We analyze the nonlinear optical response of a four-level atomic system driven into a tripod configuration. The large cross-Kerr nonlinearities that occur in such a system are shown to produce nonlinear phase shifts of order . Such a substantial shift may be observed in a cold atomic gas in a magneto-optical trap where it could be feasibly exploited towards the realization of a polarization quantum phase gate. The experimental feasibility of such a gate is here examined in detail.
The very small size of optical nonlinearities places strict restrictions on the types of novel physics one can explore. For an ensemble of multilevel systems one can synthesize a large effective optical nonlinearity using quantum coherence effects but such non-linearities are technically extremely challenging to demonstrate at the single atom level. This work describes how a single artificial multi-level Cooper Pair Box molecule, interacting with a superconducting microwave coplanar resonator, when suitably driven, can generate extremely large optical nonlinearities at microwave frequencies, with no associated absorption. We describe how the giant self-Kerr effect can be detected by measuring the second-order correlation function and quadrature squeezing spectrum.PACS numbers: 03.67Hk, 03.67Lx, 05.50.+qIntroduction:-Given a sufficiently large optical nonlinearity with low quantum noise, it should be possible to generate and observe strictly quantum effects in electromagnetic fields. Examples of such effects include quadrature squeezing [1], generation of a superposition of macroscopically distinct quantum states [2], optical switching with single photons [3] and measurements of nonlocal correlations of entangled photon states [4]. So far, the successful demonstration of these effects has been limited to implementations with photons and atoms. The main obstacle for such an implementation -spontaneous emission-can be bypassed by exploiting quantum coherence effects in multilevel atoms. Such effects include coherent population trapping (CPT) [5], electromagnetically induced transparency (EIT) [6] and others.
We present a complete analytical solution for a single four-level atom strongly coupled to a cavity field mode and driven by external coherent laser fields. The four-level atomic system consists of a three-level subsystem in an EIT configuration, plus an additional atomic level; this system has been predicted to exhibit a photon blockade effect. The solution is presented in terms of polaritons. An effective Hamiltonian obtained by this procedure is analyzed from the viewpoint of an effective two-level system, and the dynamic Stark splitting of dressed states is discussed. The fluorescence spectrum of light exiting the cavity mode is analyzed and relevant transitions identified.
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