Amplitude Higgs mode and admittance in superconductors with a moving condensate

We consider the amplitude (Higgs) mode in a superconductor with a condensate flow (supercurrent). We demonstrate that, in this case, the amplitude mode corresponding to oscillations $\delta |\Delta|_{\Omega} \exp(i \Omega t)$ of the superconducting gap is excited by an external ac electric field $\mathbf{E}_{\Omega} \exp(i \Omega t)$ already in the first order in $|\mathbf{E}_{\Omega}|$, so that ${\delta |\Delta|_{\Omega} \propto (\mathbf{v}_{0} \mathbf{E}_{\Omega})}$, where $\mathbf{v}_{0}$ is the velocity of the condensate. The frequency dependence $\delta |\Delta|_{\Omega}$ has a resonance shape with a maximum at ${\Omega = 2 \Delta}$. In contrast to the standard situation without the condensate flow, the oscillations of the amplitude $\delta |\Delta(t)|$ contribute to the admittance $Y_{\Omega}$. We provide a formula for admittance of a superconductor with a supercurrent. The predicted effect opens new ways of experimental investigation of the amplitude mode in superconductors and materials with superconductivity competing with other states.