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Banger P, Kumar RK, Roy A, Gautam S. Effective potentials in a rotating spin-orbit-coupled spin-1 spinor condensate. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:045401. [PMID: 36541536 DOI: 10.1088/1361-648x/aca7a9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Accepted: 11/30/2022] [Indexed: 06/17/2023]
Abstract
We theoretically study the stationary-state vortex lattice configurations of rotating spin-orbit (SO)- and coherently-coupled spin-1 Bose-Einstein condensates (BECs) trapped in quasi-two-dimensional harmonic potentials. The combined effects of rotation, SO and coherent couplings are analyzed systematically from the single-particle perspective. Through the single-particle Hamiltonian, which is exactly solvable for one-dimensional coupling, we illustrate that a boson in these rotating SO- and coherently-coupled condensates are subjected to effective toroidal, symmetric double-well, or asymmetric double-well potentials under specific coupling and rotation strengths. In the presence of mean-field interactions, using the coupled Gross-Pitaevskii formalism at moderate to high rotation frequencies, the analytically obtained effective potential minima and the numerically obtained coarse-grained density maxima position are in excellent agreement. On rapid rotation, we further find that the spin-expectation per particle of an antiferromagnetic spin-1 BEC approaches unity indicating a similarity in the response with ferromagnetic SO-coupled condensates.
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Affiliation(s)
- Paramjeet Banger
- Department of Physics, Indian Institute of Technology Ropar, Rupnagar 140001, Punjab, India
| | - R Kishor Kumar
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9054, New Zealand
| | - Arko Roy
- School of Physical Sciences, Indian Institute of Technology Mandi, Mandi 175075 (H.P.), India
| | - Sandeep Gautam
- Department of Physics, Indian Institute of Technology Ropar, Rupnagar 140001, Punjab, India
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2
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Spin-orbit coupling in buckled monolayer nitrogene. Sci Rep 2022; 12:3201. [PMID: 35217687 PMCID: PMC8881460 DOI: 10.1038/s41598-022-07215-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Accepted: 02/07/2022] [Indexed: 11/25/2022] Open
Abstract
Buckled monolayer nitrogene has been recently predicted to be stable above the room temperature. The low atomic number of nitrogen atom suggests, that spin–orbit coupling in nitrogene is weak, similar to graphene or silicene. We employ first principles calculations and perform a systematic study of the intrinsic and extrinsic spin–orbit coupling in this material. We calculate the spin mixing parameter \documentclass[12pt]{minimal}
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Adhikari SK. Symbiotic solitons in quasi-one- and quasi-two-dimensional spin-1 condensates. Phys Rev E 2021; 104:024207. [PMID: 34525649 DOI: 10.1103/physreve.104.024207] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2021] [Accepted: 07/26/2021] [Indexed: 11/07/2022]
Abstract
We study the formation of spin-1 symbiotic spinor solitons in a quasi-one- (quasi-1D) and quasi-two-dimensional (quasi-2D) hyperfine spin F=1 ferromagnetic Bose-Einstein condensate (BEC). The symbiotic solitons necessarily have a repulsive intraspecies interaction and are bound due to an attractive interspecies interaction. Due to a collapse instability in higher dimensions, an additional spin-orbit coupling is necessary to stabilize a quasi-2D symbiotic spinor soliton. Although a quasi-1D symbiotic soliton has a simple Gaussian-type density distribution, novel spatial periodic structure in density is found in quasi-2D symbiotic SO-coupled spinor solitons. For a weak SO coupling, the quasi-2D solitons are of the (-1,0,+1) or (+1,0,-1) type with intrinsic vorticity and multiring structure, for Rashba or Dresselhaus SO coupling, respectively, where the numbers in the parentheses are angular momenta projections in spin components F_{z}=+1,0,-1, respectively. For a strong SO coupling, stripe and superlattice solitons, respectively, with a stripe and square-lattice modulation in density, are found in addition to the multiring solitons. The stationary states were obtained by imaginary-time propagation of a mean-field model; dynamical stability of the solitons was established by real-time propagation over a long period of time. The possibility of the creation of such a soliton by removing the trap of a confined spin-1 BEC in a laboratory is also demonstrated.
