1
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Schimming CD, Reichhardt CJO, Reichhardt C. Vortex Lattices in Active Nematics with Periodic Obstacle Arrays. PHYSICAL REVIEW LETTERS 2024; 132:018301. [PMID: 38242662 DOI: 10.1103/physrevlett.132.018301] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Accepted: 11/16/2023] [Indexed: 01/21/2024]
Abstract
We numerically model a two-dimensional active nematic confined by a periodic array of fixed obstacles. Even in the passive nematic, the appearance of topological defects is unavoidable due to planar anchoring by the obstacle surfaces. We show that a vortex lattice state emerges as activity is increased, and that this lattice may be tuned from "ferromagnetic" to "antiferromagnetic" by varying the gap size between obstacles. We map the rich variety of states exhibited by the system as a function of distance between obstacles and activity, including a pinned defect state, motile defects, the vortex lattice, and active turbulence. We demonstrate that the flows in the active turbulent phase can be tuned by the presence of obstacles, and explore the effects of a frustrated lattice geometry on the vortex lattice phase.
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Affiliation(s)
- Cody D Schimming
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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2
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Almeida V, Casana R, da Hora E, Krusch S. Self-dual
CP(2)
vortex-like solitons in the presence of magnetic impurities. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.016010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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3
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Reichhardt C, Reichhardt CJO. Active matter commensuration and frustration effects on periodic substrates. Phys Rev E 2021; 103:022602. [PMID: 33735959 DOI: 10.1103/physreve.103.022602] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
We show that self-driven particles coupled to a periodic obstacle array exhibit active matter commensuration effects that are absent in the Brownian limit. As the obstacle size is varied for sufficiently large activity, a series of commensuration effects appear in which the motility induced phase separation produces commensurate crystalline states, while for other obstacle sizes we find frustrated or amorphous states. The commensuration effects are associated with peaks in the amount of sixfold ordering and the maximum cluster size. When a drift force is added to the system, the mobility contains peaks and dips similar to those found in transport studies for commensuration effects in superconducting vortices and colloidal particles.
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Affiliation(s)
- C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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4
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Libál A, Balázs T, Reichhardt C, Reichhardt CJO. Colloidal Dynamics on a Choreographic Time Crystal. PHYSICAL REVIEW LETTERS 2020; 124:208004. [PMID: 32501072 DOI: 10.1103/physrevlett.124.208004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2019] [Revised: 03/17/2020] [Accepted: 05/04/2020] [Indexed: 06/11/2023]
Abstract
A choreographic time crystal is a dynamic lattice structure in which the points comprising the lattice move in a coordinated fashion. These structures were initially proposed for understanding the motion of synchronized satellite swarms. Using simulations, we examine colloids interacting with a choreographic crystal consisting of traps that could be created optically. As a function of the trap strength, speed, and colloidal filling fraction, we identify a series of phases including states where the colloids organize into a dynamic chiral loop lattice as well as a frustrated induced liquid state and a choreographic lattice state. We show that transitions between these states can be understood in terms of vertex frustration effects that occur during a certain portion of the choreographic cycle. Our results can be generalized to a broader class of systems of particles coupled to choreographic structures, such as vortices, ions, cold atoms, and soft matter systems.
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Affiliation(s)
- András Libál
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Mathematics and Computer Science Department, Babeş-Bolyai University, Cluj 400084, Romania
| | - Tünde Balázs
- Mathematics and Computer Science Department, Babeş-Bolyai University, Cluj 400084, Romania
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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5
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Duzgun A, Nisoli C, Reichhardt CJO, Reichhardt C. Commensurate states and pattern switching via liquid crystal skyrmions trapped in a square lattice. SOFT MATTER 2020; 16:3338-3343. [PMID: 32196037 DOI: 10.1039/c9sm02312g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Using continuum based simulations we show that a rich variety of skyrmion liquid crystal states can be realized in the presence of a periodic obstacle array. As a function of the number of skyrmions per obstacle we find hexagonal, square, dimer, trimer and quadrimer ordering, where the n-mer structures are a realization of a molecular crystal state of skyrmions. As a function of external field and obstacle radius we show that there are transitions between the different crystalline states as well as mixed and disordered structures. We discuss how these states are related to commensurate effects seen in other systems, such as vortices in type-II superconductors and colloids interacting with two dimensional substrates.
