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

Adiabatic state preparation is a robust method for controlling quantum systems, but it is often limited by the need for slow evolution to avoid diabatic transitions. Counterdiabatic (CD) driving offers a solution by adding auxiliary terms to the Hamiltonian to suppress these transitions. However, standard CD protocols typically require complex, time-dependent control fields that are experimentally difficult to realize. This paper investigates whether these auxiliary fields can be made time-independent by utilizing the geometric properties of the quantum state manifold.

The authors use the Riemannian geometry of quantum states, where the distance between states is defined by the quantum metric tensor. By choosing a protocol that follows a geodesic—the shortest path in this manifold—the Hilbert-Schmidt norm of the counterdiabatic Hamiltonian remains constant. For systems that can be reduced to an effective two-level subspace, this geometric constraint allows the entire counterdiabatic correction to be represented by a constant-amplitude field.

The researchers demonstrate that for systems like the Landau-Zener model and three-level STIRAP, the counterdiabatic Hamiltonian becomes time-independent when the control parameters follow a geodesic path. This eliminates the need for temporally shaped auxiliary controls, replacing them with fixed-amplitude fields while maintaining unit-fidelity state preparation.

Crucially, the authors extend this framework to many-body systems, specifically a collectively driven Rydberg ensemble in the blockade regime. In this setting, the two-level structure is emergent rather than fundamental. They show that even in these complex systems, constant counterdiabatic driving can be implemented by incorporating the correction into the many-body Hamiltonian, effectively enlarging the energy gap and allowing for high-fidelity state preparation on significantly shorter timescales than conventional adiabatic protocols.

This work provides a powerful, simplified strategy for implementing shortcuts to adiabaticity. By reducing the experimental burden of designing time-dependent control pulses, this approach makes high-speed, high-fidelity quantum control more accessible in platforms like ultracold atoms and Rydberg arrays. It demonstrates that the geometric structure of quantum control can be leveraged to transform demanding time-dependent requirements into simpler, static hardware configurations.