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The quantum superluminality in the tunnel-ionization process of H-like atoms

Ossama Kullie, Igor A. Ivanov

Abstract

The quantum tunneling time remains the subject of heated debate, and one of its most curious features is faster-than-light or superluminal tunneling. Our tunnel-ionization model of the time-delay, presented in previous work, shows good agreement with the attoclock measurement in the adiabatic and nonadiabatic field calibrations, which also enables the determination of the barrier time-delay. In the present work, we show that the tunnel-ionization for H-like atoms with large nuclear charge can be superluminal (quantum superluminality), which in principle can be investigated experimentally using the attoclock scheme. We discuss the quantum superluminality in detail for the different regimes of the tunnel-ionization. Our result shows that quantum tunneling faster-than-light is indeed possible, albeit only under somewhat extreme conditions.

The quantum superluminality in the tunnel-ionization process of H-like atoms

Abstract

The quantum tunneling time remains the subject of heated debate, and one of its most curious features is faster-than-light or superluminal tunneling. Our tunnel-ionization model of the time-delay, presented in previous work, shows good agreement with the attoclock measurement in the adiabatic and nonadiabatic field calibrations, which also enables the determination of the barrier time-delay. In the present work, we show that the tunnel-ionization for H-like atoms with large nuclear charge can be superluminal (quantum superluminality), which in principle can be investigated experimentally using the attoclock scheme. We discuss the quantum superluminality in detail for the different regimes of the tunnel-ionization. Our result shows that quantum tunneling faster-than-light is indeed possible, albeit only under somewhat extreme conditions.
Paper Structure (20 sections, 18 equations, 9 figures)

This paper contains 20 sections, 18 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Adiabatic tunneling:
  3. Nonadiabatic tunneling:
  4. Barrier time-delay:
  5. thick-barrier and Weak measurement
  6. The Quantum Superluminaliy
  7. QS in adiabatic tunnel-ionization
  8. Barrier time-delay
  9. Adiabatic time-delay
  10. QS in nonadiabatic tunnel-ionization
  11. With $\tau^{Ad}_{c}$:
  12. With $\tau^{Nad}_{c}$:
  13. The intermediate regime
  14. Establishing a model for the intermediate regime
  15. QS in the intermediate regime
  16. ...and 5 more sections

Figures (9)

  • Figure 1: (Color online) A sketch of the atomic and the effective potential curves, showing the height and width of the barrier formed by the interaction with the laser field. The plot is for He-atom in the SAEA model with $Z_{eff}=1.6875$ and $I_{p}\approx0.9\, au$.
  • Figure 2: (Color online) Outline of tunnel-ionization in three cases: adiabatic (dashed-dotted, red), intermediate (dotted, magenta, purple) and nonadiabatic (dashed, light blue). As well as the barrier-suppression ionization at $F_{a}$ (green).
  • Figure 3: (Color online) (a): Tunnel-ionization time-delay in the adiabatic and nonadiabtic field calibration $\tau_{Ad}, \tau_{dion}$ vs. field strength $F$ (in au) for $Z=18$. (b): Time-delay of the barrier $\tau_{dB}$ (green) and the time of light $\tau_{c}^{Ad}$ (orange) vs. field strength $F$ (in au) for $Z=18$, see Eq. \ref{['zvalue']}. Hereafter "as" is the abbreviation for attosecond.
  • Figure 4: (Color online) (a): tunnel-ionization $\tau_{dB}$ (Eq. \ref{['tdb']}) vs. $Z$ for $F=1 au$, The green/white area is subluminal/superluminal. (b): $\tau_{dB}$ vs. barrier width $d_{B}(F)$ for different $Z$-values. The boundary between subluminal area (green) and superluminal area (white) is along $Z=c/8$, see Eq. \ref{['zvalue']}.
  • Figure 5: (Color online) $Q_{Nad}$ (see Eq. \ref{['qsnad']}) vs. field strength $F$ (in au) for various $Z$ values. In the colored area below the red dashed line, tunnel-ionization is superluminal, which is the case when $Z \ge 35$.
  • ...and 4 more figures