1
|
Large-S and Tensor-Network Methods for Strongly-Interacting Topological Insulators. Symmetry (Basel) 2022. [DOI: 10.3390/sym14040799] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
The study of correlation effects in topological phases of matter can benefit from a multidisciplinary approach that combines techniques drawn from condensed matter, high-energy physics and quantum information science. In this work, we exploit these connections to study the strongly-interacting limit of certain lattice Hubbard models of topological insulators, which map onto four-Fermi quantum field theories with a Wilson-type discretisation and have been recently shown to be at reach of cold-atom quantum simulators based on synthetic spin-orbit coupling. We combine large-S and tensor-network techniques to explore the possible spontaneous symmetry-breaking phases that appear when the interactions of the topological insulators are sufficiently large. In particular, we show that varying the Wilson parameter r of the lattice discretisations leads to a novel Heisenberg–Ising compass model with critical lines that flow with the value of r.
Collapse
|
2
|
Aidelsburger M, Barbiero L, Bermudez A, Chanda T, Dauphin A, González-Cuadra D, Grzybowski PR, Hands S, Jendrzejewski F, Jünemann J, Juzeliūnas G, Kasper V, Piga A, Ran SJ, Rizzi M, Sierra G, Tagliacozzo L, Tirrito E, Zache TV, Zakrzewski J, Zohar E, Lewenstein M. Cold atoms meet lattice gauge theory. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210064. [PMID: 34923836 PMCID: PMC8685612 DOI: 10.1098/rsta.2021.0064] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 08/23/2021] [Indexed: 05/17/2023]
Abstract
The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more 'accessible' and easier to manipulate for experimentalists, but this 'substitution' also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or [Formula: see text] Bose-Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz-Hubbard ladder, or Gross-Neveu-Wilson and Wilson-Hubbard models. This article is not a general review of the rapidly growing field-it reviews activities related to quantum simulations for lattice field theories performed by the Quantum Optics Theory group at ICFO and their collaborators from 19 institutions all over the world. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics. This article is part of the theme issue 'Quantum technologies in particle physics'.
Collapse
Affiliation(s)
- Monika Aidelsburger
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich 80799, Germany
- Munich Center for Quantum Science and Technology (MCQST), München 80799, Germany
| | - Luca Barbiero
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
- Institute for Condensed Matter Physics and Complex Systems, DISAT, Politecnico di Torino, I-10129 Torino, Italy
| | - Alejandro Bermudez
- Departamento de Física Teorica, Universidad Complutense, Madrid 28040, Spain
| | - Titas Chanda
- Institute of Theoretical Physics, Jagiellonian University in Kraków, Kraków 30-348, Poland
- The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
| | - Alexandre Dauphin
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Daniel González-Cuadra
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Przemysław R. Grzybowski
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University in Poznań, Poznań, Poland
| | - Simon Hands
- Department of Physics, Faculty of Science and Engineering, Swansea University, Swansea SA28PP, UK
- Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK
| | - Fred Jendrzejewski
- Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg 69120, Germany
| | - Johannes Jünemann
- Institut für Physik, Johannes Gutenberg-Universität, Mainz 55128, Germany
| | - Gediminas Juzeliūnas
- Institute of Theoretical Physics and Astronomy, Vilnius University, Vilnius 10257, Lithuania
| | - Valentin Kasper
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Angelo Piga
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
- Departament of Chemical Engineering, Universitat Rovira I Virgili, 43007, Tarragona, Catalonia, Spain
| | - Shi-Ju Ran
- Department of Physics, Capital Normal University, Beijing 100048, People’s Republic of China
| | - Matteo Rizzi
- Forschungszentrum Jülich GmbH, Institute of Quantum Control, Peter Grünberg Institut (PGI-8), Jülich 52425, Germany
- Institute for Theoretical Physics, University of Cologne, Köln 50937, Germany
| | - Germán Sierra
- Instituto de Física Teórica, UAM/CSIC, Universidad Autònoma de Madrid, Madrid, Spain
| | - Luca Tagliacozzo
- Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Barcelona, Catalonia 08028, Spain
| | - Emanuele Tirrito
- International School for Advanced Studies (SISSA), Trieste 34136, Italy
| | - Torsten V. Zache
- Center for Quantum Physics, University of Innsbruck, Innsbruck 6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck 6020, Austria
| | - Jakub Zakrzewski
- Institute of Theoretical Physics, Jagiellonian University in Kraków, Kraków 30-348, Poland
| | - Erez Zohar
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Maciej Lewenstein
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
- ICREA, Passeig Lluis Companys 23, Barcelona 08010, Spain
| |
Collapse
|
3
|
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
|
4
|
Generalized lattice Wilson-Dirac fermions in (1 + 1) dimensions for atomic quantum simulation and topological phases. Sci Rep 2018; 8:10699. [PMID: 30013212 PMCID: PMC6048181 DOI: 10.1038/s41598-018-29143-w] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2018] [Accepted: 07/05/2018] [Indexed: 11/16/2022] Open
Abstract
The Dirac fermion is an important fundamental particle appearing in high-energy physics and topological insulator physics. In particular, a Dirac fermion in a one-dimensional lattice system exhibits the essential properties of topological physics. However, the system has not been quantum simulated in experiments yet. Herein, we propose a one-dimensional generalized lattice Wilson-Dirac fermion model and study its topological phase structure. We show the experimental setups of an atomic quantum simulator for the model, in which two parallel optical lattices with the same tilt for trapping cold fermion atoms and a laser-assisted hopping scheme are used. Interestingly, we find that the model exhibits nontrivial topological phases characterized by gapless edge modes and a finite winding number in the broad regime of the parameter space. Some of the phase diagrams closely resemble those of the Haldane model. We also discuss topological charge pumping and a lattice Gross-Neveu model in the system of generalized Wilson-Dirac fermions.
