Investigation and comparison of multistate and two-state atom laser-output couplers

We investigate the spatial structure and temporal dynamics created in a Bose-Einstein condensate by radio-frequency atom laser-output couplers using a one-dimensional mean-field model. We compare the behavior of a “pure” two-state atom laser to the multilevel systems demonstrated in laboratories. In particular, we investigate the peak homogeneous output flux, classical fluctuations in the beam, and the onset of a bound state which shuts down the atom laser output.

Figure 1

Comparison of the population dynamics in the five-state system for (a) weak and (b) strong coupling. Parameters are $U=6.6\times {10}^{-4}$, $G=9.24$, and $\Delta =10.7$.

Figure 2

(Color online) Spatial profiles of the five-state system, showing the effect of the $m_F=1$ state oscillations on the output mode. The color axes are adjusted to give the best contrast for each of the Zeeman states. Each plot shows the atomic density, with the complete spatial grid in the vertical direction and the temporal grid in the horizontal. (a) Total density (the sum of the densities in all five Zeeman states) as a function of time, (b) density of the $m_F=2$ state, (c) density of the $m_F=1$ state, and (d) $m_F=0$ state. The dynamics were obtained after $15\mathrm{ms}$ of intermediate output coupling $(\Omega =1\mathrm{kHz})$.

Figure 3

Density fluctuations in the $m_F=0$ state of a five-state system at a single point in the beam as a function of time. The fluctuations due to the sloshing of the $m_F=1$ are increasingly severe as the coupling strength is increased. Parameters are $U=6.6\times {10}^{-4}$, $G=9.24$, and $\Delta =10.7$.

Figure 4

(Color online) Comparison of numerical calculations with previous experimental results (a) the total atomic population remaining in the magnetic trap after $100\mathrm{ms}$ of output coupling as a function of angular Rabi frequency for both our numerical model (solid line) and some of our previous experimental measurements (open circles). One can see the excellent qualitative agreement between both curves. (b)–(e) compare theoretical (solid lines) and experimental (dashed lines) results showing the spatial structure of an atom laser for a short time of continuous output coupling and for different Rabi frequencies. Note that all numerical simulations have no free parameters. The detailed description of the figure is given in the text.

Figure 5

Population dynamics in the three-state system for (a) weak and (b) strong coupling. Parameters are $U=6.6\times {10}^{-4}$, $G=9.24$, and $\Delta =43$.

Figure 6

Comparison of the population dynamics in the two-state system for (a) weak and (b) strong coupling. Parameters are $U=6.6\times {10}^{-4}$, $G=9.24$, and $\Delta =43$.

Figure 7

(Color online) Periodic spatial oscillations in the population dynamics of a five-state system. One can see the ejection of the untrapped dressed states as well as both oscillation periods corresponding to the $F=2$ and $F=1$ radial trapping frequencies. Note that the upper edge of the oscillations is at the minimum of the magnetic trapping potential.

Figure 8

(a) Comparison of the time-dependent density of the two- and three-state atom lasers at a point below the condensate after $15\mathrm{ms}$ of output coupling and for different Rabi frequencies. (b) The time-dependent density of the two-state atom laser at very low intensities after $100\mathrm{ms}$ of output coupling.

Figure 9

Comparison of the number of atoms in the condensate and in the $m_F=0$ atom laser state for the two-state and multi state systems after $15\mathrm{ms}$ of output coupling.