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Affiliation(s)
- S K Adhikari
- Instituto de Física Teórica, Universidade Estadual Paulista - UNESP, 01.140-070 São Paulo, São Paulo, Brazil
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Adhikari SK. Spatial order in a two-dimensional spin-orbit-coupled spin-1/2 condensate: superlattice, multi-ring and stripe formation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:425402. [PMID: 34289454 DOI: 10.1088/1361-648x/ac16ab] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Accepted: 07/21/2021] [Indexed: 06/13/2023]
Abstract
We demonstrate the formation of stable spatially-ordered states in auniformand alsotrappedquasi-two-dimensional (quasi-2D) Rashba or Dresselhaus spin-orbit (SO) coupled pseudo spin-1/2 Bose-Einstein condensate using the mean-field Gross-Pitaevskii equation. For weak SO coupling, one can have a circularly-symmetric (0, +1)- or (0, -1)-type multi-ring state with intrinsic vorticity, for Rashba or Dresselhaus SO coupling, respectively, where the numbers in the parentheses denote the net angular momentum projection in the two components, in addition to a circularly-asymmetric degenerate state with zero net angular momentum projection. For intermediate SO couplings, in addition to the above two types, one can also have states with stripe pattern in component densities with no periodic modulation in total density. The stripe state continues to exist for large SO coupling. In addition, a new spatially-periodic state appears in the uniform system: asuperlatticestate, possessing some properties of asupersolid, with a square-lattice pattern in component densities and also in total density. In a trapped system the superlattice state is slightly different with multi-ring pattern in component density and a square-lattice pattern in total density. For an equal mixture of Rashba and Dresselhaus SO couplings, in both uniform and trapped systems, only stripe states are found for all strengths of SO couplings. In a uniform system all these states are quasi-2D solitonic states.
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Affiliation(s)
- S K Adhikari
- Instituto de Física Teórica, Universidade Estadual Paulista-UNESP, 01.140-070 São Paulo, São Paulo, Brazil
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5
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Adhikari SK. Supersolid-like states in a two-dimensional trapped spin-orbit-coupled spin-1 condensate. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:265402. [PMID: 33882472 DOI: 10.1088/1361-648x/abfa5f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2021] [Accepted: 04/21/2021] [Indexed: 06/12/2023]
Abstract
We study supersolid-like states in a quasi-two-dimensional trapped Rashba and Dresselhaus spin-orbit (SO) coupled spin-1 condensate. For small strengths of SO couplingγ(γ⪅ 0.75), in the ferromagnetic phase, circularly-symmetric (0, ±1, ±2)- and (∓1, 0, ±1)-type states are formed where the numbers in the parentheses denote the angular momentum of the vortex at the center of the components and where the upper (lower) sign correspond to Rashba (Dresselhaus) coupling; in the antiferromagnetic phase, only (∓1, 0, ±1)-type states are formed. For large strengths of SO coupling, supersolid-like superlattice and superstripe states are formed in the ferromagnetic phase. In the antiferromagnetic phase, for large strengths of SO coupling, supersolid-like superstripe and multi-ring states are formed. For an equal mixture of Rashba and Dresselhaus SO couplings, only a superstripe state is found. All these states are found to be dynamically stable and hence accessible in an experiment and will enhance the fundamental understanding of crystallization onto radially periodic states in solids.
