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arXiv:quant-ph/0511205 · Physical Review A

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

Edo Waks A, Jelena Vuckovic A

Published Apr 26, 2006• 75 citations
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Abstract

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 $\ensuremath{\pi}$ 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 $\ensuremath{\pi}$ phase shift is derived.

DOI
10.1103/physreva.73.041803

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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 \ensuremathπ\ensuremath{\pi}\ensuremathπ 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 \ensuremathπ\ensuremath{\pi}\ensuremathπ phase shift is derived.
The influence of Stark shift on the phase properties when an ideal cavity is filled with a Kerr-like medium and coupling is effected through nondegenerate Raman two-photon processes is studied. This has been carried out using the Hermitian phase formalism of Pegg and Barnett. We find that the phase properties of the field reflect the collapses and revivals of the level occupation probabilities in most situations. The interaction brings about the symmetrical splitting of the phase probability distribution. A number of interesting features are found and discussed.
We investigate the effects of decoherence on the nonlinear phase shift obtained from a one-dimensional atom implemented by a one-sided microcavity. The one-dimensional atom is realized by coupling a single atom confined in the cavity to the one-dimensional input-output fields of the cavity. The nonlinear optical response obtained from the one-dimensional atom can then be analyzed by using the optical Bloch equations. It is shown that the nonlinear phase shift depends on the coupling efficiency η, which is defined by the ratio of the coherent atom-field coupling rate and the total dipole relaxation rate. In particular, a maximal phase shift of π is obtained on resonance for coupling efficiencies η larger than one half, while the maximal phase shifts for coupling efficiencies η smaller than one half are obtained off resonance and are always smaller than π/2.
In this paper we investigate the absorptive and dispersive properties in the phase-sensitive optical parametric amplification inside a cavity. First, we study the single-resonant optical parametric amplifier theoretically and experimentally. In this case, the mode splitting in the transmission spectra and the M shape in the reflection spectra are observed. However, the shape of the phase shift of the reflected field is unchanged. Then, the double-resonant optical parametric amplifier is studied theoretically, in which electromagnetically induced transparency-like effect may be emulated when the cavity linewidth for the harmonic wave is narrower than for the subharmonic field. The narrow transparency window appears in the absorption spectrum and is accompanied by a very steep variation of the dispersive profile.
The enhancement of the optical nonlinear effects at nanoscale is important in the on-chip optical information processing. We theoretically propose the mechanism of the great Kerr nonlinearity enhancement by using anisotropic Purcell factors in a double-Λ type four-level system, i.e., if the bisector of the two vertical dipole moments lies in the small/large Purcell factor axis in the space, the Kerr nonlinearity will be enhanced/decreased due to the spontaneously generated coherence accordingly. Besides, when the two dipole moments are parallel, the extremely large Kerr nonlinearity increase appears, which comes from the double population trapping. Using the custom-designed resonant plasmonic nanostructure which gives an anisotropic Purcell factor environment, we demonstrate the effective nanoscale control of the Kerr nonlinearity. Such controllable Kerr nonlinearity may be realized by the state-of-the-art nanotechnics and it may have potential applications in on-chip photonic nonlinear devices.
We propose a new method to produce self- and cross-Kerr photonic nonlinearities, using light-induced Stark shifts due to the interaction of a cavity mode with atoms. The proposed experimental set-up is simpler than in previous approaches, while the strength of the nonlinearity obtained with a single atom is the same as in the setting based on electromagnetically induced transparency. Furthermore our scheme can be applied to engineer effective photonic nonlinear interactions whose strength increases with the number of atoms coupled to the cavity mode, leading to photon–photon interactions several orders of magnitude larger than previously considered possible.
We theoretically investigate the enhancement of Kerr nonlinearity through anisotropic Purcell factors provided by plasmon nanostructures. In a three-level atomic system with crossing damping, larger anisotropism of Purcell factors leads to more enhanced Kerr nonlinearity in electromagnetically induced transparency windows. While for fixed anisotropic Purcell factors, Kerr nonlinearity with orthogonal dipole moments increases with the decrease of its crossing damping, and Kerr nonlinearity with nonorthogonal dipole moments is very sensitive to both the value of crossing damping and the orientation of the dipole moments. We design the non-resonant gold nanorods array, which only provides subwavelength-confined anisotropic Purcell factors, and demonstrate that the Kerr nonlinearity of cesium atoms close to the nanorods array can be modulated at the nanoscale. These findings should have potential application in ultracompact quantum logic devices.