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Affiliation(s)
- A Duzgun
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
| | - C Nisoli
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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6
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7
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Sarenac D, Cory DG, Nsofini J, Hincks I, Miguel P, Arif M, Clark CW, Huber MG, Pushin DA. Generation of a Lattice of Spin-Orbit Beams via Coherent Averaging. PHYSICAL REVIEW LETTERS 2018; 121:183602. [PMID: 30444408 DOI: 10.1103/physrevlett.121.183602] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2018] [Indexed: 06/09/2023]
Abstract
We describe a highly robust method, applicable to both electromagnetic and matter-wave beams, that can produce a beam consisting of a lattice of orbital angular momentum (OAM) states coupled to a two-level system. We also define efficient protocols for controlling and manipulating the lattice characteristics. These protocols are applied in an experimental realization of a lattice of optical spin-orbit beams. The novel passive devices we demonstrate here are also a natural alternative to existing methods for producing single-axis OAM and spin-orbit beams. Our techniques provide new tools for investigations of chiral and topological materials with light and particle beams.
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Affiliation(s)
- D Sarenac
- Department of Physics, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
| | - D G Cory
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
- Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada, N2L2Y5
- Canadian Institute for Advanced Research, Toronto, Ontario, Canada, M5G 1Z8
| | - J Nsofini
- Department of Physics, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
| | - I Hincks
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
- Department of Applied Math, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
| | - P Miguel
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
- Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
| | - M Arif
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Charles W Clark
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
- Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, College Park, Maryland 20742, USA
| | - M G Huber
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - D A Pushin
- Department of Physics, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L3G1
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8
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Raum PT, Scarola VW. Thermometry for Laughlin States of Ultracold Atoms. PHYSICAL REVIEW LETTERS 2017; 118:115302. [PMID: 28368627 DOI: 10.1103/physrevlett.118.115302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2016] [Indexed: 06/07/2023]
Abstract
Cooling atomic gases into strongly correlated quantum phases requires estimates of the entropy to perform thermometry and establish viability. We construct an ansatz partition function for models of Laughlin states of atomic gases by combining high temperature series expansions with exact diagonalization. Using the ansatz we find that entropies required to observe Laughlin correlations with bosonic gases are within reach of current cooling capabilities.
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Affiliation(s)
- P T Raum
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - V W Scarola
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
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9
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Reichhardt C, Olson Reichhardt CJ. Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:026501. [PMID: 27997373 DOI: 10.1088/1361-6633/80/2/026501] [Citation(s) in RCA: 89] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We review the depinning and nonequilibrium phases of collectively interacting particle systems driven over random or periodic substrates. This type of system is relevant to vortices in type-II superconductors, sliding charge density waves, electron crystals, colloids, stripe and pattern forming systems, and skyrmions, and could also have connections to jamming, glassy behaviors, and active matter. These systems are also ideal for exploring the broader issues of characterizing transient and steady state nonequilibrium flow phases as well as nonequilibrium phase transitions between distinct dynamical phases, analogous to phase transitions between different equilibrium states. We discuss the differences between elastic and plastic depinning on random substrates and the different types of nonequilibrium phases which are associated with specific features in the velocity-force curves, fluctuation spectra, scaling relations, and local or global particle ordering. We describe how these quantities can change depending on the dimension, anisotropy, disorder strength, and the presence of hysteresis. Within the moving phase we discuss how there can be a transition from a liquid-like state to dynamically ordered moving crystal, smectic, or nematic states. Systems with periodic or quasiperiodic substrates can have multiple nonequilibrium second or first order transitions in the moving state between chaotic and coherent phases, and can exhibit hysteresis. We also discuss systems with competing repulsive and attractive interactions, which undergo dynamical transitions into stripes and other complex morphologies when driven over random substrates. Throughout this work we highlight open issues and future directions such as absorbing phase transitions, nonequilibrium work relations, inertia, the role of non-dissipative dynamics such as Magnus effects, and how these results could be extended to the broader issues of plasticity in crystals, amorphous solids, and jamming phenomena.
