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Enhanced creation of many-body entanglement via geodesic counterdiabatic driving

Simon Dengis

Published Feb 6, 2026• 0 citations
OpenAlex

Abstract

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.

Related papers

Multimode NOON-state generation with ultracold atoms via geodesic counterdiabatic driving

Simon Dengis, Sandro Wimberger, Peter Schlagheck

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.

arXiv:2506.01948•Physical Review A•Sep 22, 2025•4 citations

Accelerated creation of NOON states with ultracold atoms via counterdiabatic driving

Simon Dengis, Sandro Wimberger, Peter Schlagheck

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.

arXiv:2406.17545•Physical Review A•Mar 10, 2025•8 citations

Optimizing the preparation of Dicke states using counterdiabatic driving methods

Fengzhe Tang, Gangcheng Wang

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.

quant-pharXiv:2605.14378•May 15, 2026•0 citations

Vortex NOON states for rotation sensing

Simon Dengis, Nathan Dupont, Peter Schlagheck +1 more

We introduce a scheme to generate NOON states of few-body bosonic vortices and demonstrate their application as high-precision rotation sensors. Our approach is based on cold atoms in a weakly anisotropic two-dimensional harmonic trap, where the single-particle p orbitals define an effective two-mode Bose-Hubbard model with vortex modes $(\mathrm{p}_x\pm\mathrm{i}\mathrm{p}_y)$ carrying opposite circulation. In the self-trapping regime, we show that the NOON manifold becomes spectrally isolated, and collective tunneling processes give rise to highly entangled vortex NOON states. However, these states emerge on prohibitively long timescales. To overcome this limitation, we develop two complementary acceleration strategies: geodesic counterdiabatic driving for small particle numbers, and resonance- and chaos-assisted tunneling in the semiclassical regime at larger particle numbers. Both approaches enable the generation of NOON states on experimentally relevant timescales while preserving near-unit fidelities. Finally, we quantify the metrological advantage of vortex NOON states by introducing an interferometric protocol that exploits their intrinsic sensitivity to rotation, enabling the detection of infinitesimal external rotations at the Heisenberg limit. Our work opens the door to rotation sensors based on atomic NOON states, generically realizable in bosonic Josephson junctions with vortex-type orbitals.

arXiv:2606.29509•Jun 28, 2026•0 citations

Time-independent counterdiabatic driving for emergent two-level subspaces in many-body systems

Simon Dengis, Peter Schlagheck

We show that geodesic motion in the Riemannian manifold of quantum states provides a direct route to time-independent counterdiabatic driving. Using the relation between the counterdiabatic Hamiltonian and the quantum metric tensor, we prove that a constant-speed geodesic makes the Hilbert-Schmidt norm of the counterdiabatic Hamiltonian constant. For effective two-level systems whose counterdiabatic correction has a fixed operator direction, this further implies that the full counterdiabatic Hamiltonian itself is time independent. We illustrate this result with the Landau-Zener model, three-level Stimulated Raman adiabatic passage and a collectively driven Rydberg ensemble in the blockade regime. Limitations of this approach in realistic many-body systems are discussed, where the two-level reduction is only emergent and leakage out of the effective subspace bounds the achievable speedup. In all cases, time-independent counterdiabatic driving achieves unit-fidelity state preparation on timescales substantially shorter than conventional adiabatic protocols while replacing temporally shaped auxiliary controls by fixed-amplitude fields.

quant-pharXiv:2607.12848•Jul 15, 2026•0 citations

Engineering multi-mode bosonic squeezed states using Monte-Carlo optimization

Jieqiu Shao, Diego A. R. Dalvit, Lukasz Cincio +1 more

Bosonic systems, such as photons and ultracold atoms, have played a central role in demonstrating quantum-enhanced sensing. Quantum entanglement, through squeezed and GHZ states, enables sensing beyond classical limits. However, such a quantum advantage has so far been confined to two-mode bosonic systems, as analogous multi-mode squeezed states are non-trivial to prepare. Here, we develop a Monte-Carlo based optimization technique which can be used to efficiently engineer a Hamiltonian control-sequence for multi-mode bosonic systems to prepare multi-mode squeezed states. Specifically, we consider a Bose-Einstein condensate in an optical lattice, relevant for applications in gravimetry and gradiometry, and demonstrate that metrologically useful squeezed states can be generated using the Bose-Hubbard Hamiltonian which includes on-site atomic interactions, tunable via Feshbach resonances. By analyzing the distribution (density) of the quantum Fisher information (QFI) over the Hilbert space, we identify a characteristic \textit{intermediate scaling} of the QFI: $\mathcal{O}(N^2 L+L^2 N)$, which lies between the standard quantum limit (SQL) and the Heisenberg limit (HL) for $N$ atoms in $L$ modes. We show that in general, within the Hilbert space there is a finite, $\mathcal{O}(1)$ measure subset of Hilbert space with an intermediate QFI scaling. Therefore, one can find a Hamiltonian control sequence using a Monte Carlo optimization over random control sequences, that produces a state with intermediate scaling of the QFI. We assume an experimentally accessible range of the control parameters in the Hamiltonian resources and show that the intermediate scaling can be readily achieved. Our results indicate that the HL can be approached in quantum gravimetry using realistic experimental parameters for systems with $L=\mathcal{O}(1)$ and $N\gg L$.

