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arXiv:2512.22110

Thermalization within a Stark manifold through Rydberg atom interactions

Sarah E. Spielman, Sage M. Thomas, Maja Teofilovska, Annick C van Blerkom, Juniper J. Bauroth-Sherman, Nicolaus A. Chlanda, Hannah S. Conley, Philip A. Conte, Aidan D. Kirk, Thomas J. Carroll, Michael W. Noel

quant-phSubmitted Dec 26, 2025• Announced Dec 29, 2025• 0 citations
v1 · Dec 26, 2025v2 · May 21, 2026v3 · Jul 9, 2026
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Abstract

One explanation of the thermalization of an isolated quantum system is the eigenstate thermalization hypothesis, which posits that all energy eigenstates are thermal. Based on this idea, we use dynamical typicality to predict the thermal state of ultracold Rb atoms exchanging energy via long-range dipole-dipole interactions. In a magneto-optical trap, we excite the atoms to the center of a manifold of nearly harmonically spaced clusters of Stark energy levels and then allow them to equilibrate. Comparing the equilibrium state to our thermal prediction across a range of densities, we find that the atoms generally fail to thermalize, though they approach the thermal state at the highest tested density.

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One explanation of the thermalization of an isolated quantum system is the eigenstate thermalization hypothesis, which posits that all energy eigenstates are thermal. Based on this idea, we use dynamical typicality to predict the thermal state of ultracold Rb atoms exchanging energy via long-range dipole-dipole interactions. In a magneto-optical trap, we excite the atoms to the center of a manifold of nearly harmonically spaced clusters of Stark energy levels and then allow them to equilibrate. Comparing the equilibrium state to our thermal prediction across a range of densities, we find that the atoms generally fail to thermalize, though they approach the thermal state at the highest tested density.
An isolated system of ultracold Rydberg atoms can come to equilibrium by exchanging energy through dipole-dipole interactions. In our experiment, a static electric field of a few V/cm shifts the energy levels of the atoms, so that the energy levels are nearly degenerate at zero field and fan out with increasing field to form a manifold. We excite atoms to energy levels near the center of the manifold, where the spacing is nearly harmonic. We allow them to interact for a few microseconds, by which time the population of each energy level has reached a steady state. The population is then measured at various densities and compared to simulation results. We use the notion of dynamical typicality to predict the equilibrium configuration and show that the system fails to thermalize.
Isolated quantum systems are typically observed to come to thermal equilibrium. The weak Eigenstate Thermalization Hypothesis (wETH) states that the vast majority of eigenvectors are thermal. This implies that most initial states should thermalize. Studying the rare cases in which they fail to thermalize could reveal insight into quantum dynamics. In our experiment, we excite Rydberg atoms and allow them to exchange energy via dipole-dipole interactions. We find that they do not thermalize. We present numerical and theoretical results that show that our experimental initial state is not typical.
We measure the transport of energy among the internal states of ultracold rubidium Rydberg atoms coupled by dipole-dipole exchange. In a magneto-optical trap, a static electric field of a few V/cm shifts the energy levels of the atoms. For a particular principal quantum number, nnn, the angular momentum eigenstates ℓ>4\ell > 4ℓ>4 are nearly degenerate at zero electric field. At nonzero field, a manifold of equally spaced clusters form a ladder with each rung consisting of a set of closely spaced mmm energy eigenstates. We excite Rydberg atoms to energy levels near the center of the manifold and allow them to exchange energy via resonant dipole-dipole interactions. We measure the time evolution as energy spreads away from the center of the manifold, which reveals that the system may fail to thermalize for long interaction times. A computational model that includes only a few essential features of the system qualitatively agrees with this result.
We question the microcanonical hypothesis, often made to account for the thermalization of complex closed quantum systems, on the specific example of a chain of two-level atoms optically driven by a resonant laser beam and strongly interacting via Rydberg-Rydberg dipole-dipole interactions. Along its (necessarily unitary) evolution, this system is indeed expected to thermalize, i.e. observables, such as the number of excitations, stop oscillating and reach equilibrium-like expectation values. The latter are often calculated through assuming the system can be effectively described by a thermal-like microcanonical state. Here, we compare the distribution of excitations in the chain calculated either according to the microcanonical assumption or through direct exact numerical simulation. This allows us to show the limitations of the thermal equilibrium hypothesis and precise its applicability conditions.
Systems are known to thermalize, or reach equilibrium, with the passing of time. However, when this does not occur, the quantum states of the system may be localized. Localized states carry information of the system’s initial state that is typically lost during the process of thermalization. We aim to study thermalization and localization in systems of rubidium Rydberg atoms, and to further understand these phenomena via simulation while we are developing a more refined experiment. These atoms exchange energy via tuned resonances while contained within a magneto optical trap. This process can be categorized as either a two, three, or four body interaction; localization is only expected to occur in the latter two. As the atoms transfer energy via dipole-dipole interactions, the population of atoms occupying different states shifts. Some atoms are shifted to a measurable state, and each trial of the experiment lasts for only several microseconds as data is collected. The energy transport within the system is simulated on a supercomputer in order to produce a model for the experimental data, while also allowing us to closely analyze parameters that are not accessible through experiment. From the model, we hope to learn whether the system thermalizes or localizes. We present initial simulation results exploring the energy exchange dynamics in a Rubidium many-body system.
The long-range, anisotropic nature of the interaction among atoms in an ultracold dipolar gas leads to a rich array of possibilities for studying many-body physics. In this work, an ultracold gas of highly excited atoms is used to study energy transport due to the long-range dipole-dipole interaction. A technique is developed to measure both the internal energy states of the interacting Rydberg atoms and their positions in space. This technique is demonstrated by observing energy exchange between two spatially separated groups of Rydberg atoms excited to two different internal states. Simulations confirm the general features of the energy transport in this system and highlight subtleties associated with the homogeneity of the electric field used in this experiment.