Observation of Magnetic Solitons in Two-Component Bose-Einstein Condensates

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.

Figure 1

(a) A spin-selective optical potential generates a pair of MSs that travel in opposite directions along $y$ in our two-component elongated BEC. The overall imparted phase of $2\pi$ is dealt symmetrically on the two spin components. (b) $\mathrm{\Lambda }$-coupling scheme showing all the hyperfine transitions that are used for preparation of the mixture and inducing an effective quadratic shift. (c) Full tomography of a pair of MSs 15 ms after their creation. Left column: Optical densities (OD) of $|1,-1⟩$ (red) and $|1,+1⟩$ (blue), and relative phase (purple). Right column: The measured apparent magnetization (top) is of the order of 0.5 and the expected relative-phase profile (bottom) shows two $\pi$ jumps at the soliton positions.

Figure 2

(a) Two MSs of opposite magnetization oscillate out of phase in the trap with a period of 550 ms. The BEC is centered at $y=0$. Finite temperature effects lead to the slight oscillation amplitude increase and decay of magnetization (see Supplemental Material [35]). Since the magnetization of one of the MSs is slightly smaller, it goes below our detection threshold sooner. (b) The oscillation amplitude $L/R_y$ of a single MS increases monotonically with its initial velocity $v$ in agreement with the theoretical prediction with no free parameters [24].

Figure 3

(a) The input state of the interferometer is an equal superposition of the two components (red-blue). All phases are applied to one arm without loss of generality. The two components are projected onto the readout state (purple) using a bichromatic microwave pulse. (b) Typical data showing the OD in the readout state (top), which is a direct measurement of the phase difference of the two components. The jump in $\varphi (y)$ is proportional to the ratio of the average counts on either side of an MS (shaded regions). (c) Average counts in the left versus right regions across each of the two MSs. The phase difference of the left- and right-projected populations is independent of ${\varphi }_{\mathrm{LO}}$. The anticorrelated behavior is consistent with a $\pi$ phase jump for both MSs within our statistical uncertainty.

Figure 4

Collisions of MSs with opposite (left column) or same (right column) magnetizations. (a–b) Time evolution of the MSs in the reference frame of the center of mass of the solitons. (c–d) Relative position of the MSs close to the collision point at 300 ms for $\uparrow \downarrow$ collisions (c) and 45 ms for $\uparrow \uparrow$ (d). For these $\uparrow \uparrow$ collisions ($m_0=0.86$), the MSs dissipate energy during the collision, as evident by the different velocities (slopes) before and after. The missing points in (d) are due to not being able to distinguish same magnetization MSs when they are very close together. The variance of the data is larger in the left column than in the right one since the collision happens at much later times.