Exponential improvement for quantum cooling through finite memory effects

Practical implementations of quantum technologies require one to prepare physical states with a high degree of purity---or, in thermodynamic terms, very low temperatures. The ability to do so is restricted by the Third Law of thermodynamics, which prohibits the attainability of perfect cooling given finite resources. For a finite dimensional system and environment from which to draw energy, attainable upper bounds for the asymptotic ground state population of the system repeatedly interacting with quantum machines have recently been derived. These bounds apply within a memoryless (Markovian) setting, in which each step of the process proceeds independently of those previous. Here, we expand this framework to study the effects of memory on the task of quantum cooling and derive bounds that provide an exponential advantage over the memoryless case and can be achieved asymptotically. We do this by introducing a microscopic memory mechanism through a generalized collision model, which can be embedded as a Markovian dynamics on a larger system space. For qubits, our asymptotic bound coincides with that achievable through heat-bath algorithmic cooling, of which our framework provides a generalization to arbitrary dimensions. We lastly describe the step-wise optimal protocol, which requires implementing an adaptive strategy, that outperforms all standard (non-adaptive) procedures.