Collapse
|
5
|
|
6
|
Mallick A, Chandrashekar CM. Dirac Cellular Automaton from Split-step Quantum Walk. Sci Rep 2016; 6:25779. [PMID: 27184159 PMCID: PMC4868993 DOI: 10.1038/srep25779] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2015] [Accepted: 04/22/2016] [Indexed: 11/26/2022] Open
Abstract
Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory.
Collapse
Affiliation(s)
- Arindam Mallick
- Optics and Quantum Information Group, The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India
| | - C M Chandrashekar
- Optics and Quantum Information Group, The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India
| |
Collapse
|
7
|
Zohar E, Cirac JI, Reznik B. Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:014401. [PMID: 26684222 DOI: 10.1088/0034-4885/79/1/014401] [Citation(s) in RCA: 57] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Can high-energy physics be simulated by low-energy, non-relativistic, many-body systems such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure an atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective low-energy symmetry, or as an exact symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to a new type of (table-top) experiments which will be used to study various QCD (quantum chromodynamics) phenomena, such as the confinement of dynamical quarks, phase transitions and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing the quantum simulation of Abelian and non-Abelian lattice gauge theories in 1 + 1 and 2 + 1 dimensions using ultracold atoms in optical lattices.
Collapse
Affiliation(s)
- Erez Zohar
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straß e 1, 85748 Garching, Germany
| | | | | |
Collapse
|
8
|
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
|
9
|
Sun F, Yu XL, Ye J, Fan H, Liu WM. Topological quantum phase transition in synthetic non-Abelian gauge potential: gauge invariance and experimental detections. Sci Rep 2014; 3:2119. [PMID: 23846153 PMCID: PMC3709414 DOI: 10.1038/srep02119] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2013] [Accepted: 06/13/2013] [Indexed: 11/16/2022] Open
Abstract
The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops.
Collapse
Affiliation(s)
- Fadi Sun
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
| | | | | | | | | |
Collapse
|
10
|
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
|
11
|
Abstract
Detecting topological order in cold-atom experiments is an ongoing challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of topological order exist for topological insulators and quantum Hall devices. In quantum Hall systems, the quantized conductivity and the associated robust propagating edge modes--guaranteed by the existence of nontrivial topological invariants--have been observed through transport and spectroscopy measurements. Here, we show that optical-lattice-based experiments can be tailored to directly visualize the propagation of topological edge modes. Our method is rooted in the unique capability for initially shaping the atomic gas and imaging its time evolution after suddenly removing the shaping potentials. Our scheme, applicable to an assortment of atomic topological phases, provides a method for imaging the dynamics of topological edge modes, directly revealing their angular velocity and spin structure.
Collapse
|
12
|
Zohar E, Cirac JI, Reznik B. Cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory. PHYSICAL REVIEW LETTERS 2013; 110:125304. [PMID: 25166817 DOI: 10.1103/physrevlett.110.125304] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2012] [Indexed: 05/29/2023]
Abstract
Non-Abelian gauge theories play an important role in the standard model of particle physics, and unfold a partially unexplored world of exciting physical phenomena. In this Letter, we suggest a realization of a non-Abelian lattice gauge theory-SU(2) Yang-Mills in (1 + 1) dimensions, using ultracold atoms. Remarkably, and in contrast to previous proposals, in our model gauge invariance is a direct consequence of angular momentum conservation and thus is fundamental and robust. Our proposal may serve as well as a starting point for higher-dimensional realizations.
