Thermalization within a Stark manifold through Rydberg atom interactions

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.

Figures (3)

• Figure 1: (a) Stark map showing the $|m_j|=1/2, 3/2$, and 5/2 states of the $n=34$ manifold and the $36d$ states. Manifold states are organized into clusters of energy levels with nearly harmonic spacing of approximately 530 MHz. The initially excited manifold cluster is highlighted in red and labeled 0. During an interaction time of 3 $\mu$s and at a static field of 3.9 V/cm, resonant dipole-dipole interactions transfer population to clusters above and below the initial cluster, which are highlighted in different colors and labeled with negative and positive integers respectively. A microwave pulse is scanned over frequency to transfer the population of each manifold cluster to the $36d$ state, where it can be resolved with state selective field ionization. (b) An electric field scan at a particular wavelength of the Rydberg excitation laser, showing each manifold state intersected by the horizontal dashed line in (a).
• Figure 2: Example of data processing using a Rydberg atom density of about $1.9\times10^{10}$ cm$^{-3}$. (a) The signal obtained from selective field ionization of the $36d$ states through microwave spectroscopy from the $n=34$ manifold, as a function of microwave frequency. The colored regions highlight the particular frequency ranges over which individual clusters in the manifold are driven to the $d$ state, using the same coloring and labeling scheme as Fig. \ref{['fig:starkmap']}(a). Each region has five visible peaks, which are associated with the coupling to the five $36d$ states. (b) The integrated signal within each of the colored regions shown in (a). (c) The integrated signal from (b) scaled according to the measured couplings between each cluster and the $36d$ states.
• Figure 3: The scaled and normalized population of each cluster for ten experimental densities from about (a) $0.3\times10^9$ cm$^{-3}$ to (j) $2.7\times10^{10}$ cm$^{-3}$ (solid black). Simulation results are shown in (b), (f), and (j) for the corresponding densities (dashed red). In each case, the simulations are allowed to equilibrate. The density-independent predicted thermal state is shown for the same panels (dotted blue). Limited signal for clusters above the initial cluster (-6, -5, -4, -3) results in noise that is amplified by the $d$ state coupling scaling. Statistical error bars are calculated using variations between laser shots for a given density bin.