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Affiliation(s)
- C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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10
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Goldman N, Juzeliūnas G, Öhberg P, Spielman IB. Light-induced gauge fields for ultracold atoms. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:126401. [PMID: 25422950 DOI: 10.1088/0034-4885/77/12/126401] [Citation(s) in RCA: 173] [Impact Index Per Article: 17.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
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.
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Affiliation(s)
- N Goldman
- College de France, 11 place Marcelin Berthelot & Laboratoire Kastler Brossel, CNRS, UPMC, ENS, 24 rue Lhomond, 75005 Paris, France
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11
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Tao HS, Chen YH, Lin HF, Liu HD, Liu WM. Layer anti-ferromagnetism on bilayer honeycomb lattice. Sci Rep 2014; 4:5367. [PMID: 24947369 PMCID: PMC4064339 DOI: 10.1038/srep05367] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2013] [Accepted: 05/29/2014] [Indexed: 11/09/2022] Open
Abstract
Bilayer honeycomb lattice, with inter-layer tunneling energy, has a parabolic dispersion relation, and the inter-layer hopping can cause the charge imbalance between two sublattices. Here, we investigate the metal-insulator and magnetic phase transitions on the strongly correlated bilayer honeycomb lattice by cellular dynamical mean-field theory combined with continuous time quantum Monte Carlo method. The procedures of magnetic spontaneous symmetry breaking on dimer and non-dimer sites are different, causing a novel phase transition between normal anti-ferromagnet and layer anti-ferromagnet. The whole phase diagrams about the magnetism, temperature, interaction and inter-layer hopping are obtained. Finally, we propose an experimental protocol to observe these phenomena in future optical lattice experiments.
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Affiliation(s)
- Hong-Shuai Tao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yao-Hua Chen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Heng-Fu Lin
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hai-Di Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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12
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McDermott D, Amelang J, Reichhardt CJO, Reichhardt C. Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062301. [PMID: 24483438 DOI: 10.1103/physreve.88.062301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2013] [Indexed: 06/03/2023]
Abstract
We numerically examine colloidal particles driven over a muffin tin substrate. Previous studies of this model identified a variety of commensurate and incommensurate static phases in which topological defects can form domain walls, ordered stripes, superlattices, or disordered patchy regimes as a function of the filling fraction. Here, we show that the addition of an external drive to these static phases can produce distinct dynamical responses. At incommensurate fillings the flow occurs in the form of localized pulses or solitons correlated with topological defect structures. Transitions between different modes of motion can occur as a function of increasing drive. We measure the average particle velocity for specific ranges of external drive and show that changes in the velocity response correlate with changes in the topological defect arrangements. We also demonstrate that in the different dynamic phases, the particles have distinct trajectories and velocity distributions. Dynamic transitions between ordered and disordered flows exhibit hysteresis, while in strongly disordered regimes there is no hysteresis and the velocity-force curves are smooth. When stripe patterns are present, transport can occur at an angle to the driving direction.