Collapse
Affiliation(s)
- Erez Zohar
- Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv University, Tel-Aviv 69978, Israel
| | - J Ignacio Cirac
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - Benni Reznik
- Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv University, Tel-Aviv 69978, Israel
| |
Collapse
|
13
|
Barrett S, Hammerer K, Harrison S, Northup TE, Osborne TJ. Simulating quantum fields with cavity QED. PHYSICAL REVIEW LETTERS 2013; 110:090501. [PMID: 23496696 DOI: 10.1103/physrevlett.110.090501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2012] [Revised: 01/25/2013] [Indexed: 06/01/2023]
Abstract
As the realization of a fully operational quantum computer remains distant, quantum simulation, whereby one quantum system is engineered to simulate another, becomes a key goal of great practical importance. Here we report on a variational method exploiting the natural physics of cavity QED architectures to simulate strongly interacting quantum fields. Our scheme is broadly applicable to any architecture involving tunable and strongly nonlinear interactions with light; as an example, we demonstrate that existing cavity devices could simulate models of strongly interacting bosons. The scheme can be extended to simulate systems of entangled multicomponent fields, beyond the reach of existing classical simulation methods.
Collapse
Affiliation(s)
- Sean Barrett
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom
| | | | | | | | | |
Collapse
|
14
|
Galitski V, Spielman IB. Spin–orbit coupling in quantum gases. Nature 2013; 494:49-54. [DOI: 10.1038/nature11841] [Citation(s) in RCA: 664] [Impact Index Per Article: 60.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2012] [Accepted: 12/11/2012] [Indexed: 11/09/2022]
|
15
|
Zohar E, Cirac JI, Reznik B. Simulating (2+1)-dimensional lattice QED with dynamical matter using ultracold atoms. PHYSICAL REVIEW LETTERS 2013; 110:055302. [PMID: 23414028 DOI: 10.1103/physrevlett.110.055302] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2012] [Revised: 11/26/2012] [Indexed: 05/29/2023]
Abstract
We suggest a method to simulate compact quantum electrodynamics using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows us to test the dynamical effects of confinement as well as the deformations and breaking of two-dimensional flux loops, and to observe the Wilson-loop area law.
Collapse
Affiliation(s)
- Erez Zohar
- School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel-Aviv 69978, Israel
| | | | | |
Collapse
|
16
|
Selem A. Anomalous currents on closed surfaces: extended proximity, partial quantization and qubits. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:045003. [PMID: 23220818 DOI: 10.1088/0953-8984/25/4/045003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Motivated by the surfaces of topological insulators, the Dirac anomaly's discontinuous dependence on the sign of the mass, m/|m|, is investigated on closed topologies when the mass terms are weak or only partially cover the surface. It is found that, unlike the massive Dirac theory on an infinite plane, there is a smoothly decreasing current when the mass region is not infinite; also, a massive finite region fails to exhibit a Hall current edge-exerting an extended proximity effect, which can, however, be uniformly small-and oppositely orientated Hall phases are fully quantized while accompanied by diffuse chiral modes. Examples are computed using Dirac energy eigenstates on a flat torus (genus one topology) and a closed cap cylinder (genus zero topology) for various mass-term geometries. Finally, from the resulting properties of the surface spectra, a potential application for a flux-charge qubit is presented.
Collapse
Affiliation(s)
- Alexander Selem
- Department of Physics, University of California, Berkeley, CA 94720, USA.
| |
Collapse
|
17
|
Zohar E, Cirac JI, Reznik B. Simulating compact quantum electrodynamics with ultracold atoms: probing confinement and nonperturbative effects. PHYSICAL REVIEW LETTERS 2012; 109:125302. [PMID: 23005955 DOI: 10.1103/physrevlett.109.125302] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2012] [Revised: 07/02/2012] [Indexed: 05/28/2023]
Abstract
Recently, there has been much interest in simulating quantum field theory effects of matter and gauge fields. In a recent work, a method for simulating compact quantum electrodynamics (CQED) using Bose-Einstein condensates has been suggested. We suggest an alternative approach, which relies on single atoms in an optical lattice, carrying 2l + 1 internal levels, which converges rapidly to CQED as l increases. That enables the simulation of CQED in 2 + 1 dimensions in both the weak and the strong coupling regimes, hence, allowing us to probe confinement as well as other nonperturbative effects of the theory. We provide an explicit construction for the case l = 1 which is sufficient for simulating the effect of confinement between two external static charges.
