Limits on tradeoffs between third-order optical nonlinearity, absorption loss, and pulse duration in self-induced transparency and real excitation.

Abstract

Self-induced transparency in a resonant two-level system creates a 2\ensuremath{\pi}-soliton pulse, which realizes large optical nonlinearities with a small absorption loss \ensuremath{\alpha} for a short pulse duration \ensuremath{\tau}. Quantum-mechanical zero-point field fluctuations introduce an ultimate dissipation loss in such a resonant and coherent process and place fundamental limits on the ${\mathrm{\ensuremath{\chi}}}^{(3)}$/\ensuremath{\alpha}\ensuremath{\tau} value. This value is independent of the dipole moment, atomic density, and pulse duration and is uniquely determined by an optical wavelength, e.g., ${\mathrm{\ensuremath{\chi}}}^{(3)}$/\ensuremath{\alpha}\ensuremath{\tau}\ensuremath{\sim}1.2\ifmmode\times\else\texttimes\fi{}${10}^{21}$${\ensuremath{\lambda}}^{4}$ esu cm/s. The similar limit on ${\mathrm{\ensuremath{\chi}}}^{(3)}$/\ensuremath{\alpha}\ensuremath{\tau} value is obtained in a usual operation mode, when the pulse duration becomes much longer than the atomic decay constants and the real excitation of the atoms occurs instead of the virtual excitation in self-induced transparency. The implication of these limits on optical squeezed-state generation, quantum nondemolition measurement, and reversible logic is discussed.