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Affiliation(s)
- D McDermott
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 USA and Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556 USA
| | - J Amelang
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 USA and Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125 USA
| | - C J Olson Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 USA
| | - C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 USA
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13
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Ray D, Olson Reichhardt CJ, Jankó B, Reichhardt C. Strongly enhanced pinning of magnetic vortices in type-II superconductors by conformal crystal arrays. PHYSICAL REVIEW LETTERS 2013; 110:267001. [PMID: 23848910 DOI: 10.1103/physrevlett.110.267001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2012] [Indexed: 06/02/2023]
Abstract
Conformal crystals are nonuniform structures created by a conformal transformation of regular two-dimensional lattices. We show that gradient-driven vortices interacting with a conformal pinning array exhibit substantially stronger pinning effects over a much larger range of field than found for random or periodic pinning arrangements. The pinning enhancement is partially due to matching of the critical flux gradient with the pinning gradient, but the preservation of local ordering in the conformally transformed hexagonal lattice and the arching arrangement of the pinning also play crucial roles. Our results can be generalized to a wide class of gradient-driven interacting particle systems such as colloids on optical trap arrays.
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Affiliation(s)
- D Ray
- Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
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14
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Bulgac A, Forbes MM, Sharma R. Strength of the vortex-pinning interaction from real-time dynamics. PHYSICAL REVIEW LETTERS 2013; 110:241102. [PMID: 25165904 DOI: 10.1103/physrevlett.110.241102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2013] [Indexed: 06/03/2023]
Abstract
We present an efficient and general method to compute vortex-pinning interactions--which arise in neutron stars, superconductors, and trapped cold atoms--at arbitrary separations using real-time dynamics. This method overcomes uncertainties associated with matter redistribution by the vortex position and the related choice of ensemble that plague the typical approach of comparing energy differences between stationary pinned and unpinned configurations: uncertainties that prevent agreement in the literature on the sign and magnitude of the vortex-nucleus interaction in the crust of neutron stars. We demonstrate and validate the method with Gross-Pitaevskii-like equations for the unitary Fermi gas, and demonstrate how the technique of adiabatic state preparation with time-dependent simulation can be used to calculate vortex-pinning interactions in fermionic systems such as the vortex-nucleus interaction in the crust of neutron stars.
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Affiliation(s)
- Aurel Bulgac
- Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
| | - Michael McNeil Forbes
- Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA and Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195-1550, USA
| | - Rishi Sharma
- TRIUMF, Vancouver, British Columbia V6T 2A3, Canada
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15
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Möller G, Cooper NR. Correlated phases of bosons in the flat lowest band of the dice lattice. PHYSICAL REVIEW LETTERS 2012; 108:045306. [PMID: 22400857 DOI: 10.1103/physrevlett.108.045306] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2011] [Indexed: 05/31/2023]
Abstract
We study correlated phases occurring in the flat lowest band of the dice-lattice model at flux density one-half. We discuss how to realize this model, also referred to as the T(3) lattice, in cold atomic gases. We construct the projection of the model to the lowest dice band, which yields a Hubbard Hamiltonian with interaction-assisted hopping processes. We solve this model for bosons in two limits. In the limit of large density, we use Gross-Pitaevskii mean-field theory to reveal time-reversal symmetry breaking vortex lattice phases. At low density, we use exact diagonalization to identify three stable phases at fractional filling factors ν of the lowest band, including a classical crystal at ν = 1/3, a supersolid state at ν = 1/2, and a Mott insulator at ν = 1.
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Affiliation(s)
- G Möller
- TCM Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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16
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Wang XL, Chen J, Li Y, Ding J, Guo CS, Wang HT. Optical orbital angular momentum from the curl of polarization. PHYSICAL REVIEW LETTERS 2010; 105:253602. [PMID: 21231589 DOI: 10.1103/physrevlett.105.253602] [Citation(s) in RCA: 100] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2010] [Indexed: 05/30/2023]
Abstract
We predict a new category of optical orbital angular momentum that is associated with the curl of polarization and a kind of vector field with radial-variant hybrid states of polarization that can carry such novel optical orbital angular momentum. We present a scheme for creating the desired vector fields. Optical trapping experiments validate that the vector fields, which have no additional phase vortex, exert torques to drive the orbital motion of the trapped isotropic microspheres.