Collapse
Affiliation(s)
- Erez Zohar
- School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Israel
| | | | | |
Collapse
|
18
|
Sornborger AT. Quantum simulation of tunneling in small systems. Sci Rep 2012; 2:597. [PMID: 22916333 PMCID: PMC3424524 DOI: 10.1038/srep00597] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2012] [Accepted: 08/01/2012] [Indexed: 11/13/2022] Open
Abstract
A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution, eliminating at least half of the quantum gates required for the algorithm and more than that in the general case. Such simulations are within reach of current quantum computer architectures.
Collapse
Affiliation(s)
- Andrew T Sornborger
- Department of Mathematics and College of Engineering, University of Georgia, Athens, Georgia 30602, USA.
| |
Collapse
|
19
|
Anderson BM, Juzeliūnas G, Galitski VM, Spielman IB. Synthetic 3D spin-orbit coupling. PHYSICAL REVIEW LETTERS 2012; 108:235301. [PMID: 23003967 DOI: 10.1103/physrevlett.108.235301] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2012] [Indexed: 06/01/2023]
Abstract
We describe a method for creating a three-dimensional analogue to Rashba spin-orbit coupling in systems of ultracold atoms. This laser induced coupling uses Raman transitions to link four internal atomic states with a tetrahedral geometry, and gives rise to a Dirac point that is robust against environmental perturbations. We present an exact result showing that such a spin-orbit coupling in a fermionic system always gives rise to a molecular bound state.
Collapse
Affiliation(s)
- Brandon M Anderson
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742-4111, USA
| | | | | | | |
Collapse
|
20
|
Affiliation(s)
- Stephen P Jordan
- Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
| | | | | |
Collapse
|
21
|
Lan Z, Celi A, Lu W, Öhberg P, Lewenstein M. Tunable multiple layered Dirac cones in optical lattices. PHYSICAL REVIEW LETTERS 2011; 107:253001. [PMID: 22243070 DOI: 10.1103/physrevlett.107.253001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2011] [Indexed: 05/31/2023]
Abstract
We show that multiple layered Dirac cones can emerge in the band structure of properly addressed multicomponent cold fermionic gases in optical lattices. The layered Dirac cones contain multiple copies of massless spin-1/2 Dirac fermions at the same location in momentum space, whose different Fermi velocity can be tuned at will. On-site microwave Raman transitions can further be used to mix the different Dirac species, resulting in either splitting of or preserving the Dirac point (depending on the symmetry of the on-site term). The tunability of the multiple layered Dirac cones allows us to simulate a number of fundamental phenomena in modern physics, such as neutrino oscillations and exotic particle dispersions with E~p(N) for arbitrary integer N.
Collapse
Affiliation(s)
- Z Lan
- SUPA, Department of Physics, Heriot-Watt University, EH14 4AS, Edinburgh, United Kingdom
| | | | | | | | | |
Collapse
|
22
|
Alba E, Fernandez-Gonzalvo X, Mur-Petit J, Pachos JK, Garcia-Ripoll JJ. Seeing topological order in time-of-flight measurements. PHYSICAL REVIEW LETTERS 2011; 107:235301. [PMID: 22182096 DOI: 10.1103/physrevlett.107.235301] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2011] [Revised: 08/31/2011] [Indexed: 05/31/2023]
Abstract
In this Letter, we provide a general methodology to directly measure topological order in cold atom systems. As an application, we propose the realization of a characteristic topological model, introduced by Haldane, using optical lattices loaded with fermionic atoms in two internal states. We demonstrate that time-of-flight measurements directly reveal the topological order of the system in the form of momentum-space Skyrmions.
Collapse
Affiliation(s)
- E Alba
- Instituto de Física Fundamental, IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain
| | | | | | | | | |
Collapse
|
23
|
Béri B, Cooper NR. Z(2) topological insulators in ultracold atomic gases. PHYSICAL REVIEW LETTERS 2011; 107:145301. [PMID: 22107205 DOI: 10.1103/physrevlett.107.145301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2011] [Indexed: 05/31/2023]
Abstract
We describe how optical dressing can be used to generate band structures for ultracold atoms with nontrivial Z(2) topological order. Time-reversal symmetry is preserved by simple conditions on the optical fields. We first show how to construct optical lattices that give rise to Z(2) topological insulators in two dimensions. We then describe a general method for the construction of three-dimensional Z(2) topological insulators. A central feature of our approach is a new way to understand Z(2) topological insulators starting from the nearly free electron limit.
Collapse
Affiliation(s)
- B Béri
- T.C.M. Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | | |
Collapse
|