1
|
Cheng D, Wang K, Fan S. Artificial Non-Abelian Lattice Gauge Fields for Photons in the Synthetic Frequency Dimension. PHYSICAL REVIEW LETTERS 2023; 130:083601. [PMID: 36898123 DOI: 10.1103/physrevlett.130.083601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2022] [Accepted: 01/12/2023] [Indexed: 06/18/2023]
Abstract
Non-Abelian gauge fields give rise to nontrivial topological physics. Here we develop a scheme to create an arbitrary SU(2) lattice gauge field for photons in the synthetic frequency dimension using an array of dynamically modulated ring resonators. The photon polarization is taken as the spin basis to implement the matrix-valued gauge fields. Using a non-Abelian generalization of the Harper-Hofstadter Hamiltonian as a specific example, we show that the measurement of the steady-state photon amplitudes inside the resonators can reveal the band structures of the Hamiltonian, which show signatures of the underlying non-Abelian gauge field. These results provide opportunities to explore novel topological phenomena associated with non-Abelian lattice gauge fields in photonic systems.
Collapse
Affiliation(s)
- Dali Cheng
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
| | - Kai Wang
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
| | - Shanhui Fan
- Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
| |
Collapse
|
2
|
Carmen Bañuls M, Cichy K. Review on novel methods for lattice gauge theories. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2020; 83:024401. [PMID: 31846938 DOI: 10.1088/1361-6633/ab6311] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem. In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.
Collapse
Affiliation(s)
- Mari Carmen Bañuls
- Max-Planck Institut, für Quantenoptik, Garching 85748, Germany. Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, Munich 80799, Germany
| | | |
Collapse
|
3
|
Yang Y, Peng C, Zhu D, Buljan H, Joannopoulos JD, Zhen B, Soljačić M. Synthesis and observation of non-Abelian gauge fields in real space. Science 2019; 365:1021-1025. [DOI: 10.1126/science.aay3183] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Accepted: 08/12/2019] [Indexed: 11/02/2022]
Affiliation(s)
- Yi Yang
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Chao Peng
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, Peking University, Beijing 100871, China
- Nano-optoelectronics Frontier Center of the Ministry of Education, Beijing 100871, China
| | - Di Zhu
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Hrvoje Buljan
- Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia
- MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - John D. Joannopoulos
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Bo Zhen
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Marin Soljačić
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| |
Collapse
|
4
|
Abstract
The concept of gauge field is a cornerstone of modern physics and the synthetic gauge field has emerged as a new way to manipulate particles in many disciplines. In optics, several schemes of Abelian synthetic gauge fields have been proposed. Here, we introduce a new platform for realizing synthetic SU(2) non-Abelian gauge fields acting on two-dimensional optical waves in a wide class of anisotropic materials and discover novel phenomena. We show that a virtual non-Abelian Lorentz force arising from material anisotropy can induce light beams to travel along Zitterbewegung trajectories even in homogeneous media. We further design an optical non-Abelian Aharonov-Bohm system which results in the exotic spin density interference effect. We can extract the Wilson loop of an arbitrary closed optical path from a series of gauge fixed points in the interference fringes. Our scheme offers a new route to study SU(2) gauge field related physics using optics.
Collapse
|
5
|
Abstract
We investigate the transport problem that a spinful matter wave is incident on a strong localized spin-orbit-coupled Bose-Einstein condensate in optical lattices, where the localization is admitted by atom interaction only existing at one particular site, and the spin-orbit coupling arouse spatial rotation of the spin texture. We find that tuning the spin orientation of the localized Bose-Einstein condensate can lead to spin-nonreciprocal/spin-reciprocal transport, meaning the transport properties are dependent on/independent of the spin orientation of incident waves. In the former case, we obtain the conditions to achieve transparency, beam-splitting, and blockade of the incident wave with a given spin orientation, and furthermore the ones to perfectly isolate incident waves of different spin orientation, while in the latter, we obtain the condition to maximize the conversion of different spin states. The result may be useful to develop a novel spinful matter wave valve that integrates spin switcher, beam-splitter, isolator, and converter. The method can also be applied to other real systems, e.g., realizing perfect isolation of spin states in magnetism, which is otherwise rather difficult.
