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, we give a general context to our theory, providing 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. With the same approach, we further discuss another recent experiment, where we find a suppression of odd order higher harmonics in the presence of a dc supercurrent.