Abstract
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.
Highlights
Light excitation of collective modes in condensed matter physics is typically realized due to an infrared or Raman coupling of light to the system
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
If the mode does not have a dipole moment, a linear activation is forbidden, such that the only allowed process is due to the nonlinear Raman effect. This is true for the Higgs mode in superconductors, which is a collective oscillation of the amplitude of the order parameter [1,2]
Summary
Recent efforts have shown that a linear excitation in the presence of a supercurrent is possible, resulting in a resonant enhancement at = 2 with the driving light frequency and the energy of the Higgs mode 2. This is in contrast to the usual 2 = 2 resonance condition found in nonlinear third-harmonic generation experiments. 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 resonance condition = 2 is just a special case. We further discuss another recent experiment, where we find a suppression of odd-order higher harmonics in the presence of a dc supercurrent
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