Current-assisted Raman activation of the Higgs mode in superconductors

The Higgs mode in superconductors is a scalar mode without electric or magnetic dipole moment. Thus, it is commonly believed that its excitation is restricted to a nonlinear two-photon Raman process. However, recent efforts have shown that a linear excitation in the presence of a supercurrent is possible, resulting in a new resonant enhancement at $\Omega=2\Delta$ with the driving light frequency $\Omega$ and the energy of the Higgs mode $2\Delta$. This is in contrast to the usual $2\Omega = 2\Delta$ resonance condition found in nonlinear third-harmonic generation experiments. In this communication, we show that such a linear excitation can still be described as an effective Raman two-photon process, with one photon at $\omega=2\Delta$ and one virtual photon at $\omega=0$ which represents the dc supercurrent. At the same time we demonstrate that a straightforward infrared activation with a single photon excitation is negligible. Moreover, our generalized theory provides an explanation for how the excitation of the Higgs mode in both THz quench and drive experiments can be understood within a conventional difference-frequency generation or sum-frequency generation process, respectively. In such a picture, the observed new resonance condition $\Omega = 2\Delta$ is just a special case.