Photoassociation of spin-polarized chromium

We report the homonuclear photoassociation (PA) of ultracold ${}^{52}\mathrm{Cr}$ atoms in an optical dipole trap. This constitutes the measurement of PA in an element with total electron spin $\tilde{S}>1$. Although Cr, with its ${}^{7}S_3$ ground and ${}^{7}P_{4,3,2}$ excited states, is expected to have a complicated PA spectrum we show that a spin-polarized cloud exhibits a remarkably simple PA spectrum when circularly polarized light is applied. Over a scan range of 20 GHz below the ${}^{7}P_3$ asymptote we observe two distinct vibrational series each following a LeRoy-Bernstein law for a $C_3/R^3$ potential with excellent agreement. We determine the $C_3$ coefficients of the Hund's case (c) relativistic adiabatic potentials to be $-1.83\pm 0.02$ and $-1.46\pm 0.01$ a.u.. Theoretical nonrotating Movre-Pichler calculations enable a first assignment of the series to $\mathrm{\Omega }=6_u$ and $5_g$ potential energy curves. In a different set of experiments we disturb the selection rules by a transverse magnetic field which leads to additional PA series.

Figure 1

Sketch of the relevant molecular potentials. Ground-state scattering channels are constrained to ${}^{11}\mathrm{\Sigma }_u^{+}$ and ${}^{13}\mathrm{\Sigma }_g^{+}$. For $R\to \infty ,{}^{7}S_3+{}^{7}S_3$ and ${}^{7}S_3+{}^{7}P_3$ depict the separated atom asymptotes. The insets show the $m_{\tilde{j}}\le 0$ Zeeman levels of the ${}^{7}S_3$ and ${}^{7}P_3$ states with the corresponding atomic transition frequency ${\omega }_A$. At intermediate distances the $C_3$ potentials dominate the transition energies. Vibrational quantum numbers $\tilde{\nu }$ are counted from the separated atom asymptote. Photoassociation can occur when the laser detuning $\mathrm{\Delta }$ matches the energy of a vibrational level $E\left(\tilde{\nu }\right)$. The main contribution to the PA signal stems from the $6_u$ (green) and $5_g$ (blue) relativistic adiabatic potentials.

Figure 2

Experimental PA spectrum of ${}^{52}\mathrm{Cr}$ for constant ${\mathrm{\Gamma }}_{\mathrm{SC}}$. The black (red) curve shows the observed number of atoms $N$ (cloud temperature $T$) after 4 seconds of demagnetization cooling. We find two distinct vibrational series and display their respective vibrational quantum numbers ${\tilde{\nu }}_{1,2}$ in additional axes on top of each detuning segment. Additional symbols (triangle, circle, diamond) are explained later.

Figure 3

Observed linewidths $\gamma \left({\tilde{\nu }}_i\right)$ as a function of the vibrational quantum number ${\tilde{\nu }}_i$. For series 1 (blue data) the linewidth is $\sim 10\mathrm{MHz}$. For series 2 (green data) the width increases with ${\tilde{\nu }}_2$.

Figure 4

Double-logarithmic representation of the observed resonance positions $\left[{\delta }_{\mathrm{expt}}\left({\tilde{\nu }}_i\right)\right]$ and the vibrational quantum number ${\tilde{\nu }}_i$ for (a) series 1,2 (blue, green data) and (b) series 3–5 (cyan, magenta, orange). Only resonances shown here are used in the LBE analysis to obtain the vibrational quantum numbers ${\tilde{\nu }}_i$. The error bars for series 1 and 2 are too small to be visible. Linear fits (red lines) retrieve the ${\tilde{\nu }}^6$ behavior.

Figure 5

Residuals ${\delta }_{\mathrm{expt}}-{\delta }_{\mathrm{LBE}}$ of the LeRoy-Bernstein fit. The error bars mark the standard deviations from the Lorentzian fit on the resonances.