Collapse
|
6
|
Liu ZX, Li ZH, Wang AM. Fractional charged edge states in ladder topological insulators. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:125402. [PMID: 30650403 DOI: 10.1088/1361-648x/aaff16] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We propose a model of two-leg ladder topological insulator in which the spin-orbit couplings are presented in both intra-chain and inter-chain interactions. The topological phase supports four fractional charged edge states localized at opposite ends of the ladder, which belongs to the chiral symplectic (CII) class protected by time-reversal symmetry and chiral symmetry. In our model, the presence of time-reversal and chiral symmetry generates fourfold degeneracy for the edge states, and the two edge states with same chirality at one end of the ladder each carries half charge. In contrast to the two edge states spatially localized at one end of the ladder being not distinguished, these two edge states can be detected by the momentum density. The experimental scheme for realizing our model with cold atoms in optical lattice is discussed. By introducing a magnetic field in the x direction, the system is driven from CII class to AIII class. In AIII class, there exist two distinct topological phases that exhibit four degenerate edge states and two degenerate edge states in the gap, respectively. As same as the system in CII class, each edge state carries a half charge in AIII class.
Collapse
Affiliation(s)
- Zhu-Xi Liu
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | | | | |
Collapse
|
7
|
Caio MD, Cooper NR, Bhaseen MJ. Quantum Quenches in Chern Insulators. PHYSICAL REVIEW LETTERS 2015; 115:236403. [PMID: 26684130 DOI: 10.1103/physrevlett.115.236403] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2015] [Indexed: 05/22/2023]
Abstract
We explore the nonequilibrium response of Chern insulators. Focusing on the Haldane model, we study the dynamics induced by quantum quenches between topological and nontopological phases. A notable feature is that the Chern number, calculated for an infinite system, is unchanged under the dynamics following such a quench. However, in finite geometries, the initial and final Hamiltonians are distinguished by the presence or absence of edge modes. We study the edge excitations and describe their impact on the experimentally observable edge currents and magnetization. We show that, following a quantum quench, the edge currents relax towards new equilibrium values, and that there is light-cone spreading of the currents into the interior of the sample.
Collapse
Affiliation(s)
- M D Caio
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - N R Cooper
- T.C.M. Group, Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - M J Bhaseen
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| |
Collapse
|
8
|
Quantum simulation of 2D topological physics in a 1D array of optical cavities. Nat Commun 2015; 6:7704. [PMID: 26145177 PMCID: PMC4506549 DOI: 10.1038/ncomms8704] [Citation(s) in RCA: 93] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Accepted: 06/01/2015] [Indexed: 11/14/2022] Open
Abstract
Orbital angular momentum of light is a fundamental optical degree of freedom characterized by unlimited number of available angular momentum states. Although this unique property has proved invaluable in diverse recent studies ranging from optical communication to quantum information, it has not been considered useful or even relevant for simulating nontrivial physics problems such as topological phenomena. Contrary to this misconception, we demonstrate the incredible value of orbital angular momentum of light for quantum simulation by showing theoretically how it allows to study a variety of important 2D topological physics in a 1D array of optical cavities. This application for orbital angular momentum of light not only reduces required physical resources but also increases feasible scale of simulation, and thus makes it possible to investigate important topics such as edge-state transport and topological phase transition in a small simulator ready for immediate experimental exploration. A wide variety of interesting phenomena arise in 2D systems subject to external gauge fields, but these are sometimes challenging to verify experimentally. Here the authors propose a setup to simulate 2D physics with a 1D arrangement of cavities, by exploiting the orbital angular momentum of trapped photons.
Collapse
|
9
|
Dutta O, Przysiężna A, Zakrzewski J. Spontaneous magnetization and anomalous Hall effect in an emergent Dice lattice. Sci Rep 2015; 5:11060. [PMID: 26057635 PMCID: PMC4460892 DOI: 10.1038/srep11060] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2014] [Accepted: 05/11/2015] [Indexed: 11/08/2022] Open
Abstract
Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets.
