Dipolar optimal control of quantum states

TL;DR

The paper develops a dipolar quantum optimal control framework for ultracold atoms on a lattice ring, where the two-parameter orientation of the magnetic dipole moment acts as the control to drive dynamics under the extended Bose–Hubbard model. It analyzes fundamental controllability by symmetry; demonstrates that odd-site rings are fully controllable while even-site rings face inversion-symmetry-imposed limitations, including a dipolar-immune eigenstate that blocks certain evolutions. Through GRAPE-based numerical optimization, the authors show high-fidelity preparation of entangled current states (NOON and W) and quantify fidelity bounds set by symmetry and hard-core boson constraints, both in generic and experimentally realistic parameter regimes. The results establish dipolar QOC as a robust, generalizable approach for steering dipolar quantum systems, with clear implications for scalable quantum technologies and potential extensions to higher-dimensional lattices.

Abstract

Quantum state control is a fundamental tool for quantum technologies. In this work, we propose and analyze the use of quantum optimal control to exploit the dipolar interaction of ultracold atoms on a lattice ring, focusing on the generation of selected states with entangled circulation. This scheme requires time-dependent control over the orientation of the magnetic field, a technique that is feasible in ultracold atom laboratories. The system's evolution is driven by just two independent control functions. We describe the symmetry constraints of this approach and numerically test them using the extended Bose-Hubbard model. We find that the proposed control can engineer entangled current states with perfect fidelity across a wide range of systems, and that in the remaining cases, the theoretical upper bounds for fidelity are reached.

Figures (4)

• Figure 1: (a) Schematic representation of the system with $L=7$ sites and dipole polarization along the $z$-axis. (b) Example trajectory during a dipolar QOC protocol. (c) Example of optimal trajectories for two different numbers of steps $M$.
• Figure 2: Final fidelity obtained via the dipolar QOC protocol as a function of the control time $t_c J /\hbar$ for the preparation of different entangled current states $\ket{\Psi_{\mathrm{EC}}}$. Each target state is represented with a different marker shape following the legend above the plots. Panel (a) shows systems with $N=2$ particles and varying number of sites, while panel (b) presents systems with $N=2,3$ particles for only $L=4,5$ sites. These two panels consider $U/J = 1$ and $U_d / (d^3 J)=1.25$ interaction strengths. Results shown in panel (c) are for $L=7$ sites, with experimental $U/J=74$ and $U_d/(d^3 J)=1.11$ interaction strengths. The horizontal lines represent the maximum possible fidelity given by Eqs. (\ref{['eq:symbound']}) and (\ref{['eq:boundDI']}) in panel (b), and by Eq. (\ref{['eq:boundHCB']}) in panel (c). Each point shows the best fidelity achieved over 10 optimization runs (to reduce the dependence on the initial trajectory proposed), with $M=30$ control pulses.
• Figure 3: Evaluation of (a) the quantum speed limit and (b) the triangle inequality for the optimal trajectories obtained for the system with $L=9$, $N=2$ for the preparation of the EC state with $\Omega=\{-1,1\}$.
• Figure 4: Final fidelity obtained with the dipolar QOC protocol as a function of the control time $t_c J /\hbar$ for the target states indicated in each panel. Each color corresponds to distinct combinations of $N$ and $L$. Each point shows the best fidelity achieved over 10 optimization runs using $M=30$ control steps. The results shown in both panels correspond to interaction strengths of $U/J = 1$ and $U_d / (d^3 J)=1.25$.