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Affiliation(s)
- S K Adhikari
- Instituto de Física Teórica, Universidade Estadual Paulista-UNESP, 01.140-070 São Paulo, São Paulo, Brazil
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6
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Otlaadisa P, Tabi CB, Kofané TC. Modulation instability in helicoidal spin-orbit coupled open Bose-Einstein condensates. Phys Rev E 2021; 103:052206. [PMID: 34134292 DOI: 10.1103/physreve.103.052206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2020] [Accepted: 04/08/2021] [Indexed: 06/12/2023]
Abstract
We introduce a vector form of the cubic complex Ginzburg-Landau equation describing the dynamics of dissipative solitons in the two-component helicoidal spin-orbit coupled open Bose-Einstein condensates (BECs), where the addition of dissipative interactions is done through coupled rate equations. Furthermore, the standard linear stability analysis is used to investigate theoretically the stability of continuous-wave (cw) solutions and to obtain an expression for the modulational instability gain spectrum. Using direct simulations of the Fourier space, we numerically investigate the dynamics of the modulational instability in the presence of helicoidal spin-orbit coupling. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the threshold for amplitude perturbations.
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Affiliation(s)
- Phelo Otlaadisa
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
| | - Conrad Bertrand Tabi
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
| | - Timoléon Crépin Kofané
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
- Centre d'Excellence Africain en Technologies de l'Information et de la Communication, University of Yaoundé I, Yaoundé, Cameroon
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Adhikari SK. Vortex-lattice formation in a spin-orbit coupled rotating spin-1 condensate. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:065404. [PMID: 33120369 DOI: 10.1088/1361-648x/abc5d7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We study the vortex-lattice formation in a rotating Rashba spin-orbit (SO) coupled quasi-two-dimensional (quasi-2D) hyper-fine spin-1 spinor Bose-Einstein condensate (BEC) in the x-y plane using a numerical solution of the underlying mean-field Gross-Pitaevskii equation. In this case, the non-rotating Rashba SO-coupled spinor BEC can have topological excitation in the form of vortices of different angular momenta in the three components, e.g. the (0, +1, +2)- and (-1, 0, +1)-type states in ferromagnetic and anti-ferromagnetic spinor BEC: the numbers in the parenthesis denote the intrinsic angular momentum of the vortex states of the three components with the negative sign denoting an anti-vortex. The presence of these states with intrinsic vorticity breaks the symmetry between rotation with vorticity along the z and -z axes and thus generates a rich variety of vortex-lattice and anti-vortex-lattice states in a rotating quasi-2D spin-1 spinor ferromagnetic and anti-ferromagnetic BEC, not possible in a scalar BEC. For weak SO coupling, we find two types of symmetries of these states - hexagonal and 'square'. The hexagonal (square) symmetry state has vortices arranged in closed concentric orbits with a maximum of 6, 12, 18… (8, 12, 16…) vortices in successive orbits. Of these two symmetries, the square vortex-lattice state is found to have the smaller energy.
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Affiliation(s)
- S K Adhikari
- Instituto de Física Teórica, Universidade Estadual Paulista-UNESP, 01.140-070 São Paulo, São Paulo, Brazil
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8
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Chen L, Zhang Y, Pu H. Spin-Nematic Vortex States in Cold Atoms. PHYSICAL REVIEW LETTERS 2020; 125:195303. [PMID: 33216592 DOI: 10.1103/physrevlett.125.195303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2019] [Accepted: 10/09/2020] [Indexed: 06/11/2023]
Abstract
The (pseudo)spin degrees of freedom greatly enriches the physics of cold atoms. This is particularly so for systems with high spins (i.e., spin quantum number larger than 1/2). For example, one can construct not only the rank-1 spin vector, but also the rank-2 spin tensor in high spin systems. Here we propose a simple scheme to couple the spin tensor and the center-of-mass orbital angular momentum in a spin-1 cold atom system and show that this leads to a new quantum phase of the matter: the spin-nematic vortex state that features vorticity in an SU(2) spin-nematic tensor subspace. Under proper conditions, such states are characterized by quantized topological numbers. Our work opens up new avenues of research in topological quantum matter with high spins.
