Abstract Three-dimensional (3D) strongly correlated many-body systems, especially their dynamics across quantum phase transitions, are prohibitively difficult to be numerically simulated. We experimentally demonstrate that such complex many-body dynamics can be efficiently studied in a 3D spinor Bose–Hubbard model quantum simulator, consisting of antiferromagnetic spinor Bose–Einstein condensates confined in cubic optical lattices. We find dynamics and scaling effects beyond the scope of existing theories at superfluid–insulator quantum phase transitions, and highlight spin populations as a good observable to probe the quantum critical dynamics. Our data indicate that the scaling exponents are independent of the nature of the quantum phase transitions. We also conduct numerical simulations in lower dimensions using time-dependent Gutzwiller approximations, which qualitatively describe our observations.Abstract Three-dimensional (3D) strongly correlated many-body systems, especially their dynamics across quantum phase transitions, are prohibitively difficult to be numerically simulated. We experimentally demonstrate that such complex many-body dynamics can be efficiently studied in a 3D spinor Bose–Hubbard model quantum simulator, consisting of antiferromagnetic spinor Bose–Einstein condensates confined in cubic optical lattices. We find dynamics and scaling effects beyond the scope of existing theories at superfluid–insulator quantum phase transitions, and highlight spin populations as a good observable to probe the quantum critical dynamics. Our data indicate that the scaling exponents are independent of the nature of the quantum phase transitions. We also conduct numerical simulations in lower dimensions using time-dependent Gutzwiller approximations, which qualitatively describe our observations.

arXiv:2011.07116Communications PhysicsMar 25, 202112 citations

Quantum criticality in the two-dimensional Hubbard model

Mathias Pelz

Jul 10, 20260 citations

Nonequilibrium dynamics and indirect microscopy in a three-dimensional spinor Bose-Hubbard model quantum simulator

Austin-Harris, Jared O.

Quantum simulators are easily controllable quantum systems that allow us to physically model the behavior of more complex systems, that are intractable with even the most advanced supercomputers, to gain insight into their behavior. Using lattice confined spinor Bose-Einstein condensates (BEC) as quantum simulators, we explore the quantum critical dynamics of the superfluid to Mott insulator phase transition in a three-dimensional cubic optical lattice. Our observations reveal that, in a quantum version of the Kibble-Zurek mechanism, the dynamics can be frozen by a sufficiently quick ramp across the transition. Additionally, we utilize discrete energy signatures in nonequilibrium spin mixing dynamics generated by atoms that are tightly confined to single lattice sites after a quench across this transition to understand the spatial dynamics of a BEC during this transition. This "indirect microscopy" method is required to determine the spatial distribution because achieving single lattice site resolved imaging of three dimensional lattice confined quantum gases remains experimentally challenging even with advanced quantum gas microscopy methods. The observed number distributions additionally demonstrate that it may be possible to design lattice ramp sequences to manipulate the distribution of atoms to enhance desired effects.Quantum simulators are easily controllable quantum systems that allow us to physically model the behavior of more complex systems, that are intractable with even the most advanced supercomputers, to gain insight into their behavior. Using lattice confined spinor Bose-Einstein condensates (BEC) as quantum simulators, we explore the quantum critical dynamics of the superfluid to Mott insulator phase transition in a three-dimensional cubic optical lattice. Our observations reveal that, in a quantum version of the Kibble-Zurek mechanism, the dynamics can be frozen by a sufficiently quick ramp across the transition. Additionally, we utilize discrete energy signatures in nonequilibrium spin mixing dynamics generated by atoms that are tightly confined to single lattice sites after a quench across this transition to understand the spatial dynamics of a BEC during this transition. This "indirect microscopy" method is required to determine the spatial distribution because achieving single lattice site resolved imaging of three dimensional lattice confined quantum gases remains experimentally challenging even with advanced quantum gas microscopy methods. The observed number distributions additionally demonstrate that it may be possible to design lattice ramp sequences to manipulate the distribution of atoms to enhance desired effects.

Dec 1, 20230 citations

Quantum simulators at negative absolute temperatures

Ákos Rapp

We propose that negative absolute temperatures in ultracold atomic clouds in optical lattices can be used to simulate quantum systems in new regions of phase diagrams. First we discuss how the attractive SU(3) Hubbard model in three dimensions can be realized using repulsively interacting ${}^{173}$ Yb atoms, then we consider how an antiferromagnetic $S=1$ spin chain could be simulated using spinor ${}^{87}$ Rb or ${}^{23}$ Na atoms. The general idea to achieve negative absolute temperatures is to reverse the sign of the external harmonic potential. Energy conservation in a deep optical lattice imposes a constraint on the dynamics of the cloud, which can relax toward a $T<0$ state. As the process is strongly nonadiabatic, we estimate the change of the entropy.We propose that negative absolute temperatures in ultracold atomic clouds in optical lattices can be used to simulate quantum systems in new regions of phase diagrams. First we discuss how the attractive SU(3) Hubbard model in three dimensions can be realized using repulsively interacting ${}^{173}$Yb atoms, then we consider how an antiferromagnetic $S=1$ spin chain could be simulated using spinor ${}^{87}$Rb or ${}^{23}$Na atoms. The general idea to achieve negative absolute temperatures is to reverse the sign of the external harmonic potential. Energy conservation in a deep optical lattice imposes a constraint on the dynamics of the cloud, which can relax toward a $T<0$ state. As the process is strongly nonadiabatic, we estimate the change of the entropy.

arXiv:1112.4299Physical Review AApr 17, 201210 citations

Quantum simulation of the 2D Hubbard model

Michael Köhl

Bulletin of the American Physical SocietyJun 8, 20170 citations

{}^{173}

Yb atoms, then we consider how an antiferromagnetic

S=1

spin chain could be simulated using spinor

{}^{87}

Rb or

{}^{23}

Na atoms. The general idea to achieve negative absolute temperatures is to reverse the sign of the external harmonic potential. Energy conservation in a deep optical lattice imposes a constraint on the dynamics of the cloud, which can relax toward a

T<0

state. As the process is strongly nonadiabatic, we estimate the change of the entropy.