Emulating the Wigner function of an odd cat state by means of classical light fields

Abstract

The Wigner distribution function is a very useful tool in signal analysis because it provides a representation of a signal in the conjugate variables across phase space. In the context of quantum mechanics, this function represents a quasi-probability distribution in phase space for a quantum state.

On the other hand, in signal processing, the Fourier transform and its generalization, the fractional Fourier transform (FFT), play an important role in time and frequency analysis. Moreover, research conducted in the late 1990s found that reconstruction of the Wigner function could be obtained from the collection of different fractional Fourier transforms.

In this project, the Wigner function of a quantum state, called a cat state, was emulated by obtaining the fractional Fourier transforms in the spatial frequency variables of two Gaussian beams separated by "2d" distance. This will respond to the problem of generating lower cost methods that obtain properties of quantum states through their Wigner function, since, to generate, for example, a cat state, much more sophisticated and expensive equipment is needed.