Control of Ultracold Photodissociation with Magnetic Fields

Photodissociation of a molecule produces a spatial distribution of photofragments determined by the molecular structure and the characteristics of the dissociating light. Performing this basic reaction at ultracold temperatures allows its quantum mechanical features to dominate. In this regime, weak applied fields can be used to control the reaction. Here, we photodissociate ultracold diatomic strontium in magnetic fields below 10 G and observe striking changes in photofragment angular distributions. The observations are in excellent agreement with a multichannel quantum chemistry model that includes nonadiabatic effects and predicts strong mixing of partial waves in the photofragment energy continuum. The experiment is enabled by precise quantum-state control of the molecules.

Figure 1

(a) Geometry of the photodissociation process. The molecules are trapped in an optical lattice at the origin, while the photodissociation (PD) laser propagates along the $x$ axis. The polar angle $\theta$ and azimuthal angle $\varphi$ are defined as shown to describe the photofragment angular distributions (PADs). The radii of the spherical shells containing the fragments after a fixed expansion time are given by the frequency of the PD laser and the Zeeman shifts of different atomic continua. The largest shell corresponds to a negative shift (yellow), the medium shell to an absence of shift (red), and the smallest shell to a positive shift (blue). A camera points in the $-x$ direction and images a two-dimensional projection of the nested shells. (b) Molecular potentials and quantum states relevant to the experiment. The photodissociation process is designated by the double arrow. The detuning of the PD light from the $m=0$ Zeeman component of the continuum is $\mathrm{\Delta }$, and the symmetric Zeeman splitting has a magnitude ${\mathrm{\Delta }}_Z$. The barrier of the $1_u$ potential has a height of $\sim 30\mathrm{MHz}$. The numbers in parentheses are $v$ and $J_i$. (c) An example of calculated and measured PAD images for a process where a small applied magnetic field drastically alters the outcome of the reaction. The two pairs of images differ only by the magnitude of the applied field: $B=0.5\mathrm{G}$ on the left and 10.15 G on the right.

Figure 2

Tuning of the photodissociation reaction with small magnetic fields, across a range of energies. The color coding for the continuum Zeeman components is consistent between Figs. 1 and 2. (a) Theoretical and experimental images of PADs as the magnetic field $B$ is increased from 0.5 to 10.15 G, for the detuning $\mathrm{\Delta }=29.2\mathrm{MHz}$. (b) Theoretical and experimental PAD images at $B=10.15\mathrm{G}$, covering a range of $\mathrm{\Delta }$ from $-13.8$ to 50.0 MHz. As indicated in Fig. 1, additional channels ($m=-1$, 0, and 1) become available in the continuum as $\mathrm{\Delta }$ increases, leading to extra photofragment shells. In some of the experimental images, the faint outermost shell is the result of incidental photodissociation of residual $J=2$ molecules and can be ignored. The top and bottom pairs of rows in both (a) and (b) correspond to the light polarization parallel and perpendicular to $\overrightarrow{B}$, respectively. Typically, 300 experiments with atoms and 300 without atoms (for background subtraction) are averaged to obtain each experimental PAD image. The experimental images use an arbitrary brightness scale, and the relative transition strengths for different images can be inferred from this data only qualitatively. Within each PAD, however, relative transition strengths to different $m$’s are more accurately reflected in the relative brightness of the rings.

Figure 3

Mixing of the continuum partial waves with a small magnetic field. (a) Experimental and calculated PAD images for photodissociation at $B=10.15\mathrm{G}$. The laser polarization is parallel to $\overrightarrow{B}$ and the detuning is $\mathrm{\Delta }=29.2\mathrm{MHz}$. The brightest fragment shell here corresponds to $m=0$. (b) For comparison, a calculated PAD for $B=0$ consists of a simple dipolar pattern corresponding to $J=1$. The quantum numbers $m=-1$, 0, 1 are unresolved. (c) Calculated PADs of the process in (a), each image including contributions only up to the maximum partial wave $J_{\max }=1$ through 5 that is included in the multichannel continuum wave function, as labeled. Agreement with experiment is reached for $J_{\max }=5$. (d)–(h) Plots of the anisotropy parameters ${\beta }_{\mu }$ versus the field strength $B$ for the dominant $m=0$ component of the PAD in (a). The contributions of individual continuum angular-momentum pairs ($J$, $J^{\prime }$) are shown (with $J_{\max }=5$), where the indexed notation corresponds to that of Eq. (10) in Ref. [21]. The curves in (d) are also normalized by the total ${\beta }_0$ and illustrate the relative contributions of the partial wave pairs to the photodissociation transition strength [21].