Beam-loss spectroscopy of cold collisions in a bright sodium beam

We report beam-loss photoassociation (PA) spectra of cold collisions within a slow, bright Na atom beam near the $D_1$ resonance line. The high collimation and brilliance of the atomic beam permits the detection of atomic fluorescence loss resulting from the photoassociation of cold sodium atoms. The results show that even at high PA laser intensities, where strong coupling of the colliding atoms to the optical field might obscure spectral features, vibrational and rotational progressions are surprisingly well resolved. We attribute the conservation of narrow spectral features to the properties of the saturated line shapes and to the unconventional collision energy distribution in one-dimensional (1D) single-beam collisions compared to 3D collisions in a gas cell.

Figure 1

Schematic of bright-beam apparatus with principal components labeled. See Refs. 7, 8 for a full description.

Figure 2

(a) Detail of the experimental setup of the beam-loss spectroscopy system showing the relative disposition of the PA laser, the probe laser, and the fluorescence detector. (b) Schematic of the geometry of the fluorescence depletion at the PA laser spot (left spot) and subsequent atom depletion channel cut into the beam downstream. The small spot to the right indicates the position of the probe beam.

Figure 3

Beam-loss spectrum for PA laser polarization parallel to the atom beam over the range of measurements from to $-12\text{GHz}$ to $0\text{GHz}$ detuning to the red of the ${}^{2}S_{1∕2}\left(f=2\right)+{}^{2}P_{1∕2}\left(f=2\right)$ dissociation limit for an atomic beam without spin polarization. An assignment of the spectral structure is discussed in Sec. 3C

Figure 4

Beam-loss spectrum for PA light polarization parallel to the atom beam close to the dip occurring at $\simeq -10\text{GHz}$ detuning to the red of the ${}^{2}S_{1∕2}\left(f=2\right)+{}^{2}P_{1∕2}\left(f=2\right)$ dissociation limit. The atom ground-state populations have not been spin polarized. The fluorescence-loss dips appear to be part of a rotational progression, and an assignment of the spectral features is discussed in Secs. 3B, 3C.

Figure 5

Beam-loss spectra for parallel PA light polarization close to the dip occurring at $\simeq -10\text{GHz}$ detuning to the red of the ${}^{2}S_{1∕2}\left(f=2\right)+{}^{2}P_{1∕2}\left(f=2\right)$ dissociation limit.

Figure 6

Assignment of the beam-loss spectrum. The spectrum exhibits a series of features that appear to cut off at the ${}^{2}S\left(f=1\right)+{}^{2}P_{1∕2}\left(f=1\right)$ hyperfine limit, as indicated by the vertical dashed line. The zero of detuning is the ${}^{2}S\left(f=2\right)+{}^{2}P_{1∕2}\left(f=2\right)$ hyperfine limit. Each feature of this progression is about $0.5\text{GHz}$ wide. In addition, between $-10\text{GHz}$ and $-9\text{GHz}$ there is a sharper feature which is associated with a rotational progression, as already pointed out in Secs. 3A, 3B. The spectrum labeled “$0_u^{+}$ Tiemann” refers to the determination of Ref. 19; the label “$0_g^{-}$” refers to the vibrational progression calculated from the adiabatic Movre-Pichler potential [16]. The progression labeled by “$1_g\phi =4$” refers to the $1_g$ adiabatic Movre-Pichler potential with $\phi =\Omega +\iota$, as explained in the text.

Figure 7

Hyperfine adiabatic potentials near the ${}^{2}S+{}^{2}P_{1∕2}$ fine-structure limit as a function of internuclear separation, where $1a_0=0.0529\text{nm}$. The labeled states correlate to the ${}^{2}S+{}^{2}P_{1∕2}$ fine structure limit and the $0_g^{-},1_g,$ and $0_u^{+}$ states are optically coupled to the ground state.

Figure 8

Comparison of the measured rotational progression of the $0_g^{-}$ vibrational line near $-10\text{GHz}$ shown in Fig. 6 to two calculated line shapes. The solid-line spectrum is obtained using the one-dimensional beam velocity distribution at $T=4\text{mK}$. The dotted-line spectrum assumes a thermal gas cell experiment at $T=4\text{mK}$. The inset compares the weak-field PAI spectrum (points) measured in a dark spot MOT at a collision temperature of $T=4\text{mK}$ [9] with the calculated MOT spectrum (solid line) using Eqs. (2, 3) with the isotropic gas velocity distribution function. The horizontal scale is the same for the inset as for the figure. Only $s$, $p$, and $d$ waves contribute to the MOT spectrum because of the colder MOT temperature. Note that the beam spectrum is shifted $\simeq -1\text{GHz}$ relative to the MOT spectrum.