew Forbes
Abstract
Abstract Controlling spatial mode entanglement of bi‐photon states has become paramount in quantum optics experiments, where a spontaneous parametric downconversion (SPDC) state is tailored into a desired state through control of the SPDC pump light. Particular pump shaping solutions exist but have been shown for only special cases, such as orbital angular momentum, and always at the expense of noise. Here, a basis‐independent approach to the pump shaping problem that crafts the problem in terms of an invertible tensor equation is presented, making it possible to determine the requisite pump profile for any desired downconversion joint probability spectrum, often analytically. It is first shown that this approach reproduces a number of prior results exactly and then go on to demonstrate results not possible with existing techniques, such as shaping quantum states in new bases and controlling the signal‐to‐noise ratio. It is believed that this approach is optimal as the solvable tensor equation can be tailored to focus on any desired state (sub)space and can be optimized with respect to a chosen norm. This work provides a universal approach to quantum state engineering through deterministic shaping of the SPDC pump light, making it a highly suitable workhorse of quantum optics experiments.