Dimensional advantage in network cooling with hybrid oscillator-qudit systems

TL;DR

This paper investigates the limits and advantages of using higher-dimensional auxiliary systems to cool networks of oscillators, revealing a dimensional advantage that enables more efficient and higher-energy initial state cooling, with applications to hybrid quantum systems.

Contribution

It establishes a no-cooling theorem for qubit auxiliaries and demonstrates a dimensional advantage with higher-dimensional auxiliaries for efficient oscillator cooling.

Findings

Qubit auxiliaries cannot achieve near-perfect cooling.

Higher-dimensional auxiliaries reduce the number of cycles needed for cooling.

The advantage saturates at moderate dimensions and depends on network topology.

Abstract

We examine the cooling of networks of oscillators through repeated unitary evolution followed by conditional measurement on a finite-dimensional auxiliary system, coupled via Jaynes-Cummings type interaction. We prove that near-perfect cooling of the oscillator to vacuum is fundamentally impossible when the auxiliary system is a qubit, establishing a no-cooling theorem for a two-level regulator. Moving beyond this limitation, we reveal a twofold dimensional advantage of higher-dimensional auxiliaries - reducing the number of required cycles, and enabling the efficient cooling of oscillators with higher initial energies. We further show that, while extending the network leads to a saturation of this dimensional advantage at moderate auxiliary dimensions, near-perfect cooling remains achievable for linear network configurations but fails for star networks. Moreover, we highlight the adaptability of the proposed protocol by demonstrating efficient cooling of hybrid continuous- and discrete-variable systems that naturally support the generation of non-Gaussian and entangled quantum resources.