@article {2560, title = {Noncommuting conserved charges in quantum many-body thermalization}, journal = {Phys. Rev. E }, volume = {101}, year = {2020}, month = {4/15/2020}, abstract = {

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\&$\#$39;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.

}, doi = {https://doi.org/10.1103/PhysRevE.101.042117}, url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.042117}, author = {Nicole Yunger Halpern and Michael E. Beverland and Amir Kalev} } @article {2405, title = {Equilibration to the non-Abelian thermal state in quantum many-body physics}, year = {2019}, month = {6/21/2019}, abstract = {

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\&$\#$39;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.\ 

}, url = {https://arxiv.org/abs/1906.09227}, author = {Nicole Yunger Halpern and Michael E. Beverland and Amir Kalev} } @article {1837, title = {Spectrum estimation of density operators with alkaline-earth atoms}, volume = {120}, year = {2018}, month = {2018/01/09}, abstract = {

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.

}, doi = {https://doi.org/10.1103/PhysRevLett.120.025301}, url = {http://arxiv.org/abs/1608.02045}, author = {Michael E. Beverland and Jeongwan Haah and Gorjan Alagic and Gretchen K. Campbell and Ana Maria Rey and Alexey V. Gorshkov} } @article {1187, title = {Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/05/06}, abstract = {

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.

}, doi = {10.1103/PhysRevA.93.051601}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.051601}, author = {Michael E. Beverland and Gorjan Alagic and Michael J. Martin and Andrew P. Koller and Ana M. Rey and Alexey V. Gorshkov} }