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Affiliation(s)
- Li Chen
- Institute of Theoretical Physics and State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Yunbo Zhang
- Key Laboratory of Optical Field Manipulation of Zhejiang Province and Physics Department of Zhejiang Sci-Tech University, Hangzhou 310018, China
| | - Han Pu
- Department of Physics and Astronomy, and Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
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9
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Lao D, Raman C, de Melo CARS. Nematic-Orbit Coupling and Nematic Density Waves in Spin-1 Condensates. PHYSICAL REVIEW LETTERS 2020; 124:173203. [PMID: 32412270 DOI: 10.1103/physrevlett.124.173203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Revised: 03/18/2020] [Accepted: 04/13/2020] [Indexed: 06/11/2023]
Abstract
We propose the creation of artificial nematic-orbit coupling in spin-1 Bose-Einstein condensates, in analogy with spin-orbit coupling. Using a suitably designed microwave chip, the quadratic Zeeman shift, normally uniform in space, can be made to be spatiotemporally varying, leading to a coupling between spatial and nematic degrees of freedom. A phase diagram is explored where three quantum phases with the nematic order emerge: easy axis, easy plane with single-well structure, and easy plane with double-well structure in momentum space. By including spin-dependent and spin-independent interactions, we also obtain the low energy excitation spectra in these three phases. Last, we show that the nematic-orbit coupling leads to a periodic nematic density modulation in relation to the period λ_{T} of the cosinusoidal quadratic Zeeman term. Our results point to the rich possibilities for manipulation of tensorial degrees of freedom in ultracold gases without requiring Raman lasers, and therefore, obviating light-scattering induced heating.
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Affiliation(s)
- Di Lao
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Chandra Raman
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - C A R Sá de Melo
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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Fritsch AR, Lu M, Reid GH, Piñeiro AM, Spielman IB. Creating solitons with controllable and near-zero velocity in Bose-Einstein condensates. PHYSICAL REVIEW. A 2020; 101:10.1103/PhysRevA.101.053629. [PMID: 34136731 PMCID: PMC8204714 DOI: 10.1103/physreva.101.053629] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Established techniques for deterministically creating dark solitons in repulsively interacting atomic Bose-Einstein condensates (BECs) can only access a narrow range of soliton velocities. Because velocity affects the stability of individual solitons and the properties of soliton-soliton interactions, this technical limitation has hindered experimental progress. Here we create dark solitons in highly anisotropic cigar-shaped BECs with arbitrary position and velocity by simultaneously engineering the amplitude and phase of the condensate wave function, improving upon previous techniques which explicitly manipulated only the condensate phase. The single dark soliton solution present in true one-dimensional (1D) systems corresponds to the kink soliton in anisotropic three-dimensional systems and is joined by a host of additional dark solitons, including vortex ring and solitonic vortex solutions. We readily create dark solitons with speeds from zero to half the sound speed. The observed soliton oscillation frequency suggests that we imprinted solitonic vortices, which for our cigar-shaped system are the only stable solitons expected for these velocities. Our numerical simulations of 1D BECs show this technique to be equally effective for creating kink solitons when they are stable. We demonstrate the utility of this technique by deterministically colliding dark solitons with domain walls in two-component spinor BECs.
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Wang JG, Yang SJ. Stripe and supersolid phases of spin-orbit coupled spin-2 Bose-Einstein condensates in an optical lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:035401. [PMID: 31539895 DOI: 10.1088/1361-648x/ab468d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study the ground-state phases of two-dimensional spin-orbit coupled spin-2 Bose-Einstein condensates in a one-dimensional spin-dependent optical lattice. Due to the competition among optical lattice, spin-orbit coupling and spin-exchange interaction, the exotic ground-state phases are found, i.e. three types of the stripe phases and three types of the supersolid phases. The spin-exchange interaction can adjust the direction of the stripe in the stripe phase and generate various vortex lattice structures in the supersolid phase, which shows that the spin-exchange interaction plays an important role in the formation of the stripe and supersolid phases of spin-orbit coupled spin-2 Bose-Einstein condensates in an optical lattice.
