Experimental observation of thermalization with noncommuting charges

Abstract

Quantum simulators have recently enabled experimental observations of quantum many-body systems' internal thermalisation. Often, the global energy and particle number are conserved, and the system is prepared with a well-defined particle number-in a microcanonical subspace. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information. Until now, this subfield has remained theoretical. We initiate the experimental testing of its predictions, with a trapped-ion simulator. We prepare 6-15 spins in an approximate microcanonical subspace, a generalisation of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have well-defined nontrivial values simultaneously. We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations. The noncommuting charges are the three spin components. We find that small subsystems equilibrate to near a recently predicted non-Abelian thermal state. This work bridges quantum many-body simulators to the quantum thermodynamics of noncommuting charges, whose predictions can now be tested.

Non-Abelian eigenstate thermalization hypothesis

“…This result holds under a physically reasonable assumption about the non-Abelian analog of O αα ′ . Our argument employs the Wigner-Eckart theorem; properties of Clebsch-Gordan coefficients; and approximate microcanonical subspaces, which generalize microcanonical subspaces to accommodate noncommuting charges [22,35,48]. This work extends the ETH, a mainstay of many-body physics, to the more fully quantum domain of noncommuting charges and so to quantum-information thermodynamics.…”

“…The state has an extensive energy, E = O(N ), and is far from maximally spin-polarized: N − M = O(N ). 3 The system begins in an approximate microcanonical subspace, which generalizes a microcanonical subspace for noncommuting charges [22,35,48]. Measuring any charge Q a likely yields an outcome near Q a ; the charges' variances are bounded as (…”

“…Conditions ( 10)-( 12) govern typical many-body states prepared today, including all short-range-correlated states [35,48]. 4 Having introduced the initial state, we profile observables expected to obey the non-Abelian ETH.…”

“…States of the form ( 15) are often called generalized Gibbs ensembles, especially if H is integrable and the Q a commute [55][56][57]. Signatures of ρ NATS emerged dynamically in numerical simulations [35] and a trapped-ion experiment [48]; yet full thermalization to ρ NATS has not been observed in a closed quantum many-body system. Furthermore, noncommuting charges were conjectured to alter thermalization [35].…”

“…This work opens several avenues for future research. First, our analytical results call for testing with numerics and quantum simulators, e.g., trapped ions, ultracold atoms, and superconducting qudits [47,48]. One would aim to verify the non-Abelian ETH (14); identify operators whose smooth functions T (k) satisfy our assumptions, enabling anomalous thermalization; and observe deviations (24) from the thermal prediction.…”