02031nas a2200145 4500008004100000245007100041210006900112260001400181490000800195520154100203100002801744700002701772700001601799856007001815 2020 eng d00aNoncommuting conserved charges in quantum many-body thermalization0 aNoncommuting conserved charges in quantum manybody thermalizatio c4/15/20200 v1013 a

In statistical mechanics, a small system exchanges conserved quantities—heat, particles, electric charge, etc.—with a bath. The small system thermalizes to the canonical ensemble or the grand canonical ensemble, etc., depending on the quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed “the non-Abelian thermal state (NATS).” We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which forms the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to near the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.

1 aHalpern, Nicole, Yunger1 aBeverland, Michael, E.1 aKalev, Amir uhttps://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.04211701930nas a2200133 4500008004100000245008000041210006900121260001400190520148400204100002801688700002701716700001601743856003701759 2019 eng d00aEquilibration to the non-Abelian thermal state in quantum many-body physics0 aEquilibration to the nonAbelian thermal state in quantum manybod c6/21/20193 a

In statistical mechanics, a small system exchanges conserved charges---heat, particles, electric charge, etc.---with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the charges. The charges are usually represented by operators assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed "the non-Abelian thermal state (NATS)." We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which form the system of interest. The conserved charges manifest as spin components. Heisenberg interactions push the charges between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting charges from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter. 

1 aHalpern, Nicole, Yunger1 aBeverland, Michael, E.1 aKalev, Amir uhttps://arxiv.org/abs/1906.0922701204nas a2200181 4500008004100000245007100041210006900112260001500181490000800196520064500204100002700849700001900876700001900895700002700914700002000941700002500961856003600986 2018 eng d00aSpectrum estimation of density operators with alkaline-earth atoms0 aSpectrum estimation of density operators with alkalineearth atom c2018/01/090 v1203 a

We show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose n copies are stored in the nuclear spins of n such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing, quantum simulation, and time-keeping with alkalineearth atoms are discussed.

1 aBeverland, Michael, E.1 aHaah, Jeongwan1 aAlagic, Gorjan1 aCampbell, Gretchen, K.1 aRey, Ana, Maria1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1608.0204501353nas a2200181 4500008004100000245006400041210006200105260001500167490000700182520077900189100002700968700001900995700002401014700002301038700001701061700002501078856006801103 2016 eng d00aRealizing Exactly Solvable SU(N) Magnets with Thermal Atoms0 aRealizing Exactly Solvable SUN Magnets with Thermal Atoms c2016/05/060 v933 a

We show that n thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the Sn symmetry that permutes atoms occupying different vibrational levels of the trap and the SU(N) symmetry associated with N nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU(N) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.

1 aBeverland, Michael, E.1 aAlagic, Gorjan1 aMartin, Michael, J.1 aKoller, Andrew, P.1 aRey, Ana, M.1 aGorshkov, Alexey, V. uhttp://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.051601