Symmetry Breaking Induced Multiphoton Processes

Nonlinear multi-photon processes are of important theoretical significance and have wide application prospects in optics and related disciplines.For example,they cannot only be used to produce the non-classical effects such as the squeezing effect,the anti-bunching effect and so on,but also can be used to realize the quantum logic gate and generate the quantum entangled state in the quantum information processing.Because the interaction between photons is usually extremely weak,the realization of multi-photon processes in normal nonlinear optics requires strong light field input,which is hard to apply in,for instance,quantum information processing and quantum computing.As well known that the quantum information is often encoded in thesingle photons,so how to generate nonlinear multi-photon processes at a single photon level is of great significance.In order to overcome such difficulties,several schemes have been proposed to yield strong nonlinear effects with weak input of the fields.For example,thetwo-photon absorption was realized by resorting to EIT;by using the Rydberginteraction between the atoms the high-order nonlinearity was enhanced;and very recently,a scheme was proposed to generate the multi-photon processes such as three-wave mixing and four-wave mixing by Nori's group.In recent years,thesuperconducting circuit quantum electrodynamics system provides us an almost ideal platform for interaction between light and matter.The advantages of thesuperconducting circuit QED system over the normal cavity QED system lies in the controllable ultra-strong coupling constant and the symmetry-broken potential in the interaction of the circuit qubit with the electromagnetic fields.Thus thesuperconducting circuit QED systems extend their applications.In this paper we present several schemes to generate the effective multi-photon interactions in the superconducting circuit QED system,mainly including:I)We propose a scheme to generate the effective degenerate two-photon interacting Hamiltonian for a single mode light field and a superconducting qubit.By the numerical calculation it is verified that the fidelity of our appropriate result and the numerical result is above 98.5%.II)We present a scheme to generate the effective nondegenerate two-photon interacting Hamiltonian for two modes of the light fields with frequencies ?₁ wand ?₂ and a superconducting qubit.The numerical calculation shows that the fidelity of our appropriate result and the numerical result is above 98.8%.III)We investigate interaction between a single superconducting qubit and two single mode resonators which contains the coupling between resonators,and present a scheme to generate the effective non-degenerate two-photon interacting Hamiltonian between the light fields and the qubit.The numerical calculation shows that thefidelity of our appropriate result and the numerical result is above 99.55%IV).We propose a scheme to generate the effective three-photon interacting Hamiltonian for two modes of the light fields with frequencies ?₁ wand ?₂ and a superconducting qubit.