Long-wavelength spectral shift in an ultraviolet filament

Our experiments on focusing of ultraviolet $\ensuremath{\sim}250\text{\ensuremath{-}}\mathrm{nm}, \ensuremath{\sim}100\text{\ensuremath{-}}\mathrm{fs}$, 0.2-mJ pulses into a cuvette filled with diatomic air or monatomic argon show similar spectral transformations regardless of the gas if the pressure is the same. The spectra experience broadening and the long-wavelength shift, which increases monotonically with the pressure and reaches 2 nm at 1 atm. This long-wavelength shift cannot be explained by instantaneous Kerr nonlinear response and multiphoton ionization as two additive contributions to the nonlinear refractive index. The simulations based on the 1D time-dependent Schr"odinger equation reveal that the cubic nonlinearity is delayed by $\ensuremath{\sim}100$ as with regard to the driving field. This intraperiod delay comparable with the $\ensuremath{\sim}800\text{\ensuremath{-}}\mathrm{as}$ field cycle shifts the polarization spectrum to longer wavelengths and can be obtained solely from the quantum-mechanical approach, which we uniquely applied to the description of ultraviolet femtosecond filamentation.