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arXiv:2406.17545 · Physical Review A

Accelerated creation of NOON states with ultracold atoms via counterdiabatic driving

Simon Dengis, Sandro Wimberger, Peter Schlagheck

Published Mar 10, 2025• 8 citations
arXivHTMLPDF

Abstract

The authors develop a theoretical protocol for creating highly entangled states with ultracold atoms, based on a combination of geodesic driving and counterdiabatic evolution. They demonstrate that the time required to generate high-quality NOON states robustly is reduced by several orders of magnitude using only time-independent controls.

DOI
10.1103/physreva.111.l031301

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New Journal of Physics•Sep 7, 2018•5 citations
The authors develop a theoretical protocol for creating highly entangled states with ultracold atoms, based on a combination of geodesic driving and counterdiabatic evolution. They demonstrate that the time required to generate high-quality NOON states robustly is reduced by several orders of magnitude using only time-independent controls.
We present a protocol for the generation of NOON states with ultracold atoms, leveraging the Bose-Hubbard model in the self-trapping regime. By means of an optimized adiabatic protocol, we achieve a significant reduction in the time required for the preparation of highly entangled NOON states, involving two or more modes. Our method saturates the quantum speed limit, ensuring both efficiency and high fidelity in state preparation. A detailed analysis of the geodesic counterdiabatic driving protocol and its application to the Bose-Hubbard system highlights its ability to expand the energy gap, facilitating faster adiabatic evolution. Through perturbation theory, we derive effective parameters that emulate the counterdiabatic Hamiltonian, enabling experimentally viable implementations with constant physical parameters. This approach is demonstrated to yield exponential time savings compared with standard geodesic driving, making it a powerful tool for creating complex entangled states for applications in quantum metrology and quantum information. Our findings pave the way for scalable and precise quantum state control in ultracold atomic systems.
This thesis investigates the fast and controlled generation of highly entangled many-body quantum states in systems of ultracold bosonic atoms. We focus in particular on the preparation of NOON states and their multimode generalizations, which constitute central resources for quantum metrology due to their enhanced sensitivity to parameter estimation. Working within Bose-Hubbard models in the self-trapping regime, where interaction effects dominate the dynamics, we exploit collective tunneling phenomena to isolate effective subspaces suitable for state engineering. To overcome the intrinsic slowness of adiabatic protocols, we introduce a control strategy based on the combined use of geodesic control and counterdiabatic driving, referred to as \textit{geodesic counterdiabatic driving}. This approach enables accelerated state preparation using time-independent and experimentally accessible control parameters, while reaching the quantum speed limit. We demonstrate the efficiency and robustness of the method for generating high-fidelity NOON states in optical lattices. Finally, we extend the framework to the creation of NOON states with vortices in two-dimensional harmonic traps and discuss applications to quantum-enhanced metrology, highlighting the feasibility of rotation sensing beyond classical limits.
Abstract We review a scheme for the systematic design of quantum control protocols based on shortcuts to adiabaticity in few-level quantum systems. The adiabatic dynamics is accelerated by introducing high-frequency modulations in the control Hamiltonian, which mimic a time-dependent counterdiabatic correction. We present a number of applications for the high-fidelity realization of quantum state transfers and quantum gates based on effective counterdiabatic driving, in platforms ranging from superconducting circuits to Rydberg atoms.
Recently, the technique of counterdiabatic driving, which provides an effective strategy for accelerating adiabatic quantum evolution, has been widely applied in the preparation of many-body quantum states. In this work, we propose a theoretical scheme for the efficient preparation of Dicke states in a system of non-interacting two-level atoms. Our approach leverages the one-axis twisting (OAT) interaction to generate non-classical correlations and combines it with time-dependent external fields to achieve precise control over the dynamics of the system. By employing rapid adiabatic passage (RAP), it demonstrates how the system can be steered from an initial coherent spin state to a target Dicke state with high fidelity [S. C. Carrasco, M. H. Goerz, S. A. Malinovskaya, V. Vuletić, W. P. Schleich, and V. S. Malinovsky, Phys. Rev. Lett. \textbf{132}, 153603 (2024)]. To further optimize the preparation process, we introduce counterdiabatic driving (CD), which suppresses non-adiabatic transitions. Numerical simulations confirm that our scheme can achieve high-fidelity Dicke states for a moderate number of particles. Our results provide a scalable and experimentally feasible approach to prepare Dicke states, with potential applications in quantum metrology, quantum communication, and quantum information processing.
We propose a one-step scheme for driving many atoms into a NOON state. In this scheme, two cavities are coupled to each other through the photon-hopping interaction and each cavity contains N four-level atoms. The 2 N atoms are driven into a NOON state via a phase-shift which depends on the collective atomic excitations. Interestingly, the time of generating the NOON state is independent of the atom number, i.e., it is unchanged with the increasing of the atom number. Also, our scheme is insensitive to cavity decay and can effectively suppress atomic spontaneous emission.