Heisenberg uncertainty principle: an advanced undergraduate laboratory experiment based on quantum quadrature operators

The Heisenberg uncertainty principle (HUP) plays an important role in quantum mechanics. It is necessary to demonstrate this principle experimentally for undergraduates to understand HUP clearly. In this paper, we originally employ the quantum quadrature operators to demonstrate HUP in undergraduate laboratories. Starting from the quantization of electromagnetic field, we briefly review the definition of quadrature operators and demonstrate HUP via the variances of quadrature operators. And the scheme of HUP demonstration with homodyne detection is introduced. More importantly, we develop a tabletop experimental apparatus for the demonstration of HUP in undergraduate laboratories. Our proposal focuses on the basic quantum mechanics concepts, experimental principles, and instruction as well as experimental techniques. It provides a way to help undergraduates, especially the ones who will go on graduate study in quantum technology in the future, make connections between abstract quantum mechanics concepts and concrete experiments, which makes the concepts better understood.