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Affiliation(s)
- Xi-Lin Wang
- School of Physics and Key Laboratory of Weak-Light Nonlinear Photonics, Nankai University, Tianjin 300071, China
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17
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Kapit E, Mueller E. Exact parent Hamiltonian for the quantum Hall states in a lattice. PHYSICAL REVIEW LETTERS 2010; 105:215303. [PMID: 21231318 DOI: 10.1103/physrevlett.105.215303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2010] [Revised: 07/13/2010] [Indexed: 05/30/2023]
Abstract
We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.
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Affiliation(s)
- Eliot Kapit
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York, USA
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18
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Zhang J, Jian CM, Ye F, Zhai H. Degeneracy of many-body quantum states in an optical lattice under a uniform magnetic field. PHYSICAL REVIEW LETTERS 2010; 105:155302. [PMID: 21230917 DOI: 10.1103/physrevlett.105.155302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2010] [Revised: 09/10/2010] [Indexed: 05/30/2023]
Abstract
We prove a theorem that shows the degeneracy of many-body states for particles in a periodic lattice and under a uniform magnetic field depends on the total particle number and the flux filling ratio. Noninteracting fermions and weakly interacting bosons are given as two examples. For the latter case, the phenomenon can also be physically understood in terms of destructive quantum interference of multiple symmetry-related tunneling paths between classical energy minima, which is reminiscent of the spin-parity effect discovered in magnetic molecular clusters. We also show that the quantum ground state of a mesoscopic number of bosons in this system is not a simple mean-field state but a fragmented state even for very weak interactions.
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Affiliation(s)
- Jian Zhang
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, People's Republic of China
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19
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Robert-de-Saint-Vincent M, Brantut JP, Allard B, Plisson T, Pezzé L, Sanchez-Palencia L, Aspect A, Bourdel T, Bouyer P. Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential. PHYSICAL REVIEW LETTERS 2010; 104:220602. [PMID: 20867158 DOI: 10.1103/physrevlett.104.220602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2010] [Indexed: 05/29/2023]
Abstract
We study the horizontal expansion of vertically confined ultracold atoms in the presence of disorder. Vertical confinement allows us to realize a situation with a few coupled harmonic oscillator quantum states. The disordered potential is created by an optical speckle at an angle of 30° with respect to the horizontal plane, resulting in an effective anisotropy of the correlation lengths of a factor of 2 in that plane. We observe diffusion leading to non-gaussian density profiles. Diffusion coefficients, extracted from the experimental results, show anisotropy and strong energy dependence, in agreement with numerical calculations.
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Affiliation(s)
- M Robert-de-Saint-Vincent
- Laboratoire Charles Fabry de l'Institut d'Optique, Univ. Paris Sud, CNRS, campus polytechnique RD128, 91127 Palaiseau, France
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20
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Zhai H, Umucalilar RO, Oktel MO. Pairing and vortex lattices for interacting fermions in optical lattices with a large magnetic field. PHYSICAL REVIEW LETTERS 2010; 104:145301. [PMID: 20481943 DOI: 10.1103/physrevlett.104.145301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2010] [Revised: 03/14/2010] [Indexed: 05/29/2023]
Abstract
We study the structure of a pairing order parameter for spin-1/2 fermions with attractive interactions in a square lattice under a uniform magnetic field. Because the magnetic translation symmetry gives a unique degeneracy in the single-particle spectrum, the pair wave function has both zero and finite-momentum components coexisting, and their relative phases are determined by a self-consistent mean-field theory. We present a microscopic calculation that can determine the vortex lattice structure in the superfluid phase for different flux densities. Phase transition from a Hofstadter insulator to a superfluid phase is also discussed.
