Bose-Einstein Condensation of Magnons in Superfluid 3He

Bunkov, Yu. M.; Volovik, G. E.

doi:10.1007/s10909-007-9530-7

Cited by 84 publications

(48 citation statements)

References 32 publications

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“…These vortex arrays arise without any rotation of the trap, spontaneously breaking rotational symmetry. While much of the possible physics of quantum condensates has been examined in experiments on atomic gases, superfluid Helium and superconductors, there has recently been much interest in examples of condensates of quasiparticle excitations, such as excitons [1,2] (bound electron-hole pairs), exciton-polaritons [3,4,5] (superpositions of quantum well excitons and microcavity photons), and magnons (spin-wave excitations) both in magnetic insulating crystals [6,7] [33] and in superfluid 3 He [8,9,10]. One particular difference shown by these systems is that the quasiparticles have finite lifetimes, and as a result, they can be made to form condensates out of equilibrium, which are best understood as a steady state balance between pumping and decay, rather than true thermal equilibrium.…”

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Spontaneous Rotating Vortex Lattices in a Pumped Decaying Condensate

2008

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Injection and decay of particles in an inhomogeneous quantum condensate can significantly change its behaviour. We model trapped, pumped, decaying condensates by a complex Gross-Pitaevskii equation and analyse the density and currents in the steady state. With homogeneous pumping, rotationally symmetric solutions are unstable. Stability may be restored by a finite pumping spot. However if the pumping spot is larger than the Thomas-Fermi cloud radius, then rotationally symmetric solutions are replaced by solutions with spontaneous arrays of vortices. These vortex arrays arise without any rotation of the trap, spontaneously breaking rotational symmetry.PACS numbers: 03.75. Kk,47.37.+q,71.36.+c,71.35.Lk While much of the possible physics of quantum condensates has been examined in experiments on atomic gases, superfluid Helium and superconductors, there has recently been much interest in examples of condensates of quasiparticle excitations, such as excitons [1,2] (bound electron-hole pairs), exciton-polaritons [3,4,5] (superpositions of quantum well excitons and microcavity photons), and magnons (spin-wave excitations) both in magnetic insulating crystals [6,7] [33] and in superfluid 3 He [8,9,10]. One particular difference shown by these systems is that the quasiparticles have finite lifetimes, and as a result, they can be made to form condensates out of equilibrium, which are best understood as a steady state balance between pumping and decay, rather than true thermal equilibrium. The effects of pumping and decay in these condensates have been the subject of several recent works [5,11,12,13,14,15,16,17,18,19,20] which have shown that even when collisions can rapidly thermalise the energy distribution of a system, there may yet be noticeable effects associated with the energy scale introduced by the pumping and decay.The Gross-Pitaevskii equation (GPE) has been applied to successfully describe many features of equilibrium condensates when far in the condensed regime, including density profiles, the dynamics of vortices, hydrodynamic modes -see e.g. [21] and Refs. therein. Using a meanfield description of the condensate, e.g. [18,19,20], one can recover a complex Gross-Pitaevskii equation (cGPE), including terms representing gain, loss and an external trapping potential. This letter studies the interplay between pumping and decay and the external trapping potential in the context of the cGPE in order to illustrate some of the differences between equilibrium and nonequilibrium condensates. In the absence of trapping, this is the celebrated complex Ginzburg-Landau equation that describes a vast variety of phenomena [22] from nonlinear waves to second-order phase transitions, from superconductivity to liquid crystals and cosmic strings and binary fluids [23]. What is of interest in this letter is how pumping and decay, described in the cGPE modify behaviour compared to the regular GPE as is widely applied to spatially inhomogeneous equilibrium quantum condensates [21]. Spatial inhomogeneity, due to either engineere...