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Affiliation(s)
- Ji-Guo Wang
- Department of Mathematics and Physics, Shijiazhuang TieDao University, Shijiazhuang 050043, People's Republic of China. Institute of Applied Physics, Shijiazhuang TieDao University, Shijiazhuang 050043, People's Republic of China
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Mossman ME, Hou J, Luo XW, Zhang C, Engels P. Experimental realization of a non-magnetic one-way spin switch. Nat Commun 2019; 10:3381. [PMID: 31358742 PMCID: PMC6662681 DOI: 10.1038/s41467-019-11210-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2019] [Accepted: 06/25/2019] [Indexed: 11/09/2022] Open
Abstract
Controlling magnetism through non-magnetic means is highly desirable for future electronic devices, as such means typically have ultra-low power requirements and can provide coherent control. In recent years, great experimental progress has been made in the field of electrical manipulation of magnetism in numerous material systems. These studies generally do not consider the directionality of the applied non-magnetic potentials and/or magnetism switching. Here, we theoretically conceive and experimentally demonstrate a non-magnetic one-way spin switch device using a spin-orbit coupled Bose-Einstein condensate subjected to a moving spin-independent repulsive dipole potential. The physical foundation of this unidirectional device is based on the breakdown of Galilean invariance in the presence of spin-orbit coupling. Such a one-way spin switch opens an avenue for designing quantum devices with unique functionalities and may facilitate further experimental investigations of other one-way spintronic and atomtronic devices.
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Affiliation(s)
- Maren E Mossman
- Department of Physics and Astronomy, Washington State University, Pullman, WA, 99164, USA
| | - Junpeng Hou
- Department of Physics, The University of Texas at Dallas, Dallas, TX, 75080, USA
| | - Xi-Wang Luo
- Department of Physics, The University of Texas at Dallas, Dallas, TX, 75080, USA
| | - Chuanwei Zhang
- Department of Physics, The University of Texas at Dallas, Dallas, TX, 75080, USA.
| | - Peter Engels
- Department of Physics and Astronomy, Washington State University, Pullman, WA, 99164, USA.
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Zhang S, He C, Hajiyev E, Ren Z, Song B, Jo GB. Collective dipole oscillations of a spin-orbit coupled Fermi gas. Sci Rep 2018; 8:18005. [PMID: 30573794 PMCID: PMC6301991 DOI: 10.1038/s41598-018-36337-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Accepted: 11/19/2018] [Indexed: 11/30/2022] Open
Abstract
The collective dipole mode is induced and measured in a spin-orbit (SO) coupled degenerate Fermi gas of 173Yb atoms. Using a differential optical Stark shift, we split the degeneracy of three hyperfine states in the ground manifold, and independently couple consecutive spin states with the equal Raman transitions. A relatively long-lived spin-orbit-coupled Fermi gas, readily being realized with a narrow optical transition, allows to explore a single-minimum dispersion where three minima of spin-1 system merge into and to monitor collective dipole modes of fermions in the strong coupling regime. The measured oscillation frequency of the dipole mode is compared with the semi-classical calculation in the single-particle regime. Our work should pave the way towards the characterization of spin-orbit-coupled fermions with large spin s >\documentclass[12pt]{minimal}
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Affiliation(s)
- Shanchao Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Chengdong He
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Elnur Hajiyev
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Zejian Ren
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Bo Song
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Gyu-Boong Jo
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China.