Collapse
Affiliation(s)
- Omjyoti Dutta
- Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, ulica Łojasiewicza 11, PL-30-348 Kraków, Poland
| | - Anna Przysiężna
- Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, ulica Łojasiewicza 11, PL-30-348 Kraków, Poland
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
- National Quantum Information Centre of Gdańsk, Andersa 27, 81-824 Sopot, Poland
| | - Jakub Zakrzewski
- Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, ulica Łojasiewicza 11, PL-30-348 Kraków, Poland
- Mark Kac Complex Systems Research Center, Uniwersytet Jagielloński, Kraków, Poland
| |
Collapse
|
10
|
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.
Collapse
Affiliation(s)
- N Goldman
- College de France, 11 place Marcelin Berthelot & Laboratoire Kastler Brossel, CNRS, UPMC, ENS, 24 rue Lhomond, 75005 Paris, France
| | | | | | | |
Collapse
|
11
|
Realising Haldane's vision for a Chern insulator in buckled lattices. Sci Rep 2014; 3:2736. [PMID: 24061332 PMCID: PMC3781404 DOI: 10.1038/srep02736] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2013] [Accepted: 09/03/2013] [Indexed: 11/10/2022] Open
Abstract
The Chern insulator displays a quantum Hall effect with no net magnetic field. Proposed by Haldane over 20 years ago, it laid the foundation for the fields of topological order, unconventional quantum Hall effects, and topological insulators. Despite enormous impact over two decades, Haldane's original vision of a staggered magnetic field within a crystal lattice has been prohibitively difficult to realise. In fact, in the original paper Haldane stresses his idea is probably merely a toy model. I show that buckled lattices with only simple hopping terms, within in-plane magnetic fields, can realise these models, requiring no exotic interactions or experimental parameters. As a concrete example of this very broad, and remarkably simple principle, I consider silicene, a honeycomb lattice with out-of-plane sublattice anisotropy, in an in-plane magnetic field, and show that it is a Chern insulator, even at negligibly small magnetic fields, which is analogous to Haldane's original model.
Collapse
|
12
|
Verdeny A, Rudnicki L, Müller CA, Mintert F. Optimal control of effective Hamiltonians. PHYSICAL REVIEW LETTERS 2014; 113:010501. [PMID: 25032912 DOI: 10.1103/physrevlett.113.010501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2014] [Indexed: 06/03/2023]
Abstract
We present a systematic scheme for the optimization of quantum simulations. Specifically, we show how polychromatic driving can be used to significantly improve the driving of Raman transitions in the Lambda system, which opens new possibilities for controlled driving-induced effective dynamics.
Collapse
Affiliation(s)
- Albert Verdeny
- Freiburg Institute for Advanced Studies, Albert-Ludwigs-Universität, Albertstrasse 19, 79104 Freiburg, Germany and Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Lukasz Rudnicki
- Freiburg Institute for Advanced Studies, Albert-Ludwigs-Universität, Albertstrasse 19, 79104 Freiburg, Germany and Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Cord A Müller
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore and Department of Physics, University of Konstanz, 78457 Konstanz, Germany
| | - Florian Mintert
- Freiburg Institute for Advanced Studies, Albert-Ludwigs-Universität, Albertstrasse 19, 79104 Freiburg, Germany and Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| |
Collapse
|
13
|
Wang D, Liu Z, Cao J, Fan H. Tunable band topology reflected by fractional quantum Hall States in two-dimensional lattices. PHYSICAL REVIEW LETTERS 2013; 111:186804. [PMID: 24237549 DOI: 10.1103/physrevlett.111.186804] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2013] [Indexed: 06/02/2023]
Abstract
Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from the Hofstadter model and demonstrate that the band topology transitions can be realized by simply introducing tunable longer-range hopping. The rich phase diagram of band Chern numbers is obtained for the simple rational flux density and a classification of phases is presented. In the presence of interactions, the existence of fractional quantum Hall states in both |C| = 1 and |C| > 1 bands is confirmed, which can reflect the band topologies in different phases. In contrast, when our model reduces to a one-dimensional lattice, the ground states are crucially different from fractional quantum Hall states. Our results may provide insights into the study of new fractional quantum Hall states and experimental realizations of various topological phases in optical lattices.
