Non-equilibrium nature of non-linear optical response: Application to the bulk photo voltaic effect

The bulk photo-voltaic effect (BPVE) is an example of non-linear optical response that leads to a DC current in non-centrosymmetric materials which is relevant to photo-voltaic applications. We theoretically study this effect in the presence of electron-phonon interactions. Using the response function formalism, we show that the non-linear optical response, in general, contains correlator of three operators which are not ordered in time. This out of time-ordered correlator (OTOC) for an interacting system cannot be calculated using equilibrium field theory. Using a semiclassical approach instead, we show that BPVE can be attributed to the dipole moment of generated electron hole pairs. We confirm the validity of semiclassical result for the non-linear DC response from a quantum master equation approach. From this formalism we also find that the electron-phonon coupling strength has a strong implicit effect on the scaling dependence of the non-linear DC response on the optical field. Most interestingly, the semiclassical treatment shows that the non-linear DC response for spatially inhomogeneous excitation profiles is strongly non-local and must involve the aforementioned OTOC that cannot be computed by equilibrium field theory.

Reference: https://arxiv.org/pdf/1908.01793.pdf