Measuring the boiling point of the vacuum of quantum electrodynamics

It is a long-standing nontrivial prediction of quantum electrodynamics that its vacuum is unstable in the background of a static, spatially uniform electric field and, in principle, sparks with spontaneous emission of electron-positron pairs. However, an experimental verification of this prediction seems out of reach because a sizeable rate for spontaneous pair production requires an extraordinarily strong electric field strength $|\mathbf{E}|$ of order the Schwinger critical field, ${\mathrm{E}}_c=m_e^2/e\simeq 1.3\times {10}^{18}\mathrm{V}/\mathrm{m}$, where $m_e$ is the electron mass and $e$ is its charge. Here, we show that the measurement of the rate of pair production due to the decays of high-energy bremsstrahlung photons in a high-intensity laser field allows for the experimental determination of the Schwinger critical field and, thus, the boiling point of the vacuum of quantum electrodynamics.

Figure 1

Leading-order Furry picture [31] Feynman diagram for OPPP. The double line pointing forward (backward) in time represents an electron (a positron) in the background of the electromagnetic field of the laser.

Figure 2

The dimensionless function $F_{\gamma }(\xi ,{\chi }_{\gamma })$, Eq. (6), describing the probability of laser-assisted OPPP, as a function of the laser intensity parameter $\xi$, for different values of the photon recoil parameter ${\chi }_{\gamma }$ (solid lines). The dotted (dashed) line shows the analytic result valid at small (large) values of the intensity parameter, Eq. (8) [Eq. (9)].

Figure 3

Sketch of an experiment to produce high-energy photons by bremsstrahlung conversion in a high-$Z$ thin target and to cross them with a laser beam to let them decay into electron-positron pairs. Switching off the laser allows for a determination of the bremsstrahlung spectrum. Removing the target allows in addition for the study of HICS, followed by OPPP, and of the one-step trident process.

Figure 4

Number of $e^{+}{e}^{-}$ pairs produced per electron bunch ($6\times {10}^9$ electrons of energy $E_e=17.5\mathrm{GeV}$) impinging on the converter target (thickness $X/X_0=0.01$) and per laser shot (duration 35 fs) crossed with the bremsstrahlung photons, as a function of the laser intensity parameter $\xi$, for different values of ${\chi }_e$. The dashed line shows the analytic prediction resulting from (14), valid at $\xi \gtrsim 1/\sqrt{{\chi }_e}\gg 1$.

Figure 5

Top panel: Total number of $e^{+}{e}^{-}$ pairs produced per electron bunch ($6\times {10}^9$ electrons of energy $E_e=17.5\mathrm{GeV}$) impinging on the bremsstrahlung target (thickness $X/X_0=0.01$) and per laser shot (duration 35 fs, laser frequency $\omega =1.55\mathrm{eV}$, corresponding to a laser wavelength of 800 nm) crossed with the bremsstrahlung photons at an angle of $\theta =\pi /12$, as a function of the laser intensity. The dashed line shows the analytic prediction resulting from (14), exploiting the relations (11) and (16). The dotted (dot-dashed) line shows the same analytic prediction, but for the case where the value of the Schwinger critical field ${\mathrm{E}}_c$ deviates by a multiplicative factor of $\kappa =0.9$ ($\kappa =1.1$) from its nominal value (2). Bottom panel: The laser intensity parameter $\xi$ (dotted) and the electron recoil parameter (dashed), as a function of the intensity, cf. Eqs. (11) and (16).

Figure 6

Total number of $e^{+}{e}^{-}$ pairs produced per electron bunch ($6\times {10}^9$ electrons of energy $E_e$) impinging on the bremsstrahlung target (thickness $X/X_0=0.01$) and per laser shot (duration 35 fs, laser frequency $\omega =1.55\mathrm{eV}$, intensity $I=5\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$) crossed with the bremsstrahlung photons at an angle of $\theta =\pi /12$, as a function of $E_e$. The dashed line shows the analytic prediction resulting from (14), exploiting the relations (11) and (16). The dotted (dot-dashed) line shows the same analytic prediction, but for the case where the value of the Schwinger critical field ${\mathrm{E}}_c$ deviates by a multiplicative factor of $\kappa =0.9$ ($\kappa =1.1$) from its nominal value (2).