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The Thermodynamic Fate of Isolated Quantum Systems

Keim, John, Martinez-Robles, Isabel, Chlanda, Nicolaus A., Thomas, Sage M., Teofilovska, Maja, Spielman, Sarah E., Strunk, Jordyn, Zhao, Tina, Bauroth-Sherman, Juniper J., Conley, Hannah, Conte, Philip, Kirk, Aidan, Carroll, Thomas J., Noel, Michael W.

Published Jun 16, 2025• 0 citations
OpenAlex

Abstract

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.

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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 consider the set of all initial states within a microcanonical energy shell of an isolated many-body quantum system, which exhibit an arbitrary but fixed nonequilibrium expectation value for some given observable A. On the condition that this set is not too small, it is shown by means of a dynamical typicality approach that most such initial states exhibit thermalization if and only if A satisfies the so-called weak eigenstate thermalization hypothesis (wETH). Here, thermalization means that the expectation value of A spends most of its time close to the microcanonical value after initial transients have died out. The wETH means that, within the energy shell, most eigenstates of the pertinent system Hamiltonian exhibit very similar expectation values of A.
Isolated quantum systems are anticipated to obey the eigenstate thermalization hypothesis by coming to thermal equilibrium. In our experiments, ultracold Rydberg atoms thermalize when they exchange energy via two-body interactions, but not three-body interactions. We believe this to be the result of a specially tuned initial state that maps onto quantum many body scar states. We propose an experiment in which we modify the initial state and measure the degree to which the system thermalizes. We present experimental and simulation data to support this.
We introduce a random sampling method for testing the weak Eigenstate Thermalization Hypothesis (wETH) that is particularly useful for large, sparse Hamiltonians. We test the method on a well-studied Rydberg atom system that exhibits both two- and three-body dipole-dipole interactions. Our results show that our method allows for the study of system sizes significantly beyond the limits of exact diagonalization. We find that the fluctuations in eigenstate expectation values decay as the Hilbert space dimension D−1/2D^{-1/2}D−1/2, consistent with wETH and in agreement with previous numerical results.
Isolated quantum systems are almost always observed to achieve thermal equilibrium in experiments. Understanding cases where they do not thermalize, and therefore retain memory about the initial state, could lead to the development of a quantum memory. We excite atoms in a magneto-optical trap, where they are cold enough to treat as stationary. In our experiment, our atoms exchange energy via dipole-dipole interactions and fail to thermalize. We present a theoretical and computational analysis that suggests that our system starts in an exceptional initial state.
We use dynamical quantum typicality to predict the thermal equilibrium state of ultracold Rydberg atoms exchanging energy via long-range dipole-dipole interactions. We excite 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 Rydberg densities, we find that this system generally fails to thermalize, though it approaches the thermal state at the highest tested density. This is the first direct comparison of a dynamical quantum typicality calculation to experiment.
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.