Experimental probe of weak value amplification and geometric phase through the complex zeroes of the response function

Abstract

The extraordinary concept of weak value amplification has attracted considerable attention for addressing foundational questions in quantum mechanics and for metrological applications in high precision measurement of small physical parameters. Here, we experimentally demonstrate a fundamental relationship between the weak value of an observable and complex zero of the response function of a system by employing weak value amplification of spin Hall shift of a Gaussian light beam. Using this relationship, we show that arbitrarily large weak value amplification far beyond the conventional weak measurement limit can be experimentally obtained from the position of the minima of the pointer intensity profile corresponding to the real part of the complex zero of the response function. The imaginary part of the complex zero, on the other hand, is related to the spatial gradient of geometric phase of light, which in this particular scenario evolves due to the weak interaction and the pre and post selections of the polarization states. These universal relationships between the weak values and the complex zeros of the response function may provide new insights on weak measurements in a wide class of physical systems. Extremely large weak value amplification and extraction of system parameters outside the region of validity of conventional weak measurements may open up a new paradigm of weak measurement enhancing its metrological applications.

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Cited by in corpus (4)

• Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems
• A Generalized framework of weak value amplification in path interference of polarized light for the enhancement of all possible polarization anisotropy effects
• Interferometric weak value of polarization observable and differential Jones matrix algebra
• Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation