Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0607246 · Physical Review Letters

Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials

Indubala I. Satija, Daniel C. Dakin, Charles W. Clark

Published Nov 20, 2006• 51 citations
arXivHTMLPDF

Abstract

We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. For Abelian gauges, such transitions occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum. Other key characteristics of the non-Abelian case include the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta.

DOI
10.1103/physrevlett.97.216401

Related papers

Cold Atoms in U(3) Gauge Potentials

Ipsita Mandal, Atri Bhattacharya

We explore the effects of artificial U ( 3 ) gauge potentials on ultracold atoms. We study background gauge fields with both non-constant and constant Wilson loops around plaquettes, obtaining the energy spectra in each case. The scenario of metal–insulator transition for irrational fluxes is also examined. Finally, we discuss the effect of such a gauge potential on the superfluid–insulator transition for bosonic ultracold atoms.

arXiv:1603.08526•Condensed Matter•Aug 1, 2016•3 citations

Quantum phase transition of ultracold bosons in the presence of a non-Abelian synthetic gauge field

Tobias Graß, Kush Saha, K. Sengupta +1 more

We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a SU(2)-hopping matrix for the bosons. Using a resummed hopping expansion, we calculate the excitation spectra in the Mott insulating phases and demonstrate that the superfluid-insulator phase boundary displays a nonmonotonic dependence on the gauge-field strength. We also compute the momentum distribution of the bosons in the presence of the non-Abelian field and show that they develop peaks at nonzero momenta as the superfluid-insulator transition point is approached from the Mott side. Finally, we study the superfluid phases near the transition and discuss the induced spatial pattern of the superfluid density due to the presence of the non-Abelian gauge potential.

arXiv:1108.2672•Physical Review A•Nov 28, 2011•57 citations

Cold Atoms in Non-Abelian Gauge Potentials: From the Hofstadter "Moth" to Lattice Gauge Theory

Klaus Osterloh, M. Baig, Luis Santos +2 more

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary k x k matrices. The single-particle dynamics in the case of intense U2 vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.

arXiv:cond-mat/0502251•Physical Review Letters•Jun 28, 2005•428 citations

Time-of-flight patterns of ultracold bosons in optical lattices in various Abelian artificial magnetic field gauges

T. P. Polak, T. A. Zaleski

We calculate the time-of-flight patterns of strongly interacting bosons confined in a two-dimensional square lattice in the presence of an artificial magnetic field, using a quantum rotor model that is inherently combined with the Bogoliubov approach. We consider various geometries of the magnetic flux, which are expected to be realizable, or have already been implemented in experimental settings. The flexibility of the method allowed us to study cases where the artificial magnetic field is uniform or staggered or forms a checkerboard configuration. The effects of additional temporal modulation of the optical potential that results from application of Raman lasers driving particle transitions between lattice sites are also included. The time-of-flight patterns presented may serve as a verification of the chosen gauge in experiments, but also provide important hints on unconventional, nonzero-momentum condensates, or the possibility of observing graphenelike physics resulting from the occurrence of Dirac cones in artificial magnetic fields in systems of ultracold bosons in optical lattices. Also, we elucidate the differences between the effects of magnetic fields in solids and of artificial magnetic fields in optical lattices, which can be controlled on a much higher level, leading to effects not possible in condensed matter physics.

arXiv:1304.1176•Physical Review A•Mar 14, 2013•21 citations

Cold atom dynamics in non-Abelian gauge fields

A. Goÿ

The dynamics of ultracold neutral atoms subject to a non-Abelian gauge field is investigated. In particular we analyze in detail a simple experimental scheme to achieve a con- stant, but non-Abelian gauge field, and discuss in the frame of this gauge field the non-Abelian Aharanov-Bohm effect. In the last part of this paper, we discuss intrinsic non-Abelian effects in the dynamics of cold atomic wavepackets. the implementation of these proposals, ultracold atoms would offer a unique testbed for the analysis of non-trivial non- Abelian effects on the quantum dynamics of multicomponent wavepackets. In this paper, we investigate the wave packet dynam- ics of a cloud of ultracold atoms in the presence of a non- Abelian gauge potential. In Sect. 2 we discuss how this un- doubtedly rather exotic scenario can be envisaged in a sam- ple of cold atoms where the internal electronic energy levels are addressed by laser fields with a nontrivial spatial phase and intensity distribution. This setup opens up a number of new scenarios for ultracold gases, allowing for the study of non-Abelian atom optics, which naturally ties together opti- cal and magnetic effects. Remarkably, as shown in Sect. 2, even very simple laser arrangements may induce non-trivial cold-atom dynamics. As a first example of this non-trivial dynamics, we discuss in Sect. 3 a possible optical tweezer experiment including a non-Abelian flux, for which the pop- ulation transfer between internal states crucially depends on the path taken (non-Abelian Aharonov-Bohm effect). This effect resembles indeed what one would expect from scat- tering protons onto a non-Abelian flux line where the proton can be transferred into a neutron (8). The tweezer experiment discussed in Sect. 3 just involves the internal-state dynamics, without exploring the rich dynamics resulting from the in- terplay between external and internal degrees of freedom in non-Abelian gauge fields. Section 4 is devoted to the analy- sis of this interplay. In particular, we show that the dynamics of cold-atom wavepackets can be significantly affected by in- trinsically non-Abelian effects, which are crucially dependent on the initial momentum distribution of the wavepacket. We consider in particular the relevant examples of wavepacket propagation and wavepacket reflection at an atomic mirror. Finally, we conclude in Sect. 5.