quant-pharXiv:2511.15805•Nov 21, 2025•0 citations
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.
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.
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 introduce a scheme to generate NOON states of few-body bosonic vortices and demonstrate their application as high-precision rotation sensors. Our approach is based on cold atoms in a weakly anisotropic two-dimensional harmonic trap, where the single-particle p orbitals define an effective two-mode Bose-Hubbard model with vortex modes (px±ipy)(\mathrm{p}_x\pm\mathrm{i}\mathrm{p}_y)(px​±ipy​) carrying opposite circulation. In the self-trapping regime, we show that the NOON manifold becomes spectrally isolated, and collective tunneling processes give rise to highly entangled vortex NOON states. However, these states emerge on prohibitively long timescales. To overcome this limitation, we develop two complementary acceleration strategies: geodesic counterdiabatic driving for small particle numbers, and resonance- and chaos-assisted tunneling in the semiclassical regime at larger particle numbers. Both approaches enable the generation of NOON states on experimentally relevant timescales while preserving near-unit fidelities. Finally, we quantify the metrological advantage of vortex NOON states by introducing an interferometric protocol that exploits their intrinsic sensitivity to rotation, enabling the detection of infinitesimal external rotations at the Heisenberg limit. Our work opens the door to rotation sensors based on atomic NOON states, generically realizable in bosonic Josephson junctions with vortex-type orbitals.
We show that geodesic motion in the Riemannian manifold of quantum states provides a direct route to time-independent counterdiabatic driving. Using the relation between the counterdiabatic Hamiltonian and the quantum metric tensor, we prove that a constant-speed geodesic makes the Hilbert-Schmidt norm of the counterdiabatic Hamiltonian constant. For effective two-level systems whose counterdiabatic correction has a fixed operator direction, this further implies that the full counterdiabatic Hamiltonian itself is time independent. We illustrate this result with the Landau-Zener model, three-level Stimulated Raman adiabatic passage and a collectively driven Rydberg ensemble in the blockade regime. Limitations of this approach in realistic many-body systems are discussed, where the two-level reduction is only emergent and leakage out of the effective subspace bounds the achievable speedup. In all cases, time-independent counterdiabatic driving achieves unit-fidelity state preparation on timescales substantially shorter than conventional adiabatic protocols while replacing temporally shaped auxiliary controls by fixed-amplitude fields.
Bosonic systems, such as photons and ultracold atoms, have played a central role in demonstrating quantum-enhanced sensing. Quantum entanglement, through squeezed and GHZ states, enables sensing beyond classical limits. However, such a quantum advantage has so far been confined to two-mode bosonic systems, as analogous multi-mode squeezed states are non-trivial to prepare. Here, we develop a Monte-Carlo based optimization technique which can be used to efficiently engineer a Hamiltonian control-sequence for multi-mode bosonic systems to prepare multi-mode squeezed states. Specifically, we consider a Bose-Einstein condensate in an optical lattice, relevant for applications in gravimetry and gradiometry, and demonstrate that metrologically useful squeezed states can be generated using the Bose-Hubbard Hamiltonian which includes on-site atomic interactions, tunable via Feshbach resonances. By analyzing the distribution (density) of the quantum Fisher information (QFI) over the Hilbert space, we identify a characteristic \textit{intermediate scaling} of the QFI: O(N2L+L2N)\mathcal{O}(N^2 L+L^2 N)O(N2L+L2N), which lies between the standard quantum limit (SQL) and the Heisenberg limit (HL) for NNN atoms in LLL modes. We show that in general, within the Hilbert space there is a finite, O(1)\mathcal{O}(1)O(1) measure subset of Hilbert space with an intermediate QFI scaling. Therefore, one can find a Hamiltonian control sequence using a Monte Carlo optimization over random control sequences, that produces a state with intermediate scaling of the QFI. We assume an experimentally accessible range of the control parameters in the Hamiltonian resources and show that the intermediate scaling can be readily achieved. Our results indicate that the HL can be approached in quantum gravimetry using realistic experimental parameters for systems with L=O(1)L=\mathcal{O}(1)L=O(1) and N≫LN\gg LN≫L.