Collapse
Affiliation(s)
- Dong Wang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | | | | | | |
Collapse
|
14
|
Hou JM. Hidden-symmetry-protected topological semimetals on a square lattice. PHYSICAL REVIEW LETTERS 2013; 111:130403. [PMID: 24116751 DOI: 10.1103/physrevlett.111.130403] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2012] [Revised: 07/22/2013] [Indexed: 06/02/2023]
Abstract
We study a two-dimensional fermionic square lattice, which supports the existence of a two-dimensional Weyl semimetal, quantum anomalous Hall effect, and 2π-flux topological semimetal in different parameter ranges. We show that the band degenerate points of the two-dimensional Weyl semimetal and 2π-flux topological semimetal are protected by two distinct novel hidden symmetries, which both correspond to antiunitary composite operations. When these hidden symmetries are broken, a gap opens between the conduction and valence bands, turning the system into a insulator. With appropriate parameters, a quantum anomalous Hall effect emerges. The degenerate point at the boundary between the quantum anomalous Hall insulator and trivial band insulator is also protected by the hidden symmetry.
Collapse
Affiliation(s)
- Jing-Min Hou
- Department of Physics, Southeast University, Nanjing 211189, China
| |
Collapse
|
15
|
Banerjee D, Dalmonte M, Müller M, Rico E, Stebler P, Wiese UJ, Zoller P. Atomic quantum simulation of dynamical gauge fields coupled to fermionic matter: from string breaking to evolution after a quench. PHYSICAL REVIEW LETTERS 2012; 109:175302. [PMID: 23215198 DOI: 10.1103/physrevlett.109.175302] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2012] [Revised: 08/09/2012] [Indexed: 05/28/2023]
Abstract
Using a Fermi-Bose mixture of ultracold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.
Collapse
Affiliation(s)
- D Banerjee
- Albert Einstein Center, Institute for Theoretical Physics, Bern University, CH-3012, Bern, Switzerland
| | | | | | | | | | | | | |
Collapse
|
16
|
Chern GW, Batista CD. Spontaneous quantum Hall effect via a thermally induced quadratic Fermi point. PHYSICAL REVIEW LETTERS 2012; 109:156801. [PMID: 23102349 DOI: 10.1103/physrevlett.109.156801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2012] [Indexed: 06/01/2023]
Abstract
Gapless electronic systems containing topologically nontrivial Fermi points are sources of various topological insulators. Whereas, most of these special band-crossing points are built in the electronic structure of the noninteracting lattice models, we show that a quadratic Fermi point characterized by a nonzero winding number emerges with a collinear triple-Q spin-density-wave state that arises from a perfectly nested but topologically trivial Fermi surface. We obtain a universal low-energy Hamiltonian for the quadratic Fermi point and show that such collinear orderings are unstable against the onset of scalar spin chirality that opens a gap and induces a spontaneous quantum Hall insulator as the temperature tends to zero.
Collapse
Affiliation(s)
- Gia-Wei Chern
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | |
Collapse
|
17
|
Hauke P, Tieleman O, Celi A, Olschläger C, Simonet J, Struck J, Weinberg M, Windpassinger P, Sengstock K, Lewenstein M, Eckardt A. Non-abelian gauge fields and topological insulators in shaken optical lattices. PHYSICAL REVIEW LETTERS 2012; 109:145301. [PMID: 23083256 DOI: 10.1103/physrevlett.109.145301] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2012] [Revised: 06/26/2012] [Indexed: 06/01/2023]
Abstract
Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and demonstrate the power of this method by making concrete proposals for its application to two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagome lattice. We propose the realization of a topological and a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-abelian gauge fields.
Collapse
Affiliation(s)
- Philipp Hauke
- ICFO-Institut de Ciències Fotòniques, Parc Mediterrani de la Tecnologia, E-08860 Castelldefels, Spain.
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
18
|
Radić J, Di Ciolo A, Sun K, Galitski V. Exotic quantum spin models in spin-orbit-coupled Mott insulators. PHYSICAL REVIEW LETTERS 2012; 109:085303. [PMID: 23002755 DOI: 10.1103/physrevlett.109.085303] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2012] [Indexed: 06/01/2023]
Abstract
We study cold atoms in an optical lattice with synthetic spin-orbit coupling in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model using Peierls substitution and "localized Wannier states method" and derive the low-energy spin Hamiltonian for bosons and fermions. The spin Hamiltonian is a combination of Heisenberg model, quantum compass model and Dzyaloshinskii-Moriya interactions and it has a rich classical phase diagram with collinear, spiral and vortex phases. We discuss the state of the art of experiments to realize and detect magnetic orderings in strongly correlated optical lattices.
