Drift effect on vacuum birefringence in a strong electric and magnetic field

As an important QED effect to detect the vacuum polarization, birefringence in the presence of a strong electric and magnetic field, E₀⊥B₀,E₀≤cB₀, is considered. The directional dependence of birefringence is obtained. In two special cases: E₀ = 0 and E₀ = cB₀, our results are consistent with the previous ones. The refractive index of the probe wave propagating in the E₀×B₀ direction decreases with E₀/cB₀, while that in the -E₀×B₀ direction increases with E₀/cB₀. The physics of the direction dependence of birefringence maybe the E₀×B₀ drift velocity of the virtual electrons and positrons.