Barrier Control in Tunneling $e^{\mathbf{+}}\mathbf{\text{−}}{e}^{\mathbf{-}}$ Photoproduction

Tunneling electron-positron pair production is studied in a new setup in which a strong low-frequency and a weak high-frequency laser field propagate in the same direction and collide head-on with a relativistic nucleus. The electron-positron pair-production rate is calculated analytically in the limit in which in the nucleus rest frame, the strong field is undercritical and the frequency of the weak field is below and close to the pair-production threshold. By changing the frequency of the weak field, one can reduce the tunneling barrier substantially. As a result, tunneling pair production is shown to be observable with presently available technology.

Figure 1

Part (a) Schematic setup of the considered process. An $e^{+}\mathrm{\text{−}}{e}^{-}$ pair is created by a light pulse consisting of a weak, high-frequency laser field and a strong, low-frequency laser field colliding head-on with a relativistic nucleus. Part (b) Polarization operator of a photon in a plane wave. The crossed photon lines represent the Coulomb field of the nucleus, and the thick electron lines are electron propagators in the plane wave. The vertical dashed line links the polarization operator to the pair-production diagram.

Figure 2

Schematic picture of the tunneling mechanism. The electron has initially a negative energy $-m$, absorbs one photon with energy ${\omega }_w$, and is finally transferred into the positive continuum by tunneling the distance $l=l_0-{\omega }_w/e{E}_0$ with $l_0=2m/e{E}_0$ through the barrier tilted by the electric field ${\mathbf{E}}_0=E_0\widehat{\mathbf{x}}$.

Figure 3

The ratio $\dot{W}/{\dot{W}}_0$ with ${\dot{W}}_0=(Z\alpha {)}^{2}m{\eta }^2{\chi }^2/2\pi$ and $\dot{W}$ given by Eq. (7) for circular polarization of the strong laser field (continuous curve) and by Eq. (8) for linear polarization of the strong and the weak laser fields with ${\mu }_s={\mu }_w=+1$ (dashed curve). The inset shows the region of small $\zeta$ on a logarithmic scale.