Emergence of Fermi's Golden Rule in the Probing of a Quantum Many-Body System

TL;DR

This paper investigates how Fermi's Golden Rule emerges and breaks down in a strongly interacting quantum many-body system, using ultracold Fermi gases and rf spectroscopy to map different dynamical regimes.

Contribution

It provides experimental insights into the validity regimes of FGR in quantum many-body systems, highlighting the transition from perturbative to non-perturbative dynamics.

Findings

Identification of three dynamical regimes: quadratic growth, FGR, and non-perturbative.

Observation of Rabi oscillations beyond a certain Rabi frequency.

Mapping of the response diagram versus rf pulse duration and Rabi frequency.

Abstract

Fermi's Golden Rule (FGR) is one of the most impactful formulas in quantum mechanics, providing a link between easy-to-measure observables - such as transition rates - and fundamental microscopic properties - such as density of states or spectral functions. Its validity relies on three key assumptions: the existence of a continuum, an appropriate time window, and a weak coupling. Understanding the regime of validity of FGR is critical for the proper interpretation of most spectroscopic experiments. While the assumptions underlying FGR are straightforward to analyze in simple models, their applicability is significantly more complex in quantum many-body systems. Here, we observe the emergence and breakdown of FGR, using a strongly interacting homogeneous spin-$1/2$ Fermi gas coupled to a radio-frequency (rf) field. Measuring the transition probability into an outcoupled internal state, we map the system's dynamical response diagram versus the rf-pulse duration $t$ and Rabi frequency $\Omega_0$. For weak drives, we identify three regimes: an early-time regime where the transition probability takes off as $t^2$, an intermediate-time FGR regime, and a long-time non-perturbative regime. Beyond a threshold Rabi frequency, Rabi oscillations appear. Our results provide a blueprint for the applicability of linear response theory to the spectroscopy of quantum many-body systems.