# An Exponential Bound in the Quest for Absolute Zero

## TL;DR

This paper demonstrates that the minimum temperature achievable in a quantum parametric oscillator scales exponentially with process duration, challenging previous power-law assumptions and advancing the understanding of reaching absolute zero.

## Contribution

It introduces a new exponential scaling law for minimum temperature in quantum systems, based on an optimal control solution for the quantum parametric oscillator.

## Key findings

- Minimum temperature scales exponentially with process duration
- Optimal control solution provides new insights into cooling limits
- Motivates further research towards absolute zero

## Abstract

In most studies for the quantification of the third thermodynamic law, the minimum temperature which can be achieved with a long but finite-time process scales as a negative power of the process duration. In this article, we use our recent complete solution for the optimal control problem of the quantum parametric oscillator to show that the minimum temperature which can be obtained in this system scales exponentially with the available time. The present work is expected to motivate further research in the active quest for absolute zero.