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König EJ, Pixley JH. Quantum Field Theory of Nematic Transitions in Spin-Orbit-Coupled Spin-1 Polar Bosons. PHYSICAL REVIEW LETTERS 2018; 121:083402. [PMID: 30192619 DOI: 10.1103/physrevlett.121.083402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2018] [Indexed: 06/08/2023]
Abstract
We theoretically study an ultracold gas of spin-1 polar bosons in a one-dimensional continuum, which are subject to linear and quadratic Zeeman fields and a Raman induced spin orbit coupling. Concentrating on the regime in which the background fields can be treated perturbatively, we analytically solve the model in its low-energy sector; i.e., we characterize the relevant phases and the quantum phase transitions between them. Depending on the sign of the effective quadratic Zeeman field ε, two superfluid phases with distinct nematic order appear. In addition, we uncover a spin-disordered superfluid phase at strong coupling. We employ a combination of renormalization group calculations and duality transformations to access the nature of the phase transitions. At ε=0, a line of spin-charge separated pairs of Luttinger liquids divides the two nematic phases, and the transition to the spin-disordered state at strong coupling is of the Berezinskii-Kosterlitz-Thouless type. In contrast, at ε≠0, the quantum critical theory separating nematic and strong coupling spin-disordered phases contains a Luttinger liquid in the charge sector that is coupled to a Majorana fermion in the spin sector (i.e., the critical theory at finite ε maps to a quantum critical Ising model that is coupled to the charge Luttinger liquid). Because of an emergent Lorentz symmetry, both have the same logarithmically diverging velocity. We discuss the experimental signatures of our findings that are relevant to ongoing experiments in ultracold atomic gases of ^{23}Na.
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Affiliation(s)
- E J König
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
| | - J H Pixley
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
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Wang JG, Yang SJ. Ground-state phases of spin-orbit coupled spin-1 Bose-Einstein condensate in a plane quadrupole field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:295404. [PMID: 29897338 DOI: 10.1088/1361-648x/aacc42] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study the ground-state phases of two-dimensional spin-orbit coupled spin-1 Bose-Einstein condensate loaded in a plane quadrupole field. In the absence of rotation, for the fixed spin-orbit coupling strength, the ordinary stripe phase is found when the strength of the magnetic field gradient is small. As the strength of magnetic field gradient enhances, the system realizes the phases with three layer vortices along the radial direction. The number of vortices in the second layer is successively increased and the vortices in the outermost layer disappear when the strength of magnetic field gradient surpass the critical value. For the large strength of magnetic field gradient, the system only has the inner layer vortices. The magnetic field inhibits the region of vortices. For the fixed magnetic field gradient strength, the vortices of the system elongate along the radial direction and form a series of vortex lines, the number of the vortex line increases as the strength of spin-orbit coupling enhances. By adding the rotation, for the fixed strengths of spin-orbit coupling and magnetic field gradient, the number of second layer vortices also successively increases as the rotational frequency increases. The number of vortices in the certain layer of the ground-state density can be regularly changed under the effects of the magnetic field and spin-orbit coupling.
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Affiliation(s)
- Ji-Guo Wang
- Department of Mathematics and Physics, Shijiazhuang TieDao University, Shijiazhuang 050043, People's Republic of China. Institute of Applied Physics, Shijiazhuang TieDao University, Shijiazhuang 050043, People's Republic of China
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Hu H, Hou J, Zhang F, Zhang C. Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings. PHYSICAL REVIEW LETTERS 2018; 120:240401. [PMID: 29956976 DOI: 10.1103/physrevlett.120.240401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2017] [Indexed: 06/08/2023]
Abstract
The recent discovery of triply degenerate points (TDPs) in topological materials has opened a new perspective toward the realization of novel quasiparticles without counterparts in quantum field theory. The emergence of such protected nodes is often attributed to spin-vector-momentum couplings. We show that the interplay between spin-tensor- and spin-vector-momentum couplings can induce three types of TDPs, classified by different monopole charges (C=±2, ±1, 0). A Zeeman field can lift them into Weyl points with distinct numbers and charges. Different TDPs of the same type are connected by intriguing Fermi arcs at surfaces, and transitions between different types are accompanied by level crossings along high-symmetry lines. We further propose an experimental scheme to realize such TDPs in cold-atom optical lattices. Our results provide a framework for studying spin-tensor-momentum coupling-induced TDPs and other exotic quasiparticles.
