Study Of The Nonlinear Characteristics Based On Atomic Coherence

As we all known,photons are ideal carriers of quantum information processing since they propagate at the speed of light and have extremely weak coupling to the environment.However,the processing of information based on light often requires enhanced nonlinear interactions between photons.As a result,the feasibility to achieve strong nonlinear interactions between photons is important for the applications in quantum in-formation processing.Cross-Kerr nonlinearity,also known as cross-phase modulation,has received considerable attention due to the preparation of the strong photon-photon interactions.Meanwhile,efficient manipulation of optical quanta demands medium possessing large and lossless optical nonlinearities.However,these requirements are incompatible in conventional media due to the linear absorptions and losses.Recently,it was shown theoretically and experimentally that atomic coherent effects,such as coherent population trapping(CPT)and electromagnetically induced transparency(EIT),can effectively suppress the linear absorption of the resonant multilevel media while keeping the nonlinear susceptibility at a very high level.However,an ideal CPT medium does not interact with the light at all.It means that it cannot produce any nonlinear effects.In order to get a nonlinear interaction in such a medium,we need to disturb the CPT regime by introducing perturbation of the dark state.From nonlinear optics,it is well known that the nonlinear interaction between the fields is more stronger with the order n in the susceptibility x(n)being smaller.However,in centrosy1metry medium,for instance atoms,the second-order susceptibility x(2)vanishes.In order to enhance further the nonlinear interaction between the fields,we treat two strong dressing fields and the atom as coherent medium.We only focus on the response of the CPT atom to the applied probe fields,and then the atom-field system shows new nonlinear effects.In addition,close to EIT,the great disparity of the relative amplitudes between the coupling and probe fields determines only the presence of the self-Kerr nonlinearity in three-level atomic system.To obtain the cross-Kerr nonlinearity,many schemes resort to the extra atomic level and probe field.In this case,either the self-Kerr nonlinearity or the cross-nonlinearity happens.We note that when two or more weak probe fields are confined within the common EIT window,the enhanced Kerr nonlinearities between the probe fields with suppressed linear absorption occur.The emphasis of this thesis is to produce enhanced nonlinear effects based on atomic coherence,such as EIT and CPT.The innovative contents are presented as follows1.Giant second-order cross nonlinearities via direct perturbation to the dark state in CPT.We study the nonlinearities due to direct perturbation to the dark state in CPT.To extract the susceptibilities of the CPT atoms with respect to probe fields,we treat the CPT dressing fields as control parameters and redefine susceptibilities with respect to the probe fields alone.With such a redefinition,we reveal that a CPT-based system displays an ultralarge,resona1tly enhanced second-order cross susceptibility x(2)together with vanishing linear absorption.Physically,this effect is based on the CPT dark-state shift,which is traced to the six-photon parametric processes for all involved fields(including the dressing and probe fields).Because of the lack of the direct perturbation,this effect is absent in the EIT-based system,in which only resonantly enhanced third-order(Kerr)susceptibility χ(3)is obtainable but much weaker than the second-order one.The second-order nonlinearity,because of its stronger effect,can be more sensitive for quantum nonlinear optics at low light levels than the third-order nonlinearity.Consequently,we can apply such second-order nonlinearity to quantum nondemolition measurements.2.Polychromatic Kerr nonlinearities within EIT window.We study the nonlinear effect in a three-level atomic system in A configuration.As two or more fields are confined within the common EIT window,both the self-and cross-Kerr nonlinearities with almost-vanishing absorption occur.Our scheme is different from the existed EIT-based schemes,either the self-Kerr or the cross-Kerr nonlinearity can be obtained solely.Within the common EIT window,the bi-and trichromatic nonlinearities are analyzed in considerable detail.Furthermore,our scheme can be easily generalized to produce the polychromatic Kerr nonlinearity.Since the gross atomic population is almost in the dark state,the field operators are separated from degrees of freedom of atoms,and our scheme is robust to spontaneous emission.Therefore,our scheme can be used to create good squeezing or large entanglement between two or more fields.