Theory of spin-2 Bose-Einstein condensates: Spin correlations, magnetic response, and excitation spectra

Ueda, Masahito; Koashi, Masato

doi:10.1103/physreva.65.063602

Cited by 159 publications

(237 citation statements)

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“…In addition evidence of spin dynamics was demonstrated in optically trapped 87 Rb in the F=1 state [14]. There is current interest in extending the systems under investigation to F=2 spinor condensates [15,16,17,18,19,20], which add significant new physics. F=2 spinor condensates offer richer dynamics, an additional magnetic phase, the so-called cyclic phase [16,18], as well as intrinsic connections to d-wave superconductors [21].…”

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Dynamics ofF=2Spinor Bose-Einstein Condensates

et al. 2004

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We experimentally investigate and analyze the rich dynamics in F=2 spinor Bose-Einstein condensates of 87 Rb. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is observed. In particular we measure conversion rates in the range of 10 −12 cm 3 s −1 for spin changing collisions within the F=2 manifold and spin-dependent loss rates in the range of 10 −13 cm 3 s −1 for hyperfine-changing collisions. From our data we observe a polar behavior in the F=2 ground state of 87 Rb, while we measure the F=1 ground state to be ferromagnetic. Furthermore we see a magnetization for condensates prepared with non-zero total spin.PACS numbers: 03.75. Mn, 34.50.Pi, 03.75.Hh The investigation of atomic spin systems is central for the understanding of magnetism and a highly active area of research e.g. with respect to magnetic nanosystems, spintronics and magnetic interactions in high T c superconductors. In addition entangled spin systems in atomic quantum gases show intriguing prospects for quantum optics and quantum computation [1,2,3,4,5]. Bose-Einstein condensates (BEC) of ultra-cold atoms offer new regimes for studies of collective spin phenomena [6,7,8,9,10,11,12,13]. BECs with spin degree of freedom are special in the sense that their order parameter is a vector in contrast to the "common" BEC where it is a scalar. Recent extensive studies have been made in optically trapped 23 Na in the F=1 state [10,11,12,13]. In addition evidence of spin dynamics was demonstrated in optically trapped 87 Rb in the F=1 state [14]. There is current interest in extending the systems under investigation to F=2 spinor condensates [15,16,17,18,19,20], which add significant new physics. F=2 spinor condensates offer richer dynamics, an additional magnetic phase, the so-called cyclic phase [16,18], as well as intrinsic connections to d-wave superconductors [21].In this letter we present first studies of optically trapped 87 Rb F=2 spinor condensates. We measure rates for spin changing collisions for different channels within the F=2 manifold and discuss the steady state for various initial conditions. Additionally we observe and discuss the thermalization of dynamically populated m F condensates. We also present measurements of spin-dependent hyperfine decay rates of the F=2 state in 87 Rb, as a key to further understanding the intensively studied collisional properties of 87 Rb [22,23].Our experimental setup consists of a compact double MOT apparatus which produces magnetically trapped 87 Rb Bose-Einstein condensates containing 10 6 atoms in the F=2, m F = 2 state. To confine the atoms independently of their spin state they are subsequently transferred into a far detuned optical dipole trap. It is operated at 1064 nm generating trapping frequencies of typically 2π × 891 Hz vertically, 2π × 155 Hz horizontally and 2π × 21.1 Hz along the beam direction. After transfer we further cool the ensemble for 500 ms by selective parametric excitation [24] resulting in ...

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Dynamics ofF=2Spinor Bose-Einstein Condensates

et al. 2004

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“…When the Zeeman shifts are small, the spin-2 BEC exhibits three distinct, interaction-dependent groundstate phases [20,41,42]. These may be character- T , representing the UN and BN phases, respectively.…”

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“…These are energetically degenerate for p = q = 0 [18,19]. They may be distinguished by the amplitude of spin-singlet trio formation [41] …”

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Core Structure and Non-Abelian Reconnection of Defects in a Biaxial Nematic Spin-2 Bose-Einstein Condensate

Borgh

Ruostekoski

2016

Phys. Rev. Lett.