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Spontaneous Rotating Vortex Lattices in a Pumped Decaying Condensate

2008

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“…These two methods are valid for real atoms and molecules 5,6 as well as for gases of quasiparticles (QPs) such as, excitons 7 , polaritons [8][9][10] , magnons [11][12][13] and spatially confined photons 14 .…”

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Bose–Einstein condensation in an ultra-hot gas of pumped magnons

et al. 2014

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Bose-Einstein condensation of quasi-particles such as excitons, polaritons, magnons and photons is a fascinating quantum mechanical phenomenon. Unlike the Bose-Einstein condensation of real particles (like atoms), these processes do not require low temperatures, since the high densities of low-energy quasi-particles needed for the condensate to form can be produced via external pumping. Here we demonstrate that such a pumping can create remarkably high effective temperatures in a narrow spectral region of the lowest energy states in a magnon gas, resulting in strikingly unexpected transitional dynamics of BoseEinstein magnon condensate: the density of the condensate increases immediately after the external magnon flow is switched off and initially decreases if it is switched on again. This behaviour finds explanation in a nonlinear 'evaporative supercooling' mechanism that couples the low-energy magnons overheated by pumping with all the other thermal magnons, removing the excess heat, and allowing Bose-Einstein condensate formation.

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“…• pulse, which will be discussed elsewhere, is in favor of the identification of the mode II with the HPD2 [23] -the new phase-coherent selfsustained state of precession which must be added to the known BEC states of magnons: HPD and "Q-ball" [24].…”

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Strong Orientational Effect of Stretched Aerogel on theHe3Order Parameter

et al. 2008

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Deformation of aerogel strongly modifies the orientation of the order parameter of superfluid 3 He confined in aerogel. We used a radial squeezing of aerogel to keep the orbital angular momentum of the 3 He Cooper pairs in the plane perpendicular to the magnetic field. We did not find strong evidence for a "polar" phase, with a nodal line along the equator of the Fermi surface, predicted to occur at large radial squeezing. Instead we observed 3 He-A with a clear experimental evidence of the destruction of the long-range order by random anisotropy -the Larkin-Imry-Ma effect. In 3 He-B we observed and identified new modes of NMR, which are impossible to obtain in bulk 3 He-B. One of these modes is characterized by a repulsive interaction between magnons, which is suitable for the magnon Bose-Einstein condensation (BEC). The p-wave superfluid 3 He, which is characterized by an 18-dimensional order parameter, is an amazing test system for different aspects of quantum field theory [1]. Confined in a silica aerogel, superfluid 3 He becomes an ideal system for the investigation of the effect of impurities on a long-range order. In a first approximation the aerogel reduces the superfluid transition temperature [2,3]. Here we report the influence of the aerogel anisotropy on the 3 He order parameter orientation. It was demonstrated earlier that a uniaxial squeezing of a cylindrical aerogel sample leads to the orientation of the orbital momentuml along the cylinder axis [4]. Here we report the first results of experiments with superfluid 3 He whose order parameter is deformed by radially squeezing the aerogel, which is equivalent to uniaxially stretching along the axis of a cylindrical sample. The particular interest for this kind of deformation is due to the prediction of a new phase of superfluid 3 He -the "polar" phase, which has a nodal line in the quasiparticle energy gap in the plane perpendicular to the stretching direction [5]. In our experiments no strong evidence of a polar phase has been found. However, a precursor of a polar phase formation -orientation of the orbital vectorl in the plane of the aerogel squeezing in both 3 He-A and 3 He-B -has been observed.This orientational effect allows us to study the influence of the local random anisotropy of aerogel on the U (1)-field of the vectorl, which is kept in the plane of squeezing. We find that instead of a polar phase, the Imry-Ma state of superfluid 3 He-A is formed. The quenched random anisotropy of the aerogel strands destroys the long-range orientational order (LROO) according to the famous Imry-Ma scenario [6] (see [7,8] and references therein). This is the counterpart of the effect of collective pinning in superconductors predicted by Larkin [9], in which weak impurities destroy the longrange translational order of the Abrikosov vortex lattice.The Larkin-Imry-Ma (LIM) effect has been studied experimentally in 3 He-A confined in a non-deformed aerogel [4,10]. The aerogel diminishes the value of Leggett frequency, which leads to decrease of the frequency s...

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Bose-Einstein Condensation of Magnons in Superfluid 3He

Cited by 84 publications

References 32 publications

Spontaneous Rotating Vortex Lattices in a Pumped Decaying Condensate

Spontaneous Rotating Vortex Lattices in a Pumped Decaying Condensate

Bose–Einstein condensation in an ultra-hot gas of pumped magnons

Strong Orientational Effect of Stretched Aerogel on theHe3Order Parameter

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