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Affiliation(s)
- Hui Zhai
- Institute for Advanced Study, Tsinghua University, Beijing, 100084, China.
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Itah A, Veksler H, Lahav O, Blumkin A, Moreno C, Gordon C, Steinhauer J. Direct observation of a sub-Poissonian number distribution of atoms in an optical lattice. PHYSICAL REVIEW LETTERS 2010; 104:113001. [PMID: 20366471 DOI: 10.1103/physrevlett.104.113001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2009] [Indexed: 05/29/2023]
Abstract
We report single-site resolution in a lattice with tunneling between sites, allowing for an in situ study of stochastic losses. The ratio of the loss rate to the tunneling rate is seen to determine the number fluctuations, and the overall profile of the lattice. Sub-Poissonian number fluctuations are observed. Deriving the lattice beams from a microlens array results in perfect relative stability between beams.
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Affiliation(s)
- Amir Itah
- Department of Physics, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
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22
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Williams RA, Al-Assam S, Foot CJ. Observation of vortex nucleation in a rotating two-dimensional lattice of Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2010; 104:050404. [PMID: 20366752 DOI: 10.1103/physrevlett.104.050404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2009] [Indexed: 05/29/2023]
Abstract
We report the observation of vortex nucleation in a rotating optical lattice. A 87Rb Bose-Einstein condensate was loaded into a static two-dimensional lattice and the rotation frequency of the lattice was then increased from zero. We studied how vortex nucleation depended on optical lattice depth and rotation frequency. For deep lattices above the chemical potential of the condensate we observed a linear dependence of the number of vortices created with the rotation frequency, even below the thermodynamic critical frequency required for vortex nucleation. At these lattice depths the system formed an array of Josephson-coupled condensates. The effective magnetic field produced by rotation introduced characteristic relative phases between neighboring condensates, such that vortices were observed upon ramping down the lattice depth and recombining the condensates.
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Affiliation(s)
- R A Williams
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom
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23
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Möller G, Cooper NR. Composite fermion theory for bosonic quantum Hall states on lattices. PHYSICAL REVIEW LETTERS 2009; 103:105303. [PMID: 19792327 DOI: 10.1103/physrevlett.103.105303] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2009] [Revised: 08/13/2009] [Indexed: 05/28/2023]
Abstract
We study the ground states of the Bose-Hubbard model in a uniform magnetic field, motivated by the physics of cold atomic gases on lattices at high vortex density. Mapping the bosons to composite fermions (CF) leads to the prediction of quantum Hall fluids that have no counterpart in the continuum. We construct trial states for these phases and test numerically the predictions of the CF model. We establish the existence of strongly correlated phases beyond those in the continuum limit and provide evidence for a wider scope of the composite fermion approach beyond its application to the lowest Landau level.
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Affiliation(s)
- G Möller
- Theory of Condensed Matter Group, Cavendish Laboratory, Cambridge CB3 0HE, United Kingdom
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24
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Reichhardt C, Olson Reichhardt CJ. Pattern switching and polarizability for colloids in optical-trap arrays. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:022401. [PMID: 19792182 DOI: 10.1103/physreve.80.022401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2009] [Indexed: 05/28/2023]
Abstract
We show that colloidal molecular crystal states interacting with a periodic substrate, such as an optical-trap array, and a rotating external field can undergo a rapid pattern switching in which the orientation of the crystal changes. In some cases, a martensiticlike symmetry switching occurs. It is also possible to create a polarized state where the colloids in each substrate minimum develop a director field which smoothly rotates with the external drive, similar to liquid-crystal behavior. These results open the possibility for creating different types of devices using photonic band-gap materials, and should be generalizable to a variety of other condensed matter systems with multiple particle trapping.
