High-order Harmonic Spectra in different gauges can disagree when there is confinement

We test the common wisdom that the high-order harmonic generation (HHG) spectra agree well in all three length, velocity, and acceleration gauges obtained from a typical TDSE simulation when the system is in the weak-field regime. We show that the spectra in these gauges start to disagree significantly when state mixing is introduced without changing the dynamical regime. We demonstrate this by solving the time-dependent Schrödinger's equation (TDSE) and compare spectra in different gauges in 2 different situations: when (1) the atom is free of confinement, and (2) the atom is confined inside a C₆₀ shell. When the atom is initially prepared in the ground state, size of which is smaller than the C₆₀ radius, all three gauges agree very well regardless of whether the atom is confined. In the 3s excited state, however, a perfect agreement is only achieved between different gauges when the atom is free. Introducing confinement, in this case, results in mixing into the nearby n=4 manifold which results in significant disagreement between gauges. In all our calculations, we scale the laser intensity and wavelength such that the Keldysh parameter remains the same, which keeps our system in the same dynamical regime across different situations we investigate.