Feasible optical weak measurements of complementary observables via a single Hamiltonian

TL;DR

This paper introduces a versatile optical scheme using a single Hamiltonian for joint weak measurements of complementary observables, enhancing measurement capabilities and signal quality in quantum optics.

Contribution

It presents a formalism for joint weak measurements of complementary observables using standard three-wave mixing, enabling simultaneous access to weak values of both variables with improved signal-to-noise ratio.

Findings

Enables simultaneous weak measurement of complementary observables.

Uses standard nonlinear optical processes like parametric down-conversion.

Improves signal-to-noise ratio compared to non-postselected measurements.

Abstract

A general formalism for joint weak measurements of a pair of complementary observables is given. The standard process of optical three-wave mixing in a nonlinear crystal (such as in parametric down-conversion) is suitable for such tasks. To obtain the weak value of a variable $A$ one performs weak measurements twice, with different initial states of the "meter" field. This seems to be a drawback, but as a compensation we get for free the weak value of a complementary variable $B$. The scheme is tunable and versatile: one has access to a continuous set of possible weak measurements of pair of observables. The scheme increases signal-to-noise ratio with respect to the case without postselection.