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Affiliation(s)
- Haiping Hu
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Junpeng Hou
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Fan Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Chuanwei Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
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Metastability and avalanche dynamics in strongly correlated gases with long-range interactions. Proc Natl Acad Sci U S A 2018. [PMID: 29519875 DOI: 10.1073/pnas.1720415115] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We experimentally study the stability of a bosonic Mott insulator against the formation of a density wave induced by long-range interactions and characterize the intrinsic dynamics between these two states. The Mott insulator is created in a quantum degenerate gas of 87-Rubidium atoms, trapped in a 3D optical lattice. The gas is located inside and globally coupled to an optical cavity. This causes interactions of global range, mediated by photons dispersively scattered between a transverse lattice and the cavity. The scattering comes with an atomic density modulation, which is measured by the photon flux leaking from the cavity. We initialize the system in a Mott-insulating state and then rapidly increase the global coupling strength. We observe that the system falls into either of two distinct final states. One is characterized by a low photon flux, signaling a Mott insulator, and the other is characterized by a high photon flux, which we associate with a density wave. Ramping the global coupling slowly, we observe a hysteresis loop between the two states-a further signature of metastability. A comparison with a theoretical model confirms that the metastability originates in the competition between short- and global-range interactions. From the increasing photon flux monitored during the switching process, we find that several thousand atoms tunnel to a neighboring site on the timescale of the single-particle dynamics. We argue that a density modulation, initially forming in the compressible surface of the trapped gas, triggers an avalanche tunneling process in the Mott-insulating region.
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Luo XW, Sun K, Zhang C. Spin-Tensor-Momentum-Coupled Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2017; 119:193001. [PMID: 29219479 DOI: 10.1103/physrevlett.119.193001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2017] [Indexed: 06/07/2023]
Abstract
The recent experimental realization of spin-orbit coupling for ultracold atomic gases provides a powerful platform for exploring many interesting quantum phenomena. In these studies, spin represents the spin vector (spin 1/2 or spin 1) and orbit represents the linear momentum. Here we propose a scheme to realize a new type of spin-tensor-momentum coupling (STMC) in spin-1 ultracold atomic gases. We study the ground state properties of interacting Bose-Einstein condensates with STMC and find interesting new types of stripe superfluid phases and multicritical points for phase transitions. Furthermore, STMC makes it possible to study quantum states with dynamical stripe orders that display density modulation with a long tunable period and high visibility, paving the way for the direct experimental observation of a new dynamical supersolidlike state. Our scheme for generating STMC can be generalized to other systems and may open the door for exploring novel quantum physics and device applications.
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Affiliation(s)
- Xi-Wang Luo
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
| | - Kuei Sun
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
| | - Chuanwei Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
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Pixley JH, Cole WS, Spielman IB, Rizzi M, Sarma SD. Strong coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: odd integer Mott lobes and helical magnetic phases. PHYSICAL REVIEW. A 2017; 96:10.1103/physreva.96.043622. [PMID: 38495960 PMCID: PMC10941298 DOI: 10.1103/physreva.96.043622] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/19/2024]
Abstract
We study the odd integer filled Mott phases of a spin-1 Bose-Hubbard chain and determine their fate in the presence of a Raman induced spin-orbit coupling which has been achieved in ultracold atomic gases; this system is described by a quantum spin-1 chain with a spiral magnetic field. The spiral magnetic field initially induces helical order with either ferromagnetic or dimer order parameters, giving rise to a spiral paramagnet at large field. The spiral ferromagnet-to-paramagnet phase transition is in a novel universality class, with critical exponents associated with the divergence of the correlation length ν ≈ 2 / 3 and the order parameter susceptibility γ ≈ 1 / 2 . We solve the effective spin model exactly using the density matrix renormalization group, and compare with both a large-S classical solution and a phenomenological Landau theory. We discuss how these exotic bosonic magnetic phases can be produced and probed in ultracold atomic experiments in optical lattices.
