Continuous-variable quantum swapping gate between light and atoms

In the face of the recent development of the time-domain detection method for short pulses, typically less than 1 microsecond, we consider a feasible method for a continuous variable quantum swapping gate between light polarization and atomic spin ensemble by three successive Faraday rotation interactions using short pulses. This method does not need any particular initial states and its fidelity can ideally run up to one. It also works as a quantum memory of light and a device to generate a nonclassical state of the spin. To evaluate a quantum nature of the proposed swapping gate, we calculated its average fidelity for a set of the coherent states with a Gaussian distribution and confirmed the efficiency as a quantum gate as well as a quantum memory of light.