Experimental realization of optimal time-reversal on an atom chip for quantum undo operations

TL;DR

This paper demonstrates the experimental implementation of optimal time-reversal operations on a Bose-Einstein condensate using an atom chip, achieving high accuracy and enabling quantum undo functionalities relevant for quantum computing.

Contribution

It introduces a novel experimental realization of optimal time-reversal routines on a multi-level quantum system using the dCRAB algorithm and atom chip technology.

Findings

Achieved around 92% accuracy in time-reversal transformations.

Implemented quantum undo operations on a five-level atomic system.

Provided a thermodynamic interpretation via the Loschmidt echo.

Abstract

We report on the use of the dCRAB optimal control algorithm to realize time-reversal procedures for the implementation of quantum undo operations, to be applied in quantum technology contexts ranging from quantum computing to quantum communications. By means of the undo command, indeed, the last performed operation can be time-reversed so as to perfectly restore a condition in which an arbitrary new operation, chosen by the external user, can be applied. Moreover, by further generalizing this concept, the undo command can also allow for the reversing of a quantum operation in a generic instant of the past. Here, thanks to optimal time-reversal routines, all these functionalities are experimentally implemented on the five-fold F=2 Hilbert space of a Bose-Einstein condensate (BEC) of non-interacting $^{87}$Rb atoms in the ground state, realized with an atom chip. Specifically, each time-reversal transformation is attained by designing an optimal modulated radio frequency field, achieving on average an accuracy of around 92% in any performed test. The experimental results are accompanied by a thermodynamic interpretation based on the Loschmidt echo. Our findings are expected to promote the implementation of time-reversal operations in a real scenario of gate-based quantum computing with a more complex structure than the five-level system here considered.