Optimal control of complex atomic quantum systems.

S Van Frank,T Pichler,M Bonneau,I Bloch,C Gross,J Schmiedmayer,S Hild,T Calarco,M Cheneau,S Montangero,A Negretti

doi:10.1038/srep34187

Abstract

Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit – the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.

Highlights

Of quantum systems in which the dynamics is affected by interactions between particles and where much is to be gained from speeding up the desired transformation
We simulate and optimize the dynamics by means of time-dependent Density Matrix Renormalization Group simulations and demonstrate the power of QOC to efficiently treat many-body dynamics: we cross the phase transition on a time scale compatible with the Quantum Speed Limit (QSL) — about one order of magnitude faster than the adiabatic protocol — while maintaining the same final state fidelity. This experiment is the first example of QOC applied to the crossing between different phases at the QSL and might have implications to improve the efficiency of future adiabatic quantum computation protocols
We theoretically engineered and experimentally implemented two optimally controlled processes at the numerically defined quantum speed limit, for different paradigmatic complex cold atom systems: the optimal preparation of a non-classical motional state of a Bose–Einstein condensate (BEC) in a magnetic trap and the 1D superfluid-to-Mott-insulator crossover of cold atoms in an optical lattice. The former experiment on cold atoms on an atom chip opens new perspectives for the development of accurate and sophisticated protocols for sensing, interferometry and cold atom manipulations. The latter results on the superfluid Mott-insulator (SF-MI) crossing demonstrate that the purity of the state reached by the fast optimal protocol is the same as the one obtained by means of the adiabatic protocol, and is the first experimental demonstration of optimal control of a crossover related to a quantum phase transition in a finite system

Summary

Introduction

Of quantum systems in which the dynamics is affected by interactions between particles and where much is to be gained from speeding up the desired transformation. We simulate and optimize the dynamics by means of time-dependent Density Matrix Renormalization Group simulations and demonstrate the power of QOC to efficiently treat many-body dynamics: we cross the phase transition on a time scale compatible with the QSL — about one order of magnitude faster than the adiabatic protocol — while maintaining the same final state fidelity. This experiment is the first example of QOC applied to the crossing between different phases at the QSL and might have implications to improve the efficiency of future adiabatic quantum computation protocols. This approach has been designed to solve optimal control problems where access to the knowledge of the system properties is limited and/or the computation of the figure of merit is highly demanding (see appendix A for details): for example when using tensor network methods[24,25], multi-configuration time-dependent Hartree Fock methods[26,27,28], or in a closed-loop setting whenever the optimization is performed directly as part of the experimental cycle[16]

Methods

Results

Conclusion