Optimal Work Extraction from Finite-Time Closed Quantum Dynamics

Extracting useful energy from quantum systems is a central task in quantum thermodynamics, and is also crucial for developing fast and efficient quantum technologies. While the maximum extractable work from closed quantum systems without constraints is known as the ergotropy, real experimental setups are inevitably constrained by finite operational time and bounded control strength, leaving the determination of the truly achievable optimal work an important open question.

In this talk, we tackle this problem by developing a general theoretical framework, which enables us to reduce generally intractable optimization problems to a form solvable either analytically or numerically efficiently. This framework includes many-body control problems such as Heisenberg-type models with controllable magnetic fields. The optimal protocol turns out to be remarkably simple: the optimal control Hamiltonian is time-independent in the interaction picture.

As a consequence of our theory, we obtain an exact and attainable quantum speed limit for work extraction, in contrast with generally unattainable lower bounds established in the literature. Beyond work extraction, our framework naturally extends to the optimization of the expectation values of general observables, including quantum battery charging and fidelity maximization.