Complete characterization of sub-Coulomb-barrier tunnelling with phase-of-phase attoclock

Abstract

Laser-induced electron tunneling, triggering a broad range of ultrafast phenomena such as the generation of attosecond light pulses, photoelectron diffraction and holography, has laid the foundation of strong-field physics and attosecond science. Using the attoclock constructed by single-color elliptically polarized laser fields, previous experiments have measured the tunneling rates, exit positions, exit velocities and delay times for some specific electron trajectories, which are mostly born at the field peak instant where the laser electric field and the formed potential barrier are stationary in terms of the derivative versus time. From the view of the wave-particle dualism, the electron phase under a classically forbidden, tunneling barrier has not been measured, which is at the heart of quantum tunneling physics. Here we present a robust measurement of tunneling dynamics including the electron sub-barrier phase and amplitude. We combine attoclock technique with two-color phase-of-the-phase spectroscopy to accurately calibrate the angular streaking relation and to probe the non-stationary tunneling dynamics by manipulating a rapidly changing potential barrier. This phase-of-phase attoclock (POP attoclock) directly links the measured phase of the two-color relative phase with the ionization instant for the photoelectron with any final momentum on the "detector", which allows us to reconstruct the imaginary tunneling time and the accumulated phase under the barrier. The POP attoclock provides a general time-resolved approach to access the underlying quantum dynamics in intense-light-matter interactions.

Full experimental determination of tunneling time with attosecond-scale streaking method

“…Using the present scheme, we can further retrieve the ionization time of electrons with different energies 33 . Figure 4a shows the extracted tunneling ionization time with respect to the electron momentum p r ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p 2 z þ p 2 y q and the electron emission angle from the measurement.…”

Attosecond ionization time delays in strong-field physics

“…Another variant of the phase-of-phase attoclock involves a strong elliptically polarized 800 nm laser field and a weak co-rotating circularly polarized 400 nm laser pulse. [162] The weak 400 nm pulse breaks the symmetry in the elliptical pulse such that the two lobes of the attoclock momentum distribution are no longer symmetric. As the relative phase between the two pulses varies, the relative strength of the two lobes also varies, providing thereby richer information than the common single-color attoclock, which enables the retrieval of not only the real tunneling time but also the imaginary tunneling time and the quantum phase accumulated under the tunneling barrier.…”

Does the Hartman effect exist in triangular barriers

“…These include the tunneling flight time [10,11] introduced by Rivlin et al, the selfadjoint time operator introduced in analogy with the relativistic Dirac Hamiltonian [24] and the entropic time inspired by the statistical implication from the relation between the imaginary Büttiker-Landauer time and the inverse temperature. [25] With the push from the rapid progress in attosecond science, [26] the question of whether quantum tunneling takes a finite time or is instantaneous seems closer to be answered. Even if it is acknowledged that tunneling takes a finite time, a well-accepted time definition in the academic community is still lacking.…”