Asymmetric photoelectron momentum distributions due to quantum interference in strong-field ionization by a few-cycle pulse

We calculate the left-right asymmetry of the photoelectron momentum distributions generated in a hydrogen atom exposed to an intense few-cycle laser pulse as a function of both the carrier-envelope phase and the laser intensity. We present results of the numerical solution of the three-dimensional time-dependent Schrödinger equation, semiclassical simulations accounting for both laser and Coulomb fields, and the strong-field approximation. We predict pronounced oscillations of the asymmetry parameter as a function of the intensity for a particular range of the carrier-envelope phase. In order to reveal the mechanism underlying these oscillations, we investigate in detail the electron momentum distributions in the one-dimensional case. We show that quantum interference among a large set of both bound and continuum field-free states is responsible for the oscillatory behavior of the left-right asymmetry.

Figure 1

Two-dimensional photoelectron momentum distribution for $k_z=0$ for ionization of H by a Ti:sapphire laser pulse ($\lambda =800$ nm) with a duration of $n_p=4$ cycles, field strength of $F_0=0.04$ a.u. ($5.6\times {10}^{13}$ W/cm${}^2$), and CEP of $\phi =0.83\pi$. The Keldysh parameter is $\gamma =1.4$. The color density is plotted in logarithmic scale.

Figure 2

Asymmetry of the photoelectron momentum distributions as a function of the CEP and field strength for the hydrogen atom at a wavelength of 800 nm. (a),(d) The asymmetries calculated from the solution of the 3D TDSE. (b),(e) The same asymmetries calculated using the semiclassical two-step model. (c),(f) The SFA results. (a)–(c) and (d)–(f) correspond to the pulse duration $n_p=2$ and $n_p=4$, respectively. The point corresponding to the photoelectron momentum distribution of Fig. 1 is indicated by a white square in (d).

Figure 3

Asymmetry of the photoelectron momentum distributions as a function of the CEP and field strength for a 1D model atom with soft-core potential given by Eq. (18) and for a wavelength of 800 nm. (a)–(c) and (d)–(f) correspond to the pulse durations $n_p=2$ and $n_p=4$, respectively. (a) and (d) show the asymmetries calculated from the solution of the 1D TDSE. (b) and (e) present the asymmetries calculated using the two-step model. (c) and (f) depict the results of the 1D SFA.

Figure 4

(a),(b) Ionized part of the wave function in momentum space during the laser pulse defined by the vector potential (1) for 1D model atom [Eq. (18)], and (c),(d) momentum distributions at the end of the pulse in Eq. (1). The areas contained within the dashed lines in panels (a) and (b) correspond to the bound-state part of the wave packet. Panels (a) and (c) correspond to $F_0=0.076$ a.u., whereas (b) and (d) show results for $F_0=0.079$ a.u. The wavelength is $\lambda =800$ nm, the pulse duration is $n_p=4$, and the CEP is $\phi =0.83\pi$.

Figure 5

Asymmetry of the photoelectron momentum distributions as a function of the CEP and field strength for a 1D model atom with soft-core potential given by Eq. (18) at a wavelength of 800 nm and for $n_p=4$. (a) The asymmetry when only the ground state is included. (b) The case when the ground state and first excited state are taken into account. (c) The asymmetry when the ground state and the first through fourth excited states are included. (d)–(f) The inclusion of the ground state and all the excited states up to the 10th, 20th, and 30th state, respectively. In all cases (a)–(f), all of the continuum states are taken into account in Eq. (35).

Figure 6

Asymmetry of the photoelectron momentum distributions as a function of the field strength for a 1D model atom with the potential of Eq. (18) at a wavelength $\lambda =800$ nm for some fixed values of CEP: (a) $\phi =0$, (b) $\phi =\pi /2$, (c) $\phi =3\pi /2$, and (d) $\phi =2\pi$. The dashed, thin solid, and thick solid curves show cuts of Figs. 5, 5, and 5, respectively.

Figure 7

Photoelectron momentum distributions calculated using the two-step model for ionization of a 1D model atom [Eq. (18)] by a pulse with a duration of (a) $n_p=2$ and (b) $n_p=4$. The dashed and solid curves correspond to $F_0=0.05$ a.u. and $F_0=0.09$ a.u., respectively. The wavelength is $\lambda =800$ nm and the CEP is $\phi =1.38\pi$.