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Jian Y, Qiao X, Liang JC, Yu ZF, Zhang AX, Xue JK. Stability and superfluidity of the Bose-Einstein condensate in a two-leg ladder with magnetic field. Phys Rev E 2021; 104:024212. [PMID: 34525534 DOI: 10.1103/physreve.104.024212] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Accepted: 07/27/2021] [Indexed: 11/07/2022]
Abstract
The stability and superfluidity of the Bose-Einstein condensate in two-leg ladder with magnetic field are studied. The dispersion relation and the phase diagram of the system are obtained. Three phases are revealed: the Meissner phase, the biased ladder (BL) phase, and the vortex phase. The dispersion relation and phase transition of the system strongly depend on the magnitude of atomic interaction strength, the rung-to-leg coupling ratio and the magnetic flux. Particularly, the change of the energy band structure in the phase transition region is modified significantly by the atomic interaction strength. Furthermore, based on the Bogoliubov theory, the energetic and dynamical stability of the system are invested. The stability phase diagram in the full parameter space is presented, and the dependence of superfluidity on the dispersion relation is illustrated explicitly. The atomic interaction strength can produce dynamical instability in the energetic unstable region and can expand the superfluid region. The results show that the stability of the system can be controlled by the atomic interaction strength, the rung-to-leg coupling ratio and the magnetic flux. In addition, the excitation spectrums in the Meissner phase, BL phase and vortex phase are further studied. The modulation of the excitation spectrum and the energetic stability of the system by the atomic interaction strength, the rung-to-leg coupling ratio and magnetic flux is discussed. Finally, through the numerical simulation, the dynamical instability of the system is verified by the time evolution of the Bloch wave and rung current. This provides a theoretical basis for controlling the superfluidity of the system.
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Affiliation(s)
- Yue Jian
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China.,Department of Basic Sciences, Lanzhou Institute of Technology, Lanzhou 730050, China
| | - Xin Qiao
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Jun-Cheng Liang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Zi-Fa Yu
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Ai-Xia Zhang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Ju-Kui Xue
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
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2
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Galilo B, Lee DKK, Barnett R. Topological Edge-State Manifestation of Interacting 2D Condensed Boson-Lattice Systems in a Harmonic Trap. PHYSICAL REVIEW LETTERS 2017; 119:203204. [PMID: 29219366 DOI: 10.1103/physrevlett.119.203204] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2017] [Indexed: 06/07/2023]
Abstract
In this Letter, it is shown that interactions can facilitate the emergence of topological edge states of quantum-degenerate bosonic systems in the presence of a harmonic potential. This effect is demonstrated with the concrete model of a hexagonal lattice populated by spin-one bosons under a synthetic gauge field. In fermionic or noninteracting systems, the presence of a harmonic trap can obscure the observation of edge states. For our system with weakly interacting bosons in the Thomas-Fermi regime, we can clearly see a topological band structure with a band gap traversed by edge states. We also find that the number of edge states crossing the gap is increased in the presence of a harmonic trap, and the edge modes experience an energy shift while traversing the first Brillouin zone which is related to the topological properties of the system. We find an analytical expression for the edge-state energies and our comparison with numerical computation shows excellent agreement.
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Affiliation(s)
- Bogdan Galilo
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Derek K K Lee
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Ryan Barnett
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
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Johnson TH, Yuan Y, Bao W, Clark SR, Foot C, Jaksch D. Hubbard Model for Atomic Impurities Bound by the Vortex Lattice of a Rotating Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2016; 116:240402. [PMID: 27367366 DOI: 10.1103/physrevlett.116.240402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/01/2016] [Indexed: 06/06/2023]
Abstract
We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupation-dependent parameters to capture the effects of strong impurity-impurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the Bose-Einstein condensate. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes.
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Affiliation(s)
- T H Johnson
- Centre for Quantum Technologies, National University of Singapore, 117543 Singapore
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Keble College, University of Oxford, Parks Road, Oxford OX1 3PG, United Kingdom
| | - Y Yuan
- Beijing Computational Science Research Center, Beijing 100094, China
- Department of Mathematics, National University of Singapore, 119076 Singapore
- College of Mathematics and Computer Science, Synthetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan Province 410081, China
| | - W Bao
- Department of Mathematics, National University of Singapore, 119076 Singapore
| | - S R Clark
- Keble College, University of Oxford, Parks Road, Oxford OX1 3PG, United Kingdom
- Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
| | - C Foot
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - D Jaksch
- Centre for Quantum Technologies, National University of Singapore, 117543 Singapore
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Keble College, University of Oxford, Parks Road, Oxford OX1 3PG, United Kingdom
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Galilo B, Lee DKK, Barnett R. Selective Population of Edge States in a 2D Topological Band System. PHYSICAL REVIEW LETTERS 2015; 115:245302. [PMID: 26705639 DOI: 10.1103/physrevlett.115.245302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2015] [Indexed: 06/05/2023]
Abstract
We consider a system of interacting spin-one atoms in a hexagonal lattice under the presence of a synthetic gauge field. Quenching the quadratic Zeeman field is shown to lead to a dynamical instability of the edge modes. This, in turn, leads to a spin current along the boundary of the system which grows exponentially fast in time following the quench. Tuning the magnitude of the quench can be used to selectively populate edge modes of different momenta. Implications of the intrinsic symmetries of the Hamiltonian on the dynamics are discussed. The results hold for atoms with both antiferromagnetic and ferromagnetic interactions.
