Observing crossover between quantum speed limits

TL;DR

This study experimentally investigates quantum speed limits in a multi-level system, revealing a crossover between the Mandelstam-Tamm and Margolus-Levitin bounds, with implications for quantum computing performance.

Contribution

It demonstrates the first experimental observation of the crossover between two fundamental quantum speed limits in a multi-level system.

Findings

Identified regimes where each quantum speed limit constrains evolution

Measured deviation from geodesic paths in Hilbert space

Established quantum speed limits beyond two-level systems

Abstract

Quantum mechanics sets fundamental limits on how fast quantum states can be transformed in time. Two well-known quantum speed limits are the Mandelstam-Tamm and the Margolus-Levitin bounds, which relate the maximum speed of evolution to the system's energy uncertainty and mean energy, respectively. Here, we test concurrently both limits in a multi-level system by following the motion of a single atom in an optical trap using fast matter wave interferometry. Our data reveal two different regimes: one where the Mandelstam-Tamm limit constrains the evolution at all times, and a second where a crossover to the Margolus-Levitin limit is manifested at longer times. We take a geometric approach to quantify the deviation from the speed limit, measuring how much the matter wave's quantum evolution deviates from the geodesic path in the Hilbert space of the multi-level system. Our results, establishing quantum speed limits beyond the simple two-level system, are important to understand the ultimate performance of quantum computing devices and related advanced quantum technologies.