Quantum Process Tomography of an Optically-Controlled Kerr Non-linearity.

Connor Kupchak,Samuel Rind,Eden Figueroa,Bertus Jordaan

doi:10.1038/srep16581

Abstract

Any optical quantum information processing machine would be comprised of fully-characterized constituent devices for both single state manipulations and tasks involving the interaction between multiple quantum optical states. Ideally for the latter, would be an apparatus capable of deterministic optical phase shifts that operate on input quantum states with the action mediated solely by auxiliary signal fields. Here we present the complete experimental characterization of a system designed for optically controlled phase shifts acting on single-photon level probe coherent states. Our setup is based on a warm vapor of rubidium atoms under the conditions of electromagnetically induced transparency with its dispersion properties modified through the use of an optically triggered N-type Kerr non-linearity. We fully characterize the performance of our device by sending in a set of input probe states and measuring the corresponding output via time-domain homodyne tomography and subsequently performing the technique of coherent state quantum process tomography. This method provides us with the precise knowledge of how our optical phase shift will modify any arbitrary input quantum state engineered in the mode of the reconstruction.

Highlights

Any optical quantum information processing machine would be comprised of fully-characterized constituent devices for both single state manipulations and tasks involving the interaction between multiple quantum optical states
While a majority of recent experimental advancements regarding light-matter interaction at the quantum level have focused on operations involving a single quantum optical state[1,2,3,4], further functionalities are necessary in order to implement a future quantum processing machine
The creation of fully-characterized quantum light-matter interfaces suited for the interaction between weak quantum optical states and triggering signal fields mediated by atoms

Summary

Experimental Setup

We start with a three-level, Lambda atomic EIT scheme composed of two hyperfine grounds states that couple to a common excited state by a weak probe field ωp and a strong control field ωc. The phase shift undergone by the probe pulse can be controllably reduced by applying a particular power of the continuous wave signal field, as changes in transmission correspond to strong dispersion modifications in the atomic medium. The magnitude of this phase shift is quantified using time domain homodyne tomography[29]. From this data, the shape and length of the probe’s electric field envelope were calculated. This data is entered into a maximum-likelihood algorithm in order to generate the quantum state (see Fig. 3) or to perform quantum process reconstruction in the Fock basis (see Fig. 4)

Discussion

Findings

Additional Information