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Affiliation(s)
- J H Pixley
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742-4111 USA
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, NJ 08854 USA
| | - William S Cole
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742-4111 USA
| | - I B Spielman
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, Maryland, 20899, USA
| | - Matteo Rizzi
- Universität Mainz, Institut für Physik, Staudingerweg 7, D-55099 Mainz, Germany
| | - S Das Sarma
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742-4111 USA
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Kunz PD, Meyer DH, Fatemi FK. Twists in nonlinear magneto-optic rotation with cold atoms. OPTICS EXPRESS 2017; 25:16392-16399. [PMID: 28789143 DOI: 10.1364/oe.25.016392] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Accepted: 06/25/2017] [Indexed: 06/07/2023]
Abstract
We observe a narrow secondary dispersive feature nested within conventional nonlinear magneto-optical rotation (NMOR) signals obtained with a laser-cooled rubidium vapor. A similar feature has been previously named a "twist" by Budker et. al., in the context of warm vapor optical magnetometry [Phys. Rev. A. 81, 5788-5791 (1998)], and was ascribed to simultaneous optical pumping through multiple nearby hyperfine levels. In this work the twist is observed in a cold atom vapor, where the hyperfine levels are individually addressable, and thus is due to a different mechanism. We experimentally and numerically characterize this twist in terms of magnetic field strength, polarization, and optical intensity and find good agreement between our data and numerical models. We find that the twist width is proportional to the magnetic field in the transverse direction, and therefore two independent directions of the magnetic field can be measured simultaneously. This technique is useful as a simple and rapid in-situ method for nulling background magnetic fields.
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Valdés-Curiel A, Trypogeorgos D, Marshall EE, Spielman IB. Fourier transform spectroscopy of a spin-orbit coupled Bose gas. NEW JOURNAL OF PHYSICS 2017; 19:033025. [PMID: 29731685 PMCID: PMC5935008 DOI: 10.1088/1367-2630/aa6279] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We describe a Fourier transform spectroscopy technique for directly measuring band structures, and apply it to a spin-1 spin-orbit coupled Bose-Einstein condensate. In our technique, we suddenly change the Hamiltonian of the system by adding a spin-orbit coupling interaction and measure populations in different spin states during the subsequent unitary evolution. We then reconstruct the spin and momentum resolved spectrum from the peak frequencies of the Fourier transformed populations. In addition, by periodically modulating the Hamiltonian, we tune the spin-orbit coupling strength and use our spectroscopy technique to probe the resulting dispersion relation. The frequency resolution of our method is limited only by the coherent evolution timescale of the Hamiltonian and can otherwise be applied to any system, for example, to measure the band structure of atoms in optical lattice potentials.
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Affiliation(s)
| | | | | | - IB Spielman
- Author to whom any correspondence should be addressed.
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Martone GI, Pepe FV, Facchi P, Pascazio S, Stringari S. Tricriticalities and Quantum Phases in Spin-Orbit-Coupled Spin-1 Bose Gases. PHYSICAL REVIEW LETTERS 2016; 117:125301. [PMID: 27689283 DOI: 10.1103/physrevlett.117.125301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2015] [Indexed: 06/06/2023]
Abstract
We study the zero-temperature phase diagram of a spin-orbit-coupled Bose-Einstein condensate of spin 1, with equally weighted Rashba and Dresselhaus couplings. Depending on the antiferromagnetic or ferromagnetic nature of the interactions, we find three kinds of striped phases with qualitatively different behaviors in the modulations of the density profiles. Phase transitions to the zero-momentum and the plane-wave phases can be induced in experiments by independently varying the Raman coupling strength and the quadratic Zeeman field. The properties of these transitions are investigated in detail, and the emergence of tricritical points, which are the direct consequence of the spin-dependent interactions, is explicitly discussed.
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Affiliation(s)
- Giovanni I Martone
- Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Bari, I-70126 Bari, Italy
| | - Francesco V Pepe
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Bari, I-70126 Bari, Italy
- Museo Storico della Fisica e Centro Studi e Ricerche "Enrico Fermi", I-00184 Roma, Italy
| | - Paolo Facchi
- Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Bari, I-70126 Bari, Italy
| | - Saverio Pascazio
- Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Bari, I-70126 Bari, Italy
| | - Sandro Stringari
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, I-38123 Povo, Italy
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