Exploiting Soliton Decay and Phase Fluctuations in Atom Chip Interferometry of Bose-Einstein Condensates

We show that the decay of a soliton into vortices provides a mechanism for measuring the initial phase difference between two merging Bose-Einstein condensates. At very low temperatures, the mechanism is resonant, operating only when the clouds start in antiphase. But at higher temperatures, phase fluctuations trigger vortex production over a wide range of initial relative phase, as observed in recent experiments at MIT. Choosing the merge time to maximize the number of vortices created makes the interferometer highly sensitive to spatially varying phase patterns and hence atomic movement.

Figure 1

(a) Atom density profile of the two BECs in the $y=0$ plane (axes inset) at $t=0$. (b)–(g) Density profiles within the region enclosed by the dashed rectangle in (a) at key stages of the merging process ($\tau =5\mathrm{ms}$) calculated for $\Delta =0$ at $t=3\mathrm{ms}$ (b), 4 ms (c), 5 ms (d), and for $\Delta =\pi$ at $t=3\mathrm{ms}$ (e), 4 ms (f), and 5 ms (g). Upper [lower] horizontal bars show scales in (a) [(b)–(g)].

Figure 2

Atom density profiles within the region of the $y=0$ plane (axes inset) shown by the dashed rectangle in Fig. 1a, at $t=\tau =1\mathrm{ms}$ for $\Delta =0$ (a) and $\pi$ (b), and at $t=\tau =50\mathrm{ms}$ for $\Delta =0$ (c) and $\pi$ (d). Horizontal bar shows scale.

Figure 3

Fourier power spectra $F(k_z)$ obtained from simulations without fluctuations at $t=\tau =5\mathrm{ms}$, for $\Delta =0$ [solid curve in (a)], $0.8\pi$ [filled circles in (a)], and $\pi$ [solid curve in (b)]. The vertical dotted lines indicate $k_z=\pm k_c$. (c) $N_c/N$ versus $\Delta$ curves ($t=\tau =5\mathrm{ms}$) obtained from simulations without fluctuations (solid curve with crosses), including quantum fluctuations (dotted curve with circles), and including both quantum and thermal fluctuations at $T=T_1$ (dashed curve with downward pointing triangles) and $T_2$ (dot-dashed curve with upward pointing triangles).

Figure 4

Atom density profiles in the $y=0$ plane (axes inset) showing interference between the two BECs after 8 ms time of flight with $\Delta =0$ at $T=T_1$ (a) and $T_2$ (b). Vertical bar shows scale.

Figure 5

Atom density profiles in the $y=0$ plane (axes inset) of merged BECs ($t=\tau =5\mathrm{ms}$) calculated, without fluctuations, for $\Delta =4\times {10}^{4}z$ (a) and $\Delta =0.05\pi \sin ({10}^4\pi z)+\pi$ (b). Large dashed rectangles contain enlargements of density profiles within smaller rectangles. Horizontal bar shows scale.