Fluctuations and flux: The limits of multistate atom lasers

By direct comparison between experiment and theory with no adjustable parameters, we show how the classical fluctuations on a multistate atom laser beam increase with increasing flux. The fluctuations are inherent to state changing out coupling, rf, Raman, or otherwise and are likely to be present in all atom lasers, pulsed or continuous, that employ such out coupling. If not removed or avoided, these classical fluctuations will prevent shot noise limited measurement employing atom lasers of this kind.

Figure 1

Out-coupled fraction as a function of rf amplitude. The solid square is the power at which the results of Fig. 2 were generated. Theoretical curves are: Solid line, $m_F=2,1$ trapped states, dot-dashed $m_F=0$ and dashed, $m_F=-2,-1$ antitrapped states. The experimental results are: triangles, $m_F=2,1$ trapped states, circles $m_F=0$. Typical error bars are $\pm 5\%$ vertically and $\pm 10\%$ horizontally. Simulation parameter: $\Delta =-640$.

Figure 2

(Color online) A series of pulsed atom lasers at different pulse rates. The applied radio-frequency (rf) pulses are varied from (a) four pulses, (b) five pulses, (c) six pulses, (d) seven pulses, (e) ten pulses in an $8\text{ms}$ window. The lower plots show a cross-section down the center of the absorption data. The three dashed lines correspond in descending order to the center of the condensate, the half-width of the $200\text{kHz}$ rf resonance ($100\text{kHz}$ $\approx 12\mu \mathrm{m}$ in our trap), and the position coinciding with the final rf out-coupling pulse ($4\text{ms}$ prior to imaging).

Figure 3

(Color online) Numerical simulations of the cases of Figs. 2c, 2b. Figure 2c is to the left of vertical line. Each image shows the GP wave function density, in arbitrary units, integrated through the tight trap direction. Density is indicated by the colobar at the bottom of the figure, with black and white corresponding to zero and high density, respectively. Each image is $120\mu \mathrm{m}$ in both directions. From top to bottom the rows are $t=1.2\text{ms}$, just before the second rf pulse; just after the second rf pulse; $t=2.4\text{ms}$, just before the third rf pulse; just after the third rf pulse. $t=0$ is the beginning of the first rf pulse. The columns from left to right are the $m_F=2,1,0,-1,-2$ states. The top-left image therefore shows the trapped position of the initial $m_F=2$ condensate. Figure 2b is to the right of vertical line. Only the $m_F=0$ state is shown. The rows are as before but the rf pulses occur at $t=1.6\text{ms}$ and $t=3.2\text{ms}$. Each image is $120\mu \mathrm{m}$ vertically and $140\mu \mathrm{m}$ horizontally. The rightmost image shows the $m_F=0$ state density on a slice plane through the tight trap direction, just after the third rf pulse. It is $40\mu \mathrm{m}$ horizontally and about $150\mu \mathrm{m}$ vertically, allowing the first pulse to be seen. Simulation parameters: $\Delta =-633$, $\Omega =457$. See text for discussion.