Pulsed atomic soliton laser

It is shown that simultaneously changing the scattering length of an elongated, harmonically trapped Bose-Einstein condensate from positive to negative and inverting the axial portion of the trap, so that it becomes expulsive, results in a train of self-coherent solitonic pulses. Each pulse is itself a nondispersive attractive Bose-Einstein condensate that rapidly self-cools. The axial trap functions as a waveguide. The solitons can be made robustly stable with the right choice of trap geometry, number of atoms, and interaction strength. Theoretical and numerical evidence suggests that such a pulsed atomic soliton laser can be made in present experiments.

Figure 1

Shown is the evolution of an attractive Bose-Einstein condensate into a pulsed atomic soliton laser. Time slices of the line density in $z$ are shown for $x$, $y=0$. Modulational instability of the initial density profile is seeded by self-interference of the order parameter, so that solitons form first at the cloud edges and later towards the center. The latest, top panel, shows that a well-separated set of stable solitonic pulses are produced. Note that, for $N={10}^4$ atoms, $a=-3a_0$, and a trap geometry of ${\omega }_{\rho }=2\pi \times 2.44\mathrm{kHz}$, ${\omega }_z=2\pi i\times 2.26\mathrm{Hz}$, the time units are scaled to $22\mathrm{ms}$ and the spatial units to $10\mu \mathrm{m}$.

Figure 2

(Color online) Shown are the evolution of the density and phase along a two-dimensional cut at $y=0$ for the simulation of Fig. 1. A set of well-defined solitonic pulses is evident in the latest (top) panel. The strong variations in the phase at late times is due to the high momentum of the solitons caused by the expulsive harmonic potential. Note that the phase is shown modulo $2\pi$ in black-to-white-to-black (color: on the color circle) while the density is in arbitrary relative units rescaled for each plot. The aspect ratio of the plots showing a region of 0.822 by 153 length units was changed for visualization; length and time units are the same as in Fig. 1.

Figure 3

Shown are the self-interference fringes of the order parameter which seed modulational instability, according to the Feynman propagator for a harmonic oscillator. The initial density profile was Thomas-Fermi; shown is the ratio of the density $66\mathrm{ms}$ later to the original density. Since the wavelength of the instability must be on the order of $2\pi \xi$, where $\xi$ is the healing length, solitons form first on the edges of the cloud, due to the early long-wavelength fringes in this region. At later times the wavelength of the fringes in the center also becomes longer. Shown is the linear equivalent of the panel depicting $t=3$ in the full simulation of the 3D Gross-Pitaevskii equation illustrated in Figs. 1, 2; all parameters are the same as the simulation, with length units scaled to $10\mu \mathrm{m}$.

Figure 4

Shown is the evolution of the density along a one-dimensional cut at $x$, $y=0$, with the same parameters as the simulation of Fig. 1 but with the addition of noise, as described in the text. The time scale is shorter than that observed in Fig. 1, and the solitons form first in the center of the cloud, rather than on the outside, but the end result is the same: a set of well-defined solitonic pulses is evident in the latest (top) panel. The length and time units are the same as in Fig. 1.