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Affiliation(s)
- C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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25
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Porter MA. Experimental Results Related to DNLS Equations. SPRINGER TRACTS IN MODERN PHYSICS 2009. [DOI: 10.1007/978-3-540-89199-4_8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/12/2023]
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26
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Dahl EK, Babaev E, Sudbø A. Unusual states of vortex matter in mixtures of Bose-Einstein condensates on rotating optical lattices. PHYSICAL REVIEW LETTERS 2008; 101:255301. [PMID: 19113720 DOI: 10.1103/physrevlett.101.255301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2008] [Revised: 10/31/2008] [Indexed: 05/27/2023]
Abstract
In a single-component superfluid under rotation a broken symmetry in the order parameter space results in a broken translational symmetry in real space: a vortex lattice. If translational symmetry is restored, the phase of the order parameter disorders and thus the broken symmetry in the order parameter space is also restored. We show that for Bose-Einstein condensate mixtures in optical lattices with negative dissipationless drag, a new situation arises. This state is a modulated vortex liquid which breaks translational symmetry in the direction transverse to the rotation vector.
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Affiliation(s)
- E K Dahl
- Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
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27
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Williams RA, Pillet JD, Al-Assam S, Fletcher B, Shotter M, Foot CJ. Dynamic optical lattices: two-dimensional rotating and accordion lattices for ultracold atoms. OPTICS EXPRESS 2008; 16:16977-16983. [PMID: 18852806 DOI: 10.1364/oe.16.016977] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We demonstrate a novel experimental arrangement which can rotate a 2D optical lattice at frequencies up to several kilohertz. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields, allowing investigation of phenomena such as the fractional quantum Hall effect. Our arrangement also allows the periodicity of a 2D optical lattice to be varied dynamically, producing a 2D accordion lattice.
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Affiliation(s)
- R A Williams
- Clarendon Laboratory, University of Oxford, Oxford, United Kingdom.
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28
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Terhalle B, Richter T, Desyatnikov AS, Neshev DN, Krolikowski W, Kaiser F, Denz C, Kivshar YS. Observation of multivortex solitons in photonic lattices. PHYSICAL REVIEW LETTERS 2008; 101:013903. [PMID: 18764113 DOI: 10.1103/physrevlett.101.013903] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2008] [Indexed: 05/26/2023]
Abstract
We report on the first observation of topologically stable spatially localized multivortex solitons generated in optically induced hexagonal photonic lattices. We demonstrate that topological stabilization of such nonlinear localized states can be achieved through self-trapping of truncated two-dimensional Bloch waves and confirm our experimental results by numerical simulations of the beam propagation in weakly deformed lattice potentials in anisotropic photorefractive media.
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Affiliation(s)
- Bernd Terhalle
- Nonlinear Physics Center and Laser Physics Center, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia
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29
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Umucalilar RO, Zhai H, Oktel MO. Trapped Fermi gases in rotating optical lattices: realization and detection of the topological hofstadter insulator. PHYSICAL REVIEW LETTERS 2008; 100:070402. [PMID: 18352527 DOI: 10.1103/physrevlett.100.070402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2007] [Revised: 01/09/2008] [Indexed: 05/26/2023]
Abstract
We consider a gas of noninteracting spinless fermions in a rotating optical lattice and calculate the density profile of the gas in an external confinement potential. The density profile exhibits distinct plateaus, which correspond to gaps in the single particle spectrum known as the Hofstadter butterfly. The plateaus result from insulating behavior whenever the Fermi energy lies within a gap. We discuss the necessary conditions to realize the Hofstadter insulator in a cold atom setup and show how the quantized Hall conductance can be measured from density profiles using the Streda formula.