Collapse
Affiliation(s)
- J Radić
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
| | | | | | | |
Collapse
|
19
|
Boada O, Celi A, Latorre JI, Lewenstein M. Quantum simulation of an extra dimension. PHYSICAL REVIEW LETTERS 2012; 108:133001. [PMID: 22540696 DOI: 10.1103/physrevlett.108.133001] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2011] [Indexed: 05/22/2023]
Abstract
We present a general strategy to simulate a D+1-dimensional quantum system using a D-dimensional one. We analyze in detail a feasible implementation of our scheme using optical lattice technology. The simplest nontrivial realization of a fourth dimension corresponds to the creation of a bi-volume geometry. We also propose single- and many-particle experimental signatures to detect the effects of the extra dimension.
Collapse
Affiliation(s)
- O Boada
- Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, 647 Diagonal, 08028 Barcelona, Spain
| | | | | | | |
Collapse
|
20
|
Casanova J, Lamata L, Egusquiza IL, Gerritsma R, Roos CF, García-Ripoll JJ, Solano E. Quantum simulation of quantum field theories in trapped ions. PHYSICAL REVIEW LETTERS 2011; 107:260501. [PMID: 22243143 DOI: 10.1103/physrevlett.107.260501] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2011] [Indexed: 05/31/2023]
Abstract
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Collapse
Affiliation(s)
- J Casanova
- Departamento de Química Física, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao, Spain
| | | | | | | | | | | | | |
Collapse
|
21
|
Ho TL, Zhang S. Bose-Einstein condensates with spin-orbit interaction. PHYSICAL REVIEW LETTERS 2011; 107:150403. [PMID: 22107273 DOI: 10.1103/physrevlett.107.150403] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2011] [Revised: 08/04/2011] [Indexed: 05/31/2023]
Abstract
Motivated by recent experiments carried out by Spielman's group at NIST, we study a general scheme for generating families of gauge fields, spanning the scalar, spin-orbit, and non-Abelian regimes. The NIST experiments, which impart momentum to bosons while changing their spin state, can in principle realize all these. In the spin-orbit regime, we show that a Bose gas is a spinor condensate made up of two non-orthogonal dressed spin states carrying different momenta. As a result, its density shows a stripe structure with a contrast proportional to the overlap of the dressed states, which can be made very pronounced by adjusting the experimental parameters.
Collapse
Affiliation(s)
- Tin-Lun Ho
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | | |
Collapse
|
22
|
Cirac JI, Maraner P, Pachos JK. Cold atom simulation of interacting relativistic quantum field theories. PHYSICAL REVIEW LETTERS 2010; 105:190403. [PMID: 21231152 DOI: 10.1103/physrevlett.105.190403] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2010] [Indexed: 05/30/2023]
Abstract
We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.
Collapse
Affiliation(s)
- J Ignacio Cirac
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
| | | | | |
Collapse
|
23
|
Burrello M, Trombettoni A. Non-Abelian anions from degenerate landau levels of ultracold atoms in artificial gauge potentials. PHYSICAL REVIEW LETTERS 2010; 105:125304. [PMID: 20867652 DOI: 10.1103/physrevlett.105.125304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2010] [Revised: 07/11/2010] [Indexed: 05/29/2023]
Abstract
We show that non-Abelian potentials acting on ultracold gases with two hyperfine levels can give rise to ground states with non-Abelian excitations. We consider a realistic gauge potential for which the Landau levels can be exactly determined: The non-Abelian part of the vector potential makes the Landau levels nondegenerate. In the presence of strong repulsive interactions, deformed Laughlin ground states occur in general. However, at the degeneracy points of the Landau levels, non-Abelian quantum Hall states appear: These ground states, including deformed Moore-Read states (characterized by Ising anyons as quasiholes), are studied for both fermionic and bosonic gases.
Collapse
Affiliation(s)
- Michele Burrello
- SISSA and INFN, Sezione di Trieste, Via Bonomea 265, I-34136 Trieste, Italy
| | | |
Collapse
|