Photoassociation of a Bose-Einstein Condensate near a Feshbach Resonance

We measure the effect of a magnetic Feshbach resonance (FR) on the rate and light-induced frequency shift of a photoassociation resonance in ultracold ${}^7\mathrm{Li}$. The photoassociation-induced loss-rate coefficient $K_p$ depends strongly on magnetic field, varying by more than a factor of ${10}^4$ for fields near the FR. At sufficiently high laser intensities, $K_p$ for a thermal gas decreases with increasing intensity, while saturation is observed for the first time in a Bose-Einstein condensate. The frequency shift is also strongly field dependent and exhibits an anomalous blueshift for fields just below the FR.

Figure 1

$K_p$ for PA to $v=83$ for a thermal gas. $I$ is fixed at $1.65\mathrm{W}/{\mathrm{cm}}^2$, while $\tau$ is adjusted between 0.07 and 270 ms to keep the fractional loss at $30\pm 6\%$ ($\tau \propto 1/K_p$). The fitted temperatures range between 9 and $18\mu \mathrm{K}$. The spread in initial peak density, $0.5–10\times {10}^{12}{\mathrm{cm}}^{-3}$, reflects a significant decrease in density near the FR, which we ascribe to enhanced three-body loss. The axial and radial trapping frequencies are 20 Hz and 3 kHz, respectively. A systematic uncertainty in $K_p$ of 25% reflects the uncertainty in the evolution of the density (see text), as well as uncertainties in probe detuning and intensity. The statistical uncertainty is 20%. The measurements of the highest values of $K_p$ are saturated (Fig. 3) and are therefore lower limits. The inset shows $K_p$ (same scale as main figure) for three different excited state vibrational levels.

Figure 2

Slope of the intensity-dependent spectral light shift $\Sigma$. The error bars are the standard error of the fitted slope at each field. For most of the data, this statistical uncertainty is smaller than the size of the plotted points. The systematic uncertainty in $\Sigma$ is 10% due to uncertainty in $I$. Condensates and thermal gases were found to exhibit the same $\Sigma$.

Figure 3

$K_p$ vs $I$ in a thermal gas at 755 G, with $T\simeq 16\mu \mathrm{K}$ and a peak density of $7.5\times {10}^{11}{\mathrm{cm}}^{-3}$. $\tau$ is between 210 and $250\mu \mathrm{s}$ for all of the data except at the lowest intensity, for which $\tau =2\mathrm{ms}$. The error bars are the statistical uncertainties from the fitted $T$. The systematic uncertainties are 30% for $K_p$ and 10% for $I$. The solid line is a weighted fit to the data using Eq. (1), with the fitted parameters $K_{\max }=9.5\times {10}^{-9}{\mathrm{cm}}^3/\mathrm{s}$ and $I_{\mathrm{sat}}=4.1\mathrm{W}/{\mathrm{cm}}^2$. A linear fit to the slope for small $I$ gives $8.2\pm 1.1\times {10}^{-9}{\mathrm{cm}}^3{\mathrm{s}}^{-1}/(\mathrm{W}{\mathrm{cm}}^{-2})$, where the uncertainty refers only to statistical uncertainty.

Figure 4

$K_p$ for a BEC at 732 G ($a\simeq 1000a_0$). The $1/e^2$ intensity radius of the PA beam of $560\mu \mathrm{m}$ is much larger than the radial Thomas-Fermi radius of the BEC. The pulse duration $\tau \propto 1/K_p$ is $3\mu \mathrm{s}$ for the highest $I$ and $50\mu \mathrm{s}$ for the lowest. The peak density is $1.6\times {10}^{12}{\mathrm{cm}}^{-3}$. The axial and radial trapping frequencies are 4.5 and 200 Hz, respectively. The solid line is a fit to Eq. (1) with fit parameters $K_{\max }=1.4\times {10}^{-7}{\mathrm{cm}}^3/\mathrm{s}$ and $I_{\mathrm{sat}}=26\mathrm{W}/{\mathrm{cm}}^2$. A linear fit to the low intensity data gives a slope of $1.6\times {10}^{-8}{\mathrm{cm}}^3{\mathrm{s}}^{-1}/(\mathrm{W}{\mathrm{cm}}^{-2})$, as indicated by the dashed line. The error bars are the statistical uncertainties, due mainly to the measured Thomas-Fermi radius of the initial density distribution. A systematic uncertainty of 12% reflects the uncertainty in the image probe detuning and intensity. $I$ could not be increased further without producing loss from dipole forces.