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Affiliation(s)
- R O Umucalilar
- Department of Physics, Bilkent University, 06800 Ankara, Turkey
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30
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Ryu C, Andersen MF, Cladé P, Natarajan V, Helmerson K, Phillips WD. Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap. PHYSICAL REVIEW LETTERS 2007; 99:260401. [PMID: 18233561 DOI: 10.1103/physrevlett.99.260401] [Citation(s) in RCA: 68] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2007] [Indexed: 05/25/2023]
Abstract
We have observed the persistent flow of Bose-condensed atoms in a toroidal trap. The flow persists without decay for up to 10 s, limited only by experimental factors such as drift and trap lifetime. The quantized rotation was initiated by transferring one unit variant Planck's over 2pi of the orbital angular momentum from Laguerre-Gaussian photons to each atom. Stable flow was only possible when the trap was multiply connected, and was observed with a Bose-Einstein condensate fraction as small as 20%. We also created flow with two units of angular momentum and observed its splitting into two singly charged vortices when the trap geometry was changed from multiply to simply connected.
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Affiliation(s)
- C Ryu
- Atomic Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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31
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Cuevas J, Malomed BA, Kevrekidis PG. Two-dimensional discrete solitons in rotating lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:046608. [PMID: 17995128 DOI: 10.1103/physreve.76.046608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2007] [Indexed: 05/25/2023]
Abstract
We introduce a two-dimensional discrete nonlinear Schrödinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong optical lattice, or light propagation in a twisted bundle of nonlinear fibers. Two types of localized states are constructed: off-axis fundamental solitons (FSs), placed at distance R from the rotation pivot, and on-axis (R=0) vortex solitons (VSs), with vorticities S=1 and 2 . At a fixed value of rotation frequency Omega , a stability interval for the FSs is found in terms of the lattice coupling constant C , 0<C<C_{cr}(R) , with monotonically decreasing C_{cr}(R) . VSs with S=1 have a stability interval, C[over ]_{cr};{(S=1)}(Omega)<C<C_{cr};{(S=1)}(Omega) , which exists for Omega below a certain critical value, Omega_{cr};{(S=1)} . This implies that the VSs with S=1 are destabilized in the weak-coupling limit by the rotation. On the contrary, VSs with S=2 , that are known to be unstable in the standard DNLS equation, with Omega=0 , are stabilized by the rotation in region 0<C<C_{cr};{(S=2)} , with C_{cr};{(S=2)} growing as a function of Omega . Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by Omega not equal 0 .
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Affiliation(s)
- Jesús Cuevas
- Departamento de Física Aplicada I, Escuela Universitaria Politécnica, C/ Virgen de Africa, 7, 41011 Sevilla, Spain
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32
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Hemmerich A, Morais Smith C. Excitation of a d-Density wave in an optical lattice with driven tunneling. PHYSICAL REVIEW LETTERS 2007; 99:113002. [PMID: 17930433 DOI: 10.1103/physrevlett.99.113002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2007] [Indexed: 05/25/2023]
Abstract
Quantum phases with unusual symmetries may play a key role in the understanding of solid state systems at low temperatures. We propose a realistic scenario, well in reach of present experimental techniques, which should permit us to produce a stationary quantum state with d x2-y2 symmetry in a two-dimensional bosonic optical square lattice. This state, characterized by alternating rotational flux in each plaquette, arises from driven tunneling implemented by a stimulated Raman scattering process. We discuss bosons in a square lattice; however, more complex systems involving other lattice geometries appear possible.
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Affiliation(s)
- A Hemmerich
- Institut für Laser-Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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33
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Scarola VW, Das Sarma S. Edge transport in 2D cold atom optical lattices. PHYSICAL REVIEW LETTERS 2007; 98:210403. [PMID: 17677753 DOI: 10.1103/physrevlett.98.210403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2007] [Indexed: 05/16/2023]
Abstract
We theoretically study the observable response of edge currents in two-dimensional cold atom optical lattices. As an example, we use Gutzwiller mean-field theory to relate persistent edge currents surrounding a Mott insulator in a slowly rotating trapped Bose-Hubbard system to time of flight measurements. We briefly discuss an application, the detection of the Chern number using edge currents of a topologically ordered optical lattice insulator.
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Affiliation(s)
- V W Scarola
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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