Terahertz Attoclock

Abstract

The attoclock provides a powerful tool for studying ultrafast electron dynamics on the attosecond timescale. We demonstrate an all-optical terahertz (THz) attoclock that reconstructs electron dynamics during photoionization by detecting THz radiation emitted from gases ionized by the fundamental and second harmonic two-color laser fields, without the need for photoelectron detection. The polarization direction of the emitted THz field reflects the direction of the photoelectron drift velocity and thus encodes the effective delay. By measuring the THz waves from argon atoms ionized by the two-color fields, and by precisely controlling their relative phase and ellipticity, we observe intensity-dependent rotations of the THz polarization direction. Both experiment and time-dependent Schrodinger equation simulations reveal that the effective delay extracted from the THz polarization direction decreases with increasing laser intensity, consistent with conventional photoelectron attoclock results. Our experiment establishes the feasibility of the THz attoclock as a contactless probe of tunneling dynamics, with promising applications to condensed matter systems where photoelectron detection is impractical.

Figures (4)

• Figure 1: Schematic of THz attoclock. A fundamental field with an ellipticity of $\epsilon_\omega\approx 0.81$ and its major axis direction along the $y$ axis, together with a circularly polarized second harmonic field ($\varphi=0$), jointly ionize Ar atoms. The ionized photoelectrons are accelerated and radiate THz waves under the action of the two-color fields. Because the drift velocity of tunneling electrons accelerated in the two-color fields determines the magnitude and direction of the radiated THz field, the THz polarization direction ($\hat{\boldsymbol{E}}_{\mathrm{THz}}$) aligns with the asymmetric direction of the PMD ($\hat{\boldsymbol{P}}_{\mathrm{PMD}}$). Equivalent to photoelectron attoclock, the time when electrons appear in the continuous state can also be mapped to the deflection of $\hat{\boldsymbol{E}}_{\mathrm{THz}}$. The angular offset $\Delta\theta$ refers to the angle between $\hat{\boldsymbol{E}}_{\mathrm{THz}}$ (or $\hat{\boldsymbol{P}}_{\mathrm{PMD}}$) and the minor axis of the $\omega$ field, which can be mapped to the effective delay in tunneling ionization. $\hat{\boldsymbol{E}}_{\mathrm{max}}$ refers to the direction at the peak of the total electric field.
• Figure 2: THz yield at different laser intensities $I$. (a,b) Measured and TDSE-calculated THz peak electric fields along the horizontal and vertical polarizations as a function of the relative phase of the two-color fields, $E_x(\varphi)$ (blue) and $E_y(\varphi)$ (red), at $I = 2.9\times10^{14}~\mathrm{W/cm}^2$. The $\varphi$ axis is calibrated. $\varDelta \varphi$ is defined as the phase difference between the $\varphi$ at the maximum of $E_x$ and that where $E_y = 0$. $\varDelta E$ denotes the absolute value of $E_y$ at the maximum of $E_x$. (c) TDSE-calculated PMD, along with the TDSE-calculated $\hat{\boldsymbol{E}}_{\mathrm{THz}}$ (red arrow) and measured THz polarization direction $\hat{\boldsymbol{E}}_{\mathrm{THz}}$ (black arrow) at $\varphi$ = 0 and $I = 2.9\times10^{14}~\mathrm{W/cm}^2$. (d,e) Same as (a,b), but for $I = 1.6\times10^{14}~\mathrm{W/cm}^2$. Error bars in (a) and (d) represent the standard deviation. (f) Same as (c), but for $I = 1.6\times10^{14}~\mathrm{W/cm}^2$.
• Figure 3:
• Figure 4: Polarization angle $\theta$ of the THz field $\hat{\boldsymbol{E}}_{\mathrm{THz}}$ as a function of the two-color relative phase $\varphi$ for different laser intensities $I$. (a) Experimental results for Ar. (b) TDSE and photocurrent simulations. The solid curves show the TDSE results. The green dotted curve shows the photocurrent prediction at a laser intensity of $1.3\times10^{14}~\mathrm{W/cm}^2$.