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We calculate the energetic structure of defect cores and propose controlled methods to imprint a nontrivially entangled vortex pair that undergoes non-Abelian vortex reconnection in a biaxial nematic spin-2 condensate. For a singular vortex, we find three superfluid cores in addition to depletion of the condensate density. These exhibit order parameter symmetries that are different from the discrete symmetry of the biaxial nematic phase, forming an interface between the defect and the bulk superfluid. We provide a detailed analysis of phase mixing in the resulting vortex cores and find an instability dependent upon the orientation of the order parameter. We further show that the spin-2 condensate is a promising system for observing spontaneous deformation of a point defect into an "Alice ring" that has so far avoided experimental detection.Topological defects and textures are ubiquitous across physical systems that seemingly have little in common [1], from liquid crystals [2] and superfluids [3] to cosmic strings [4]. They arise generically from symmetries of a ground state that is described by an order parameter [5]-a function parametrizing the set of physically distinguishable, energetically degenerate states. In the simple example of a scalar superfluid, the order parameter is the phase of the macroscopic wave function. More generally it may be a vector or tensor that is symmetric under particular transformations. In a uniaxial nematic (UN), the order parameter is cylindrically symmetric around a locally defined axis. It also exhibits a twofold discrete symmetry under reversal of the cylinder axis, which leads to half-quantum vortices (HQVs) in atomic spinor BoseEinstein condensates (BECs) [6][7][8][9] and superfluid liquid 3 He [10], and to π disclinations in liquid crystals [1,2]. In a biaxial nematic (BN), also the cylindrical symmetry is broken into the fully discrete symmetry of a rectangular brick, with dramatic consequences: the BN is the simplest order parameter that supports non-Abelian vortices that do not commute [5,11]. As a result, colliding non-Abelian vortices cannot reconnect without leaving traces of the process, but must instead form a connecting rung vortex. Noncommuting defects appear as cosmic strings in theories of the early universe [4], and have been predicted in BN liquid crystals [11].Despite long-standing experimental efforts, BN phases in liquid crystals have experimentally proved more elusive than originally anticipated [12]. In atomic systems, the topological classification and dynamics of non-Abelian vortices have theoretically been studied in the cyclic phase of spin-2 [13-16] and in spin-3 BECs [17], though it remains uncertain whether any alkali-metal atoms exhibit the corresponding ground states. Consequently, any physical system where non-Abelian defects may be reliably studied is still lacking.Spin-2 BECs exhibit-in addition to the ferromagnetic (FM) and cyclic phases-both UN and BN phases [18][19][20], which, however, are degenerate at the mean-field level. Beyond mean-fi...

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“…a boson with F z = α. In the single-mode regime, spin-two condensates are described by the Hamiltonian [48] …”

Section: Extension To Higher Spinsmentioning

confidence: 99%

Quantum rotor theory of spinor condensates in tight traps

et al. 2011

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In this work, we theoretically construct exact mappings of many-particle bosonic systems onto quantum rotor models. In particular, we analyze the rotor representation of spinor Bose-Einstein condensates. In a previous work [1] it was shown that there is an exact mapping of a spin-one condensate of fixed particle number with quadratic Zeeman interaction onto a quantum rotor model. Since the rotor model has an unbounded spectrum from above, it has many more eigenstates than the original bosonic model. Here we show that for each subset of states with fixed spin Fz, the physical rotor eigenstates are always those with lowest energy. We classify three distinct physical limits of the rotor model: the Rabi, Josephson, and Fock regimes. The last regime corresponds to a fragmented condensate and is thus not captured by the Bogoliubov theory. We next consider the semiclassical limit of the rotor problem and make connections with the quantum wave functions through use of the Husimi distribution function. Finally, we describe how to extend the analysis to higher-spin systems and derive a rotor model for the spin-two condensate. Theoretical details of the rotor mapping are also provided here.

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Theory of spin-2 Bose-Einstein condensates: Spin correlations, magnetic response, and excitation spectra

Cited by 159 publications

References 12 publications

Dynamics ofF=2Spinor Bose-Einstein Condensates

Dynamics ofF=2Spinor Bose-Einstein Condensates

Core Structure and Non-Abelian Reconnection of Defects in a Biaxial Nematic Spin-2 Bose-Einstein Condensate

Quantum rotor theory of spinor condensates in tight traps

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