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arXiv:1601.00369 · New Journal of Physics

Non-adiabatic generation of NOON states in a Tonks–Girardeau gas

James Schloss, Albert Benseny, Jérémie Gillet, Jacob Swain, Thomas Busch

Published Mar 22, 2016• 9 citations
arXivHTMLPDF

Abstract

Adiabatic techniques can be used to control quantum states with high fidelity while exercising limited control over the parameters of a system. However, because these techniques are slow compared to other timescales in the system, they are usually not suitable for creating highly unstable states or performing time-critical processes. Both of these situations arise in quantum information processing, where entangled states may be isolated from the environment only for a short time and where quantum computers require high-fidelity operations to be performed quickly. Recently it has been shown that techniques like optimal control and shortcuts to adiabaticity can be used to prepare quantum states non-adiabatically with high fidelity. Here we present two examples of how these techniques can be used to create maximally entangled many-body NOON states in one-dimensional Tonks–Girardeau gases.

DOI
10.1088/1367-2630/18/3/035012

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Adiabatic techniques can be used to control quantum states with high fidelity while exercising limited control over the parameters of a system. However, because these techniques are slow compared to other timescales in the system, they are usually not suitable for creating highly unstable states or performing time-critical processes. Both of these situations arise in quantum information processing, where entangled states may be isolated from the environment only for a short time and where quantum computers require high-fidelity operations to be performed quickly. Recently it has been shown that techniques like optimal control and shortcuts to adiabaticity can be used to prepare quantum states non-adiabatically with high fidelity. Here we present two examples of how these techniques can be used to create maximally entangled many-body NOON states in one-dimensional Tonks–Girardeau gases.
Shortcuts to adiabaticity (STA) are powerful tools that can be used to control quantum systems with high fidelity. They work particularly well for single particle and noninteracting systems which can be described exactly and which possess invariant or self-similar dynamics. However, finding an exact STA for strongly correlated many-body systems can be difficult, as their complex dynamics may not be easily described, especially for larger systems that do not possess self-similar solutions. Here, we design STAs for one-dimensional bosonic gas in the Tonks-Girardeau limit by using a mean-field approach that succinctly captures the strong interaction effects through a quintic nonlinear term in the Schrödinger equation. We show that for the case of the harmonic oscillator with a time-dependent trap frequency the mean-field approach works exactly and recovers the well-known STA from literature. To highlight the robustness of our approach we also show that it works effectively for anharmonic potentials, achieving higher fidelities than other typical control techniques. Published by the American Physical Society 2024
Abstract One of the key questions in quantum information is the preparation of desired multipartite quantum states with high fidelity. Adiabatic evolution has been widely explored to achieve state preparation in quantum many-body systems. However, in noisy quantum systems, the adiabatic approach faces a dilemma: either extending the evolution timescales to reduce diabatic transitions or shortening the timescales to mitigate decoherence effects. Various quantum control approaches have been studied to resolve this dilemma. In a few recent works, we utilized Jaynes-Cummings (JC) lattices as a platform to investigate the potential of several quantum control techniques in preparing quantum many-body states, including the optimized adiabatic evolution approach, the quantum optimal control technique, and quantum shortcuts to adiabaticity. Here we first give an overview of our previous results on utilizing quantum optimal control in JC lattices with unit filling and utilizing local counterdiabatic driving in JC lattices with a single excitation. Then we present our results on the energy costs and energy fluctuations in these approaches. Our studies give insights into the implementation of different approaches in practical quantum devices and the connection between the energy costs and the quantum speed limit in preparing desired quantum many-body states for quantum simulation and quantum computation.
We work out the theory and applications of a fast quasiadiabatic approach to speed up slow adiabatic manipulations of quantum systems by driving a control parameter as near to the adiabatic limit as possible over the entire protocol duration. We find characteristic time scales, such as the minimal time to achieve fidelity 1, and the optimality of the approach within the iterative superadiabatic sequence. Specifically, we show that the population inversion in a two-level system, the splitting and cotunneling of two-interacting bosons, and the stirring of a Tonks-Girardeau gas on a ring to achieve mesoscopic superpositions of many-body rotating and nonrotating states can be significantly speeded up.
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.