Finite-temperature phase diagram of a spin-1 Bose gas

Kawaguchi, Yuki; Phuc, Nguyen Thanh; Blakie, P. B.

doi:10.1103/physreva.85.053611

Cited by 24 publications

(35 citation statements)

References 35 publications

(69 reference statements)

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“…The model of [28] treats the non-condensed cloud as a gas of non-interacting free particles evolving in a self-consistent mean field potential accounting for spinexchange interactions [28]. Importantly, this mean field potential is not diagonal in the Zeeman basis due to spin-mixing interactions.…”

Section: Appendix A: Calculation Of Spin-mixing Dynamicsmentioning

confidence: 99%

Spin-nematic order in antiferromagnetic spinor condensates

et al. 2016

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Large spin systems can exhibit unconventional types of magnetic ordering different from the ferromagnetic or Néel-like antiferromagnetic order commonly found in spin 1/2 systems. Spin-nematic phases, for instance, do not break time-reversal invariance and their magnetic order parameter is characterized by a second rank tensor with the symmetry of an ellipsoid. Here we show direct experimental evidence for spin-nematic ordering in a spin-1 Bose-Einstein condensate of sodium atoms with antiferromagnetic interactions. In a mean field description this order is enforced by locking the relative phase between spin components. We reveal this mechanism by studying the spin noise after a spin rotation, which is shown to contain information hidden when looking only at averages. The method should be applicable to high spin systems in order to reveal complex magnetic phases.

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Section: Appendix A: Calculation Of Spin-mixing Dynamicsmentioning

confidence: 99%

Spin-nematic order in antiferromagnetic spinor condensates

et al. 2016

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“…For an isolated system driven to equilibrium only by binary collisions (in contrast with solid-state magnetic materials [14]), and where magnetic dipole-dipole interactions are negligible (in contrast with dipolar atoms [15]), the longitudinal magnetization m z is then a conserved quantity. This conservation law has deep consequences on the thermodynamic phase diagram.The thermodynamics of spinor gases with conserved magnetization has been extensively studied theoretically using various assumptions and methods [16][17][18][19][20][21][22]. A generic conclusion is that Bose-Einstein condensation occurs in steps, where BEC occurs first in one specific component and magnetic order appears at lower temperatures when two or more components condense.…”

mentioning

confidence: 99%

“…The thermodynamics of spinor gases with conserved magnetization has been extensively studied theoretically using various assumptions and methods [16][17][18][19][20][21][22]. A generic conclusion is that Bose-Einstein condensation occurs in steps, where BEC occurs first in one specific component and magnetic order appears at lower temperatures when two or more components condense.…”

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confidence: 99%

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Stepwise Bose-Einstein Condensation in a Spinor Gas

et al. 2017

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We observe multi-step condensation of sodium atoms with spin F = 1, where the different Zeeman components mF = 0, ±1 condense sequentially as the temperature decreases. The precise sequence changes drastically depending on the magnetization mz and on the quadratic Zeeman energy q (QZE) in an applied magnetic field. For large QZE, the overall structure of the phase diagram is the same as for an ideal spin 1 gas, although the precise locations of the phase boundaries are significantly shifted by interactions. For small QZE, antiferromagnetic interactions qualitatively change the phase diagram with respect to the ideal case, leading for instance to condensation in mF = ±1, a phenomenon that cannot occur for an ideal gas with q > 0.Multi-component quantum fluids described by a vector or tensor order parameter are often richer than their scalar counterparts. Examples in condensed matter are superfluid 3 He [1] or some unconventional superconductors with spin-triplet Cooper pairing [2]. In atomic physics, spinor Bose-Einstein condensates (BEC) with several Zeeman components m F inside a given hyperfine spin F manifold can display non-trivial spin order at low temperatures [3][4][5][6]. The macroscopic population of the condensate enhances the role of small energy scales that are negligible for normal gases. This mechanism (sometimes termed Bose-enhanced magnetism [6]) highlights the deep connection between Bose-Einstein condensation and magnetism in bosonic gases, and raises the question of the stability of spin order against temperature.In simple cases, magnetic order appears as soon as a BEC forms. Siggia and Ruckenstein [7] pointed out for two-component BECs [7] that a well-defined relative phase between the two components implies a macroscopic transverse spin. BEC and ferromagnetism then occur simultaneously, provided the relative populations can adjust freely. A recent experiment confirmed this scenario for bosons with spin-orbit coupling [8]. This conclusion was later generalized to spin-F bosons without [9] or with spin-independent [10] interactions. These results indicate that without additional constraints, bosonic statistics favors ferromagnetism.In atomic quantum gases with F > 1/2, this type of ferromagnetism competes with spin-exchange interactions, which may favor other spin orders such as spinnematics [6]. Spin-exchange collisions can redistribute populations among the Zeeman states [11][12][13], but are also invariant under spin rotations. The allowed redistribution processes are therefore those preserving the total spin, such as 2 × (m F = 0) ↔ (m F = +1) + (m F = −1). For an isolated system driven to equilibrium only by binary collisions (in contrast with solid-state magnetic materials [14]), and where magnetic dipole-dipole interactions are negligible (in contrast with dipolar atoms [15]), the longitudinal magnetization m z is then a conserved quantity. This conservation law has deep consequences on the thermodynamic phase diagram.The thermodynamics of spinor gases with conserved magnetization has b...

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“…These interactions are quite weak for the case of 87 Rb, but can have an appreciable role on the low-energy spectrum, which would affect large-cell fluctuation measurements (also see [49]). Finally, beyond the Bogoliubov approach we presented here there are many avenues for extending the theory including the role of quantum and thermal back-action on the condensate [50,51] and detailed behavior of the system near phase boundaries (e.g., see [52][53][54][55][56][57]). …”

Section: Discussionmentioning

confidence: 99%

Fluctuations of spinor Bose-Einstein condensates

2014

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We develop theory for fluctuations in atom number and spin within finite-sized cells of a spinor Bose-Einstein condensate. This theory provides a model of measurements that can be performed in current experiments using finite resolution in situ imaging. We develop analytic results for quantum and thermodynamic limits of the fluctuations and apply our theory to the four equilibrium phases of a spin-1 condensate. We then validate these limits and examine the behaviour over a wide parameter regime using numerical calculations specialised to the case of a spinor condensate confined to be quasi-two-dimensional (quasi-2D).Comment: 11 pages, 9 figure

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Finite-temperature phase diagram of a spin-1 Bose gas

Cited by 24 publications

References 35 publications

Spin-nematic order in antiferromagnetic spinor condensates

Spin-nematic order in antiferromagnetic spinor condensates

Stepwise Bose-Einstein Condensation in a Spinor Gas

Fluctuations of spinor Bose-Einstein condensates

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