$\delta$-Quench measurement of quantum wavefunction.

Measurement of quantum state wavefunction not only acts as a fundamental part in quantum physics but also plays an important role in developing practical quantum technologies. Conventional quantum state tomography has been widely used to estimate quantum wavefunctions, which, however, requires huge measurement resources exponentially growing with the dimension of state. The recent weak-value-based quantum measurement circumvents this resources issue but relies on an extra pointer space. Here, we propose and demonstrate a simple and direct measurement strategy based on $\delta$-quench probe: By quenching its complex probability amplitude one by one ($\delta$-quench) in the given bases, we can directly obtain the quantum wavefunction by projecting the quenched state onto a post-selection state. As compared to the conventional approaches, it needs only one projection basis. We confirm its power by experimentally measuring photonic complex temporal wavefunctions. This new method is versatile and can find applications in quantum information science and engineering.