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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 ω) and a weak, second color component (e.g., 2ω). 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 2ω-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 π 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 Schrödinger 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.

Phase-of-the-phase (PoP) spectroscopy is extended to two-color laser fields having a circularly counter-rotating polarization. In particular, the higher harmonics of the (two-color) phase information are analyzed in order to extract the laser-coherent part of the photoelectron spectra taken under complex target conditions. We illustrate this with a proof-of-principle simulation by considering strong-field electron emission from argon atoms within helium nanodroplets under realistic experimental conditions, i.e. a limited number of photoemission events. Multiple elastic scattering on neutral helium atoms creates a laser-incoherent background, but the higher harmonics of the PoP-signal allow to resolve the coherent contribution to the photoemission.

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A way to considerably enhance terahertz radiation, emitted in the interaction of intense mid-infrared laser pulses with atomic gases, in both the total energy and the electric-field amplitude is suggested. The scheme is based on the application of a two-color field consisting of a strong circularly polarized mid-infrared pulse with wavelengths of 1.6 ÷ 4 µm and its linearly or circularly polarized second harmonic of lower intensity. By combining the strong-field approximation for the ionization of a single atom with particle-in-cell simulations of the collective dynamics of the generated plasma it is shown that the application of such two-color circularly polarized laser pulses may lead to an order-of-magnitude increase in the energy emitted in the terahertz frequency domain as well as in a considerable enhancement in the maximal electric field of the terahertz pulse. Our results support recently reported experimental and numerical findings. arXiv:1810.08834v1 [physics.atom-ph]