Role of quantum dynamics in coherent and incoherent radiation during tunneling ionization

TL;DR

The paper investigates radiation emitted during strong-field tunneling ionization, separating coherent and incoherent components and assessing the impact of under-the-barrier quantum dynamics. Using the strong-field approximation (SFA) to compute current densities and a Drude model to isolate continuum contributions, it maps spectral features to distinct mechanisms: three-step HHG for high frequencies and Brunel/Thomson processes for low frequencies, with continuum dynamics and free-free transitions shaping near-zero-frequency emission. It finds that quantum dynamics modify the near-zero-frequency Brunel radiation (while spontaneous radiation widths are governed by the Keldysh time), and that under-the-barrier recollisions contribute negligibly to the spectra, a conclusion reinforced by comparison with experiment and by correlated electron–photon measurements. The work provides a practical framework for probing quantum tunneling dynamics through radiation and informs future low-frequency (THz to mid-IR) strong-field experiments.

Abstract

Radiation during strong-field tunneling ionization is investigated. The spontaneous as well as the coherent components of the radiation are calculated describing the ionization dynamics via the strong field approximation and the role of the quantum dynamics at tunneling is analyzed. The competition between different mechanisms in different spectral regions is examined. Transition-like radiation (Brunel radiation) is dominated at low-frequencies, Thomson scattering at the laser frequency, and radiative recombination via the three-step process at high-order harmonics. To distinguish the role of the quantum dynamics, simple man Drude models are developed for the coherent as well as for spontaneous radiation, which are based on the electron trajectory out of the tunneling barrier. The quantum dynamics is shown to modify the coherent Brunel radiation for near-zero-frequencies in asymmetric laser pulses. The significant role of free-free transitions is demonstrated for the spontaneous radiation in the low-frequency region.

Figures (5)

• Figure 1: Coherent radiation spectra during tunneling ionization with $E_0=0.1$, $\omega_0=0.05$, and $N=12$: (a) in the asymmetric laser pulse ${\cal A}=0.1$ [Eq. (\ref{['alpha']})], (b) in the symmetric laser pulse ${\cal A}=0$. Comparison of the Brunel radiation via $J_{11}$ with the three-step HHG ($J_{01}+J_{10}$) and with the Drude model ($J_{\rm D}$). The total radiation with the full current $J=J_{01}+J_{10}+J_{11}$ is given for comparison.
• Figure 2: Coherent radiation spectra during tunneling ionization in the asymmetric laser pulse: (first column) $E_0 = 0.1$ [zoomed-in view Fig. \ref{['JJ']}(a)]; (second column) $E_0 = 0.075$. Comparison of the Brunel radiation via $J_{11}$ with the three-step HHG ($J_{01}+J_{10}$) and with the Drude model ($J_{\rm D}$).
• Figure 3: Spontaneous radiation spectrum during tunneling ionization: (left column) asymmetric few-cycle laser pulse, (right column) symmetric laser pulse, in both case $N=4$; (a,b) for $E_0=0.1$, (c,d) for $E_0=0.075$. The contributions of amplitudes in different approximations $m_0$, $m_1$, and $m_0+m_1$ are specified. The results of the simple man Drude model are indicated by $m_D$.
• Figure 4: Total probability of photon emission vs electron final momenta in the case of the correlated electron and photon measurement, for $E_0=0.2$ a.u. and a half-cycle pulse; the value for the $m_0$ contribution is multiplied by $20$.
• Figure 5: The radiation spectrum at strong field ionization near the low-frequency region for the approximate parameters of the experiment of Ref. Clerici_2013: $E_0=0.1$, ${\cal A}=0.2$.