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Affiliation(s)
- Bogdan Galilo
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Derek K K Lee
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Ryan Barnett
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
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El-Sherbini TM. Advances in atomic physics: Four decades of contribution of the Cairo University - Atomic Physics Group. J Adv Res 2015; 6:643-61. [PMID: 26425356 PMCID: PMC4563599 DOI: 10.1016/j.jare.2013.08.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2013] [Revised: 08/19/2013] [Accepted: 08/19/2013] [Indexed: 11/24/2022] Open
Abstract
In this review article, important developments in the field of atomic physics are highlighted and linked to research works the author was involved in himself as a leader of the Cairo University - Atomic Physics Group. Starting from the late 1960s - when the author first engaged in research - an overview is provided of the milestones in the fascinating landscape of atomic physics.
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Experimental realization of the topological Haldane model with ultracold fermions. Nature 2014; 515:237-40. [PMID: 25391960 DOI: 10.1038/nature13915] [Citation(s) in RCA: 384] [Impact Index Per Article: 38.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2014] [Accepted: 09/29/2014] [Indexed: 11/08/2022]
Abstract
The Haldane model on a honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band structure, rather than being caused by an external magnetic field. Although physical implementation has been considered unlikely, the Haldane model has provided the conceptual basis for theoretical and experimental research exploring topological insulators and superconductors. Here we report the experimental realization of the Haldane model and the characterization of its topological band structure, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The Haldane model is based on breaking both time-reversal symmetry and inversion symmetry. To break time-reversal symmetry, we introduce complex next-nearest-neighbour tunnelling terms, which we induce through circular modulation of the lattice position. To break inversion symmetry, we create an energy offset between neighbouring sites. Breaking either of these symmetries opens a gap in the band structure, which we probe using momentum-resolved interband transitions. We explore the resulting Berry curvatures, which characterize the topology of the lowest band, by applying a constant force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between the two broken symmetries gives rise to a transition between topologically distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line experimentally and quantitatively compare it to calculations using Floquet theory without free parameters. We verify that our approach, which allows us to tune the topological properties dynamically, is suitable even for interacting fermionic systems. Furthermore, we propose a direct extension to realize spin-dependent topological Hamiltonians.
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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: 179] [Impact Index Per Article: 17.9] [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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Jiménez-García K, LeBlanc LJ, Williams RA, Beeler MC, Perry AR, Spielman IB. Peierls substitution in an engineered lattice potential. PHYSICAL REVIEW LETTERS 2012; 108:225303. [PMID: 23003612 DOI: 10.1103/physrevlett.108.225303] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2012] [Indexed: 06/01/2023]
Abstract
Artificial gauge fields open the possibility to realize quantum many-body systems with ultracold atoms, by engineering Hamiltonians usually associated with electronic systems. In the presence of a periodic potential, artificial gauge fields may bring ultracold atoms closer to the quantum Hall regime. Here, we describe a one-dimensional lattice derived purely from effective Zeeman shifts resulting from a combination of Raman coupling and radio-frequency magnetic fields. In this lattice, the tunneling matrix element is generally complex. We control both the amplitude and the phase of this tunneling parameter, experimentally realizing the Peierls substitution for ultracold neutral atoms.
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Affiliation(s)
- K Jiménez-García
- Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA
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Kapit E, Ginsparg P, Mueller E. Non-Abelian braiding of lattice bosons. PHYSICAL REVIEW LETTERS 2012; 108:066802. [PMID: 22401101 DOI: 10.1103/physrevlett.108.066802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2011] [Indexed: 05/31/2023]
Abstract
We report on a numerical experiment in which we use time-dependent potentials to braid non-Abelian quasiparticles. We consider lattice bosons in a uniform magnetic field within the fractional quantum Hall regime, where ν, the ratio of particles to flux quanta, is near 1/2, 1, or 3/2. We introduce time-dependent potentials which move quasiparticle excitations around one another, explicitly simulating a braiding operation which could implement part of a gate in a quantum computation. We find that different braids do not commute for ν near 1 and 3/2, with Berry matrices, respectively, consistent with Ising and Fibonacci anyons. Near ν=1/2, the braids commute.
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Affiliation(s)
- Eliot Kapit
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA.
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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: 16] [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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Cho J, Kim MS. Two-dimensional imaging of gauge fields in optical lattices. PHYSICAL REVIEW LETTERS 2011; 107:260402. [PMID: 22243142 DOI: 10.1103/physrevlett.107.260402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2011] [Revised: 08/25/2011] [Indexed: 05/31/2023]
Abstract
We propose a scheme to generate an arbitrary Abelian vector potential for atoms trapped in a two-dimensional optical lattice. By making the optical lattice potential dependent on the atomic state, we transform the problem into that of a two-dimensional imaging. It is shown that an arbitrarily fine pattern of the gauge field in the lattice can be realized without need of diffraction-limited imaging.
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Affiliation(s)
- Jaeyoon Cho
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom
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12
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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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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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Powell S, Barnett R, Sensarma R, Das Sarma S. Interacting Hofstadter spectrum of atoms in an artificial gauge field. PHYSICAL REVIEW LETTERS 2010; 104:255303. [PMID: 20867393 DOI: 10.1103/physrevlett.104.255303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2010] [Revised: 06/01/2010] [Indexed: 05/29/2023]
Abstract
Motivated by experimental advances in the synthesis of gauge potentials for ultracold atoms, we consider the superfluid phase of interacting bosons on a square lattice in the presence of a magnetic field. We show that superfluid order implies spatial symmetry breaking, and predict clear signatures of many-body effects in time-of-flight measurements. By developing a Bogoliubov expansion based on the exact Hofstadter spectrum, we find the dispersion of the quasiparticle modes within the superfluid phase, and describe the consequences for Bragg spectroscopy measurements. The theory also provides an estimate of the critical interaction strength at the transition to the Mott insulator phase.
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Affiliation(s)
- Stephen Powell
- Joint Quantum Institute and Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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