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arXiv:1006.2962 · Physical Review Letters

Rotonlike Instability and Pattern Formation in Spinor Bose-Einstein Condensates

Michał Matuszewski

Published Jul 9, 2010• 26 citations
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Abstract

We show that metastable phases of an antiferromagnetic spin-1 condensate in a simple model with pure contact interactions can exhibit a rotonlike minimum in the excitation spectrum. The introduction of a magnetic field gives rise to the instability of roton modes, which can lead to spontaneous emergence of regular periodic, polygonal, polyhedral, or crystalline patterns, as shown in numerical simulations within the truncated Wigner approximation. An explanation of the occurrence of rotonlike instability is given based on the energy and spin conservation laws.

DOI
10.1103/physrevlett.105.020405

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We show that metastable phases of an antiferromagnetic spin-1 condensate in a simple model with pure contact interactions can exhibit a rotonlike minimum in the excitation spectrum. The introduction of a magnetic field gives rise to the instability of roton modes, which can lead to spontaneous emergence of regular periodic, polygonal, polyhedral, or crystalline patterns, as shown in numerical simulations within the truncated Wigner approximation. An explanation of the occurrence of rotonlike instability is given based on the energy and spin conservation laws.
Superfluids with a tendency towards periodic crystalline order have both a phonon and roton like spectrum of collective modes. The softening of the roton spectrum provides one route to a supersolid. We show that roton softening occurs in 87Rb spinor condensates once dipolar interactions and spin dynamics are taken into account. By including the effects of a quasi-two-dimensional geometry and rapid Larmor precession, we show a dynamical instability develops in the collective mode spectrum at finite wavevectors. We construct phase diagrams showing a variety of instabilities as a function of the direction of the magnetic field and strength of the quadratic Zeeman shift. Our results provide a possible explanation of current experiments in the Berkeley group Phys. Rev. Lett. 100:170403 (2008).
In this Letter we report on the spontaneous formation of surprisingly regular periodic magnetic patterns in an antiferromagnetic Bose-Einstein condensate (BEC). The structures evolve within a quasi-one-dimensional BEC of 87Rb atoms on length scales of a millimeter with typical periodicities of 20…30 μm, given by the spin healing length. We observe two sets of characteristic patterns which can be controlled by an external magnetic field. We identify these patterns as linearly unstable modes within a mean-field approach and calculate their mode structure as well as time and energy scales, which we find to be in good agreement with observations. These investigations open new prospects for controlled studies of symmetry breaking and complex quantum magnetism in bulk BEC.
We theoretically investigate four types of dynamical instability, in particular the periodic and oscillatory type IO{I}_{O}IO​, in an antiferromagnetic spin-1 Bose-Einstein condensate in a nonzero magnetic field, by employing the coupled-mode theory and numerical method. This is in sharp contrast to the dynamical stability of the same system in zero field. Remarkably, a pattern transition from a periodic dynamical instability IO{I}_{O}IO​ to a uniform one IIIO{\mathit{\text{III}}}_{O}IIIO​ occurs at a critical magnetic field. All four types of dynamical instability and the pattern transition are ready to be detected in 23Na^{23}\mathrm{Na}23Na condensates within the availability of the current experimental techniques.
We analyze the structure of spin-one Bose-Einstein condensates in the presence of a homogeneous magnetic field. We classify the homogeneous stationary states and study their existence, bifurcations, and energy spectra. We reveal that phase separation can occur in the ground state of antiferromagnetic (polar) condensates while the spin components of the ferromagnetic condensates are always miscible and no phase separation occurs. Our theoretical model, confirmed by numerical simulations, explains that this phenomenon takes place when the energy of the lowest homogeneous state is a concave function of the magnetization. In particular, we predict that phase separation can be observed in a 23Na^{23}\text{N}\text{a}23Na condensate confined in a highly elongated harmonic trap. Finally, we discuss the phenomena of dynamical instability and spin domain formation.
Roton-type excitations usually emerge from strong correlations or long-range interactions, as in superfluid helium or dipolar ultracold atoms. However, in a weakly short-range interacting quantum gas, the recently synthesized spin-orbit (SO) coupling can lead to various unconventional phases of superfluidity and give rise to an excitation spectrum of roton-maxon character. Using Bragg spectroscopy, we study a SO-coupled Bose-Einstein condensate of ^{87}Rb atoms and show that the excitation spectrum in a "magnetized" phase clearly possesses a two-branch and roton-maxon structure. As Raman coupling strength Ω is decreased, a roton-mode softening is observed, as a precursor of the phase transition to a stripe phase that spontaneously breaks spatially translational symmetry. The measured roton gaps agree well with theoretical calculations. Furthermore, we determine sound velocities both in the magnetized and in the nonmagnetized phases, and a phonon-mode softening is observed around the phase transition in between. The validity of the f-sum rule is examined.
We consider the phenomenon of spin-pattern formation reported in recent experiments in spin-2 rubidium condensate [J. Kronj\"ager, C. Becker, P. Soltan-Panahi, K. Bongs, and K. Sengstock, Phys. Rev. Lett. 105, 090402 (2010)]. To understand the mechanism underlying the process and explain the parameters such as pattern period and growth rate, we employ the Bogoliubov--de Gennes equations and an alternative method based on energy conservation and the uncertainty principle. While the two methods agree in the spin-1 case, only the second method can provide analytical results in the spin-2 case. Using these results, we explain the occurrence of two regimes, the spin-dominated and the Zeeman-dominated, with the prevalence of spin-wave modes and quadrupole modes, respectively. We obtain very good agreement between theory and experiment for the pattern period and growth rate over several orders of magnitude of the magnetic field strength.