Phase-dependent asymmetries in strong-field photoionization by few-cycle laser pulses

Using numerical solutions of the time-dependent Schrödinger equation for a hydrogen and a helium atom in a linearly polarized laser field, we calculate the photoelectron signal $P_{+}$, $P_{-}$ measured by two opposing detectors placed along the laser polarization vector, with laser focus in the center. Our calculations show a significant sensitivity of the normalized asymmetry coefficient $a=(P_{+}-P_{-})∕(P_{+}+P_{-})$ to the carrier-envelope (CE) phase for few-cycle laser pulses. We find a very simple dependence of this coefficient on the CE phase $\varphi$ and on pulse duration for laser intensities slightly below the tunneling regime, i.e., for the intensities range between the perturbative-multiphoton and tunneling regime, for laser pulses shorter than two laser cycles. In particular, we find that in this intensity regime, the asymmetry is zero for a fixed, particular value of $\varphi ={\varphi }_0\simeq -0.3\pi$ and is maximum for $\varphi ={\varphi }_M={\varphi }_0+\pi ∕2$. These regularities would allow one to measure the CE phase. In particular, the condition of zero asymmetry for few-cycle pulses can be useful for stabilizing the CE phase.