•Jan 1, 2007•0 citations

Gauge fields for ultracold atoms in optical superlattices

Fabrice Gerbier, Jean Dalibard

We present a scheme that produces a strong U(1)-like gauge field on cold atoms confined in a two-dimensional square optical lattice. Our proposal relies on two essential features, a long-lived metastable excited state that exists for alkaline-earth or ytterbium atoms and an optical superlattice. As in the proposal by Jaksch and Zoller (2003 New J. Phys. 5 56), laser-assisted tunneling between adjacent sites creates an effective magnetic field. In the tight-binding approximation, atomic motion is described by the Harper Hamiltonian, with a flux across each lattice plaquette that can realistically take any value between 0 and π. We show how one can take advantage of the superlattice to ensure that each plaquette acquires the same phase, thus simulating a uniform magnetic field. We discuss the observable consequences of the artificial gauge field on non-interacting bosonic and fermionic gases. We also outline how the scheme can be generalized to non-Abelian gauge fields.

arXiv:0910.4606•New Journal of Physics•Mar 9, 2010•303 citations
We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. For Abelian gauges, such transitions occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum. Other key characteristics of the non-Abelian case include the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta.
We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a SU(2)-hopping matrix for the bosons. Using a resummed hopping expansion, we calculate the excitation spectra in the Mott insulating phases and demonstrate that the superfluid-insulator phase boundary displays a nonmonotonic dependence on the gauge-field strength. We also compute the momentum distribution of the bosons in the presence of the non-Abelian field and show that they develop peaks at nonzero momenta as the superfluid-insulator transition point is approached from the Mott side. Finally, we study the superfluid phases near the transition and discuss the induced spatial pattern of the superfluid density due to the presence of the non-Abelian gauge potential.
We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary k x k matrices. The single-particle dynamics in the case of intense U2 vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.
We calculate the time-of-flight patterns of strongly interacting bosons confined in a two-dimensional square lattice in the presence of an artificial magnetic field, using a quantum rotor model that is inherently combined with the Bogoliubov approach. We consider various geometries of the magnetic flux, which are expected to be realizable, or have already been implemented in experimental settings. The flexibility of the method allowed us to study cases where the artificial magnetic field is uniform or staggered or forms a checkerboard configuration. The effects of additional temporal modulation of the optical potential that results from application of Raman lasers driving particle transitions between lattice sites are also included. The time-of-flight patterns presented may serve as a verification of the chosen gauge in experiments, but also provide important hints on unconventional, nonzero-momentum condensates, or the possibility of observing graphenelike physics resulting from the occurrence of Dirac cones in artificial magnetic fields in systems of ultracold bosons in optical lattices. Also, we elucidate the differences between the effects of magnetic fields in solids and of artificial magnetic fields in optical lattices, which can be controlled on a much higher level, leading to effects not possible in condensed matter physics.
The dynamics of ultracold neutral atoms subject to a non-Abelian gauge field is investigated. In particular we analyze in detail a simple experimental scheme to achieve a con- stant, but non-Abelian gauge field, and discuss in the frame of this gauge field the non-Abelian Aharanov-Bohm effect. In the last part of this paper, we discuss intrinsic non-Abelian effects in the dynamics of cold atomic wavepackets. the implementation of these proposals, ultracold atoms would offer a unique testbed for the analysis of non-trivial non- Abelian effects on the quantum dynamics of multicomponent wavepackets. In this paper, we investigate the wave packet dynam- ics of a cloud of ultracold atoms in the presence of a non- Abelian gauge potential. In Sect. 2 we discuss how this un- doubtedly rather exotic scenario can be envisaged in a sam- ple of cold atoms where the internal electronic energy levels are addressed by laser fields with a nontrivial spatial phase and intensity distribution. This setup opens up a number of new scenarios for ultracold gases, allowing for the study of non-Abelian atom optics, which naturally ties together opti- cal and magnetic effects. Remarkably, as shown in Sect. 2, even very simple laser arrangements may induce non-trivial cold-atom dynamics. As a first example of this non-trivial dynamics, we discuss in Sect. 3 a possible optical tweezer experiment including a non-Abelian flux, for which the pop- ulation transfer between internal states crucially depends on the path taken (non-Abelian Aharonov-Bohm effect). This effect resembles indeed what one would expect from scat- tering protons onto a non-Abelian flux line where the proton can be transferred into a neutron (8). The tweezer experiment discussed in Sect. 3 just involves the internal-state dynamics, without exploring the rich dynamics resulting from the in- terplay between external and internal degrees of freedom in non-Abelian gauge fields. Section 4 is devoted to the analy- sis of this interplay. In particular, we show that the dynamics of cold-atom wavepackets can be significantly affected by in- trinsically non-Abelian effects, which are crucially dependent on the initial momentum distribution of the wavepacket. We consider in particular the relevant examples of wavepacket propagation and wavepacket reflection at an atomic mirror. Finally, we conclude in Sect. 5.
We present a scheme that produces a strong U(1)-like gauge field on cold atoms confined in a two-dimensional square optical lattice. Our proposal relies on two essential features, a long-lived metastable excited state that exists for alkaline-earth or ytterbium atoms and an optical superlattice. As in the proposal by Jaksch and Zoller (2003 New J. Phys. 5 56), laser-assisted tunneling between adjacent sites creates an effective magnetic field. In the tight-binding approximation, atomic motion is described by the Harper Hamiltonian, with a flux across each lattice plaquette that can realistically take any value between 0 and π. We show how one can take advantage of the superlattice to ensure that each plaquette acquires the same phase, thus simulating a uniform magnetic field. We discuss the observable consequences of the artificial gauge field on non-interacting bosonic and fermionic gases. We also outline how the scheme can be generalized to non-Abelian gauge fields.