The magnetic-field dependence of the third-order excitonic nonlinear susceptibility (3) in a quantum wire is explored within the rotating wave approximation. Both the real and imaginary parts of (3) , arising from population saturation of the excitonic state under optical pumping, are calculated for a GaAs wire as a function of magnetic field and pump-probe detuning frequencies. The imaginary part of (3) exhibits a negative peak associated with the bleaching of the excitonic resonance and a

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... tive, broad, off-resonance absorption peak associated with biexciton formation. The amplitude, line shape, and spectral frequency of both these peaks can be modulated by a magnetic field which indicates the possibility of using such a field to probe the mechanism underlying optical nonlinearity in a quantum wire. Furthermore, the field can also be used to tune the optical nonlinearity over a range of frequencies which has device applications.