  Phase-of-the-phase spectroscopy using two-color colinearly polarized laser
pulses has been introduced and experimentally applied to strong-field tunneling
ionization in S. Skruszewicz et al., Phys. Rev. Lett. 115, 043001 (2015) and
recently to multiphoton ionization in M. A. Almajid et al., J. Phys. B: At.
Mol. Opt. Phys. 50, 194001 (2017). The idea behind phase-of-the-phase
spectroscopy is to study in a systematic way the change in the photoelectron
yield as a function of the relative phase between the strong fundamental field
component (of carrier frequency $\omega$) and a weak, second color component
(e.g., $2\omega$). The observable of interest is the
photoelectron-momentum-dependent phase of the change in the electron yield with
respect to the relative phase, hence the name "phase of the phase." In the
present paper, phase-of-the-phase spectroscopy is extended to circularly
polarized light. With a small, counter-rotating $2\omega$-component,
photoelectron spectra have a three-fold symmetry in the polarization plane. The
same is true for the corresponding phase-of-the-phase spectra. However, a
peculiar, very sharp phase-flip by $\pi$ occurs at a certain radial momentum of
the photoelectron that is sensitive to both laser parameters and the ionization
potential. Results from the numerical solution of the time-dependent
Schr\"odinger equation are compared to those from the strong-field
approximation. An analytical expression for the momentum at which the
phase-of-the-phase flipping occurs is presented.
