Fermi’s golden rule is one of the most widely applied formulas in quantum physics. It gives the rate at which a quantum system transitions between states under a weak perturbation, and it is taught to every physics undergraduate. But the rule, proposed by Enrico Fermi in the 1940s, is an approximation rooted in perturbation theory. It assumes the perturbation is weak enough and the system large enough that the initial state population does not deplete. When those assumptions fail, so does the rule.
Exactly when and how that happens in a strongly interacting many-body system has been difficult to observe directly, until now.
A team led by Professor Nir Navon at Yale University has experimentally mapped the emergence, validity, and breakdown of Fermi’s golden rule in a strongly interacting unitary Fermi gas of lithium-6 atoms. Their results, published July 9 in Nature Physics (DOI: 10.1038/s41567-026-03316-1), reveal three distinct dynamical regimes and a sharp threshold at which the system crosses from dissipative thermalizing behavior into coherent quantum oscillations.
A Many-Body System as Its Own Bath
The experiment begins with a balanced mixture of about 400,000 lithium-6 atoms in two spin states, held in a uniform optical box trap at a temperature of about 15% of the Fermi energy, deeply degenerate. The atoms are tuned to unitarity via a magnetic field of about 690 gauss, where the s-wave scattering length diverges and interactions are as strong as quantum mechanics allows.
A weak radio-frequency field then drives atoms from one spin state into a third, non-interacting state. By measuring the transfer fraction as a function of time at a fixed detuning, corresponding to the peak of the spectral response, the researchers could watch Fermi’s golden rule emerge and eventually fail.
“We are essentially using the strongly interacting gas as its own thermal bath,” said first author Jianyi Chen, a postdoctoral researcher in the Navon group. “The RF probe lets us watch how the system transitions from early-time coherent evolution to genuine dissipation, and then to the breakdown of that dissipation at stronger drives.”
Three Dynamical Regimes
The data reveal a clean sequence of three regimes as time progresses after the RF drive is turned on.
At the earliest times, the transfer fraction grows quadratically with time, the universal short-time limit of perturbation theory, where the system has not yet “discovered” its own continuum of states. For an ideal gas this quadratic growth follows a simple expression; for the interacting gas, the slope is reduced by a factor the team measures as 0.70(4). This factor is the quasiparticle residue, a quantity from Landau’s Fermi liquid theory that encodes how interactions renormalize the single-particle spectral weight.
At intermediate times, the transfer fraction becomes linear in time. This is the hallmark of Fermi’s golden rule: the transition rate is constant, and the system behaves as if it couples to a genuine dissipative environment. The measured rate collapses onto a universal curve for transfer fractions below 0.1 and times up to about 12 milliseconds.
At long times, the transfer fraction saturates and can even reverse. The initial state is depleted, the perturbation can no longer be considered weak, and the golden rule fails.
The Critical Threshold
Beyond mapping the three regimes in time, the team also identified a sharp boundary in driving strength. Below a critical coupling of about Planck’s constant times 0.17 times the Fermi energy, the dynamics remain monotonic and dissipative, the golden rule framework holds. Above that threshold, coherent Rabi oscillations emerge, signaling the complete breakdown of the perturbative description.
The ratio of this critical coupling to the low-power spectral width, about 0.7, is remarkably similar to values seen in much simpler atom-photon systems, suggesting the threshold may be a universal feature of open quantum systems.
A Cautionary Tale for Spectroscopy
The study carries a practical warning for experimental physics. Under commonly used driving conditions, the extracted spectral width can overestimate the true low-power limit by 50% or more. The boundary of golden-rule validity occurs at surprisingly low power, on resonance, the drive amplitude must be below about 1% of the Fermi energy for the rule to hold.
“The threshold is much lower than many of us assumed,” said co-first author Songtao Huang. “Our data show that even apparently reasonable experimental parameters can introduce 50% systematic errors in extracted quantities like linewidth.”
Deeper Implications
The three-regime sequence, quadratic growth, linear dissipation, and saturation, is the many-body analogue of how a finite quantum system thermalizes. The quadratic regime represents universal short-time coherent evolution. The linear regime represents genuine dissipative dynamics in which the system acts as its own bath. And the threshold for Rabi oscillations defines the sharp boundary between thermalizing and coherent behavior.
The results also provide a direct measurement of the quasiparticle residue, a fundamental parameter of Fermi liquid theory, in a regime where interactions are maximal. The measured value of 0.70(4) quantifies how interactions renormalize the single-particle response in the unitary limit.
“This gives us a rigorous experimental framework for understanding when linear response theory applies to spectroscopy of quantum many-body systems,” Navon said. “It serves as a blueprint for interpreting experiments across cold atoms, condensed matter, and quantum simulation.”
Source: Chen, J., Huang, S., Ji, Y. et al. “Emergence of Fermi’s golden rule in a quantum many-body system.” Nature Physics (2026). DOI: 10.1038/s41567-026-03316-1