Dispersive properties and large Kerr nonlinearities using dipole-induced transparency in a single-sided cavity

We calculate the dispersive properties of a single-sided cavity coupled to a single dipole. We show that when a field is resonant with the dipole and the Purcell factor exceeds the bare cavity reflection coefficient, the field experiences a $\pi$ phase shift relative to reflection from a bare cavity. We then show that optically Stark shifting the dipole resonance with a second field creates large Kerr nonlinearities. An approximate expression for the total number of photons needed to create a $\pi$ phase shift is derived.

Figure 1

(Color online) Setup for large Kerr nonlinearities off of reflection from a cavity coupled to a single dipole.

Figure 2

Cavity reflection coefficient for different values of $g$: (a) $g=0.3\mathrm{THz}$, (b) $g=0.15\mathrm{THz}$, (c) $g=0.33\mathrm{THz}$.

Figure 3

Phase shift after reflection from cavity, normalized by $\pi$, for several values of $g$: (a) $g=0\mathrm{THz}$, (b) $g=0.15\mathrm{THz}$, (c) $g=0.33\mathrm{THz}$.

Figure 4

Reflection phase shift in presence of a single photon inside the cavity at frequency $\nu +\Delta$. It is assumed that $g_1=g_2=g=0.3\mathrm{THz}$. (a) $\Delta =\infty$, (b) $\Delta =-3g$.