Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields
TL;DR: A quantum gas trapped in an optical lattice of triangular symmetry can be driven from a paramagnetic to an antiferromagnetic state by a tunable artificial magnetic field as discussed by the authors.
Abstract: A quantum gas trapped in an optical lattice of triangular symmetry can now be driven from a paramagnetic to an antiferromagnetic state by a tunable artificial magnetic field
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TL;DR: The experimental realization of the Haldane model and the characterization of its topological band structure are reported, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice and a direct extension to realize spin-dependent topological Hamiltonians is proposed.
Abstract: The Haldane model on a honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band structure, rather than being caused by an external magnetic field. Although physical implementation has been considered unlikely, the Haldane model has provided the conceptual basis for theoretical and experimental research exploring topological insulators and superconductors. Here we report the experimental realization of the Haldane model and the characterization of its topological band structure, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The Haldane model is based on breaking both time-reversal symmetry and inversion symmetry. To break time-reversal symmetry, we introduce complex next-nearest-neighbour tunnelling terms, which we induce through circular modulation of the lattice position. To break inversion symmetry, we create an energy offset between neighbouring sites. Breaking either of these symmetries opens a gap in the band structure, which we probe using momentum-resolved interband transitions. We explore the resulting Berry curvatures, which characterize the topology of the lowest band, by applying a constant force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between the two broken symmetries gives rise to a transition between topologically distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line experimentally and quantitatively compare it to calculations using Floquet theory without free parameters. We verify that our approach, which allows us to tune the topological properties dynamically, is suitable even for interacting fermionic systems. Furthermore, we propose a direct extension to realize spin-dependent topological Hamiltonians.
1,727 citations
Cites methods from "Engineering Ising-XY spin-models in..."
...Using a Wannier function calculation(27), we extract the corresponding tight-binding parameters t0,1,2,3/h 5 [2746(81), 2527(17), 2527(17), 2126(7)] Hz, for the horizontal, the left and right vertical nearest-neighbour tunnelling links, and the horizontal link across the honeycomb cell, respectively (see Supplementary Information)....
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TL;DR: In this article, the authors review recent experimental progress in quantum many-body simulation and comment on future directions, and present a review of the current state-of-the-art in this field.
Abstract: Quantum simulation, a subdiscipline of quantum computation, can provide valuable insight into difficult quantum problems in physics or chemistry. Ultracold atoms in optical lattices represent an ideal platform for simulations of quantum many-body problems. Within this setting, quantum gas microscopes enable single atom observation and manipulation in large samples. Ultracold atom–based quantum simulators have already been used to probe quantum magnetism, to realize and detect topological quantum matter, and to study quantum systems with controlled long-range interactions. Experiments on many-body systems out of equilibrium have also provided results in regimes unavailable to the most advanced supercomputers. We review recent experimental progress in this field and comment on future directions.
1,056 citations
TL;DR: Different realized and proposed techniques for creating gauge potentials-both Abelian and non-Abelian-in atomic systems and their implication in the context of quantum simulation are reviewed.
Abstract: Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle—the graviton—that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms ‘feeling’ laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials—both Abelian and non-Abelian—in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.
960 citations
TL;DR: The Harper Hamiltonian for neutral particles in optical lattices is implemented using laser-assisted tunneling and a potential energy gradient provided by gravity or magnetic field gradients to describe the motion of charged particles in strong magnetic fields.
Abstract: We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices using laser-assisted tunneling and a potential energy gradient provided by gravity or magnetic field gradients. This Hamiltonian describes the motion of charged particles in strong magnetic fields. Laser-assisted tunneling processes are characterized by studying the expansion of the atoms in the lattice. The band structure of this Hamiltonian should display Hofstadter's butterfly. For fermions, this scheme should realize the quantum Hall effect and chiral edge states.
946 citations
TL;DR: In this article, a general overview of the high-frequency regime in periodically driven systems and three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian are identified.
Abstract: We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper–Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case, one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particul...
942 citations
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TL;DR: In this article, a review of recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases is presented, focusing on effects beyond standard weakcoupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation.
Abstract: This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.
6,601 citations
TL;DR: The universe itself is thought to have passed through several phase transitions as the high-temperature plasma formed by the big bang cooled to form the world as we know it today as mentioned in this paper.
Abstract: Nature abounds with phase transitions. The boiling and freezing of water are everyday examples of phase transitions, as are more exotic processes such as superconductivity and superfluidity. The universe itself is thought to have passed through several phase transitions as the high-temperature plasma formed by the big bang cooled to form the world as we know it today.
3,749 citations
TL;DR: The Bose-Einstein condensation (BEC) phenomenon was first introduced by Bose as discussed by the authors, who derived the Planck law for black-body radiation by treating the photons as a gas of identical particles.
Abstract: In 1924 the Indian physicist Satyendra Nath Bose sent Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein generalized Bose's theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved and, in the same year, predicted that at sufficiently low temperatures the particles would become locked together in the lowest quantum state of the system. We now know that this phenomenon, called Bose-Einstein condensation (BEC), only happens for "bosons" – particles with a total spin that is an integer multiple of h, the Planck constant divided by 2π.
3,298 citations
15 Dec 2007
TL;DR: In this paper, a review of quantumphase transition from one state to another is provided by adjusting a tuning parameter other than temperature, and their consequences for finite temperature experiments are discussed.
Abstract: Thermal fluctuations induced by increasing temperature can change the state of matter, for example, when water boils to steam. It also is possible to change the state of matter at absolute zero temperature by quantum fluctuations demanded by Heisenberg's uncertainty principle. In this case, the quantumphase transition from one state to another is provided by adjusting a tuning parameter other than temperature. A few characteristic examples of quantumphase transitions are reviewed, and their consequences for finite temperature experiments are discussed.
Keywords:
quantum phase transitions;
broken symmetry;
Landau theory;
Berry phases;
confinement;
quantum criticality;
deconfined criticality;
spin gap;
monopole;
valence bond solid
1,270 citations