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arXiv:1602.06147 · Physical Review Letters

Magnetic Solitons in a Binary Bose-Einstein Condensate

Chunlei Qu, Лев П. Питаевский, S. Stringari

Published Apr 20, 2016• 98 citations
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Abstract

We study solitary waves of polarization (magnetic solitons) in a two-component Bose gas with slightly unequal repulsive intra- and interspin interactions. In experimentally relevant conditions we obtain an analytical solution which reveals that the width and the velocity of magnetic solitons are explicitly related to the spin healing length and the spin sound velocity of the Bose mixture, respectively. We calculate the profiles, the energy, and the effective mass of the solitons in the absence of external fields and investigate their oscillation in a harmonic trap where the oscillation period is calculated as a function of the oscillation amplitude. The stability of magnetic solitons in two dimensions and the conditions for their experimental observation are also briefly discussed.

DOI
10.1103/physrevlett.116.160402

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We study solitary waves of polarization (magnetic solitons) in a two-component Bose gas with slightly unequal repulsive intra- and interspin interactions. In experimentally relevant conditions we obtain an analytical solution which reveals that the width and the velocity of magnetic solitons are explicitly related to the spin healing length and the spin sound velocity of the Bose mixture, respectively. We calculate the profiles, the energy, and the effective mass of the solitons in the absence of external fields and investigate their oscillation in a harmonic trap where the oscillation period is calculated as a function of the oscillation amplitude. The stability of magnetic solitons in two dimensions and the conditions for their experimental observation are also briefly discussed.
We experimentally investigate the dynamics of spin solitary waves (magnetic solitons) in a harmonically trapped, binary superfluid mixture. We measure the in situ density of each pseudospin component and their relative local phase via an interferometric technique we developed and as such, fully characterize the magnetic solitons while they undergo oscillatory motion in the trap. Magnetic solitons exhibit nondispersive, dissipationless longtime dynamics. By imprinting multiple magnetic solitons in our ultracold gas sample, we engineer binary collisions between solitons of either the same or opposite magnetization and map out their trajectories.
We study magnetic solitons, solitary waves of spin polarization (i.e., magnetization), in binary Bose-Einstein condensates in the presence of Rabi coupling. We show that the system exhibits two types of magnetic solitons, called $2\ensuremath{\pi}$ and $0\ensuremath{\pi}$ solitons, characterized by a different behavior of the relative phase between the two spin components. $2\ensuremath{\pi}$ solitons exhibit a $2\ensuremath{\pi}$ jump of the relative phase, independent of their velocity, the static domain wall explored by Son and Stephanov being an example of such $2\ensuremath{\pi}$ solitons with vanishing velocity and magnetization. $0\ensuremath{\pi}$ solitons instead do not exhibit any asymptotic jump in the relative phase. Systematic results are provided for both types of solitons in uniform matter. Numerical calculations in the presence of a one-dimensional harmonic trap reveal that a $2\ensuremath{\pi}$ soliton evolves in time into a $0\ensuremath{\pi}$ soliton, and vice versa, oscillating around the center of the trap. Results for the effective mass, the Landau critical velocity, and the role of the transverse confinement are also discussed.
We investigate magnetic solitons in an immiscible binary Bose-Einstein condensate (BEC), where the intraspecies interactions are slightly weaker than the interspecies interactions. While their density and phase profiles are analogous to dark-bright solitons, other characteristic properties such as maximum velocities, widths, total density depletions, and in-trap oscillations are different. In the low-velocity regime, a magnetic soliton reduces to a traveling pair of magnetic domain walls. Collisional behaviors of the solitons are also briefly discussed. We further demonstrate that these solitonic states can be realized in a quasi-one-dimensional spin-1 ferromagnetic BEC with a weak spin interaction, e.g., a 87Rb^{87}\mathrm{Rb}87Rb BEC.
In this thesis, we investigate polarised solitary waves, known as magnetic solitons and dark-antidark solitons, in binary (two-component) Bose-Einstein condensates in the miscible phase. These solitons have been recently realised in experiments and are predicted to form bound states. We calculate the interaction potentials between magnetic solitons with the same and opposite polarisation, uncovering the mechanisms underlying bound state formation. By considering two superimposed counter-propagating magnetic solitons with opposite polarisation, we analytically calculate the dissociation energy of the bound states and find good agreement with full numerical simulations. Furthermore, we show that the oscillation period of bound states depends on the maximum soliton separation. We subsequently extend these results to dark-antidark solitons. For binary dipolar Bose- Einstein condensates, we derive the dispersion relation of elementary excitations and find that, in the presence of a spin-roton, spin-density modulations form around dark-antidark solitons. These modulations lead to additional local maxima and minima in the inter-soliton potentials, enabling the formation of additional bound state regions. Additionally, we compare the collision characteristics of magnetic solitons in non-dipolar systems with dark-antidark solitons in dipolar–nondipolar condensate mixtures and explore the collisions between bound states in the non-dipolar case.
Two-component Bose-Einstein condensates in the miscible phase can support polarization solitary waves, known as magnetic solitons. By calculating the interaction potential between two magnetic solitons, we elucidate the mechanisms and conditions for the formation of bound states—or —and support these predictions with dynamical simulations. We analytically determine the of bound states consisting of two oppositely polarized solitons and find good agreement with full numerical simulations. Collisions between bound states—either with other bound states or with individual solitons—produce intriguing dynamics. Notably, collisions between a pair of bound states exhibit a dipole-like behavior. We anticipate that such bound states, along with their rich collision dynamics, are within reach of current experimental capabilities.
Vector solitons are a type of solitary or nonspreading wave packet occurring in a nonlinear medium composed of multiple components. As such, a variety of synthetic systems can be constructed to explore their properties, from nonlinear optics to ultracold atoms, and even in metamaterials. Bose-Einstein condensates have a rich panoply of internal hyperfine levels, or spin components, which make them a unique platform for exploring these solitary waves. However, existing experimental work has focused largely on binary systems confined to the Manakov limit of the nonlinear equations governing the soliton behavior, where quantum magnetism plays no role. Here we observe, using a "magnetic shadowing" technique, a new type of soliton in a spinor Bose-Einstein condensate, one that exists only when the underlying interactions are antiferromagnetic and which is deeply embedded within a full spin-1 quantum system. Our approach opens up a vista for future studies of "solitonic matter" whereby multiple solitons interact with one another at deterministic locations.