Perspectives for coherent optical formation of strontium molecules in their electronic ground state

Optical Feshbach resonances [Phys. Rev. Lett. 94, 193001 (2005)] and pump-dump photoassociation with short laser pulses [Phys. Rev. A 73, 033408 (2006)] have been proposed as means to coherently form stable ultracold-alkali-metal dimer molecules. In an optical Feshbach resonance, the intensity and possibly frequency of a cw laser are ramped up linearly followed by a sudden switch-off of the laser. This is applicable to tightly trapped atom pairs. In short-pulse photoassociation, the pump pulse forms a wave packet in an electronically excited state. The ensuing dynamics carries the wave packet to shorter internuclear distances where, after half a vibrational period, it can be deexcited to the electronic ground state by the dump pulse. Short-pulse photoassociation is suited for both shallow and tight traps. The applicability of these two means to produce ultracold molecules is investigated here for ${}^{88}\mathrm{Sr}$. Dipole-allowed transitions proceeding via the $B{}^1{\Sigma }_u^{+}$ excited state as well as transitions near the intercombination line are studied.

Figure 1

(Color online) Coherent formation of ultracold strontium molecules in their electronic ground state via (a) an optical Feshbach resonance where an atom pair in the lowest state of a tight trap is adiabatically compressed to a molecule and (b) by short-pulse photoassociation where molecules are formed in a pump-dump sequence.

Figure 2

(Color online) Excited-state population (bottom) and projection onto the last bound level (top) as a function of laser intensity and detuning for three different pairs of photoassociation resonances.

Figure 3

(Color online) Projection of the time-dependent wave function $\mid \Psi \left(t\right)⟩$ onto the last bound level and the first trap states as a function of time for a ramp of intensity followed by a ramp of frequency (bottom panel). The field amplitude (solid line) and detuning (dashed line) are shown in the upper panel.

Figure 4

(Color online) The same as in Fig. 3 for a ramp of intensity only. The detuning is kept constant at $-6.36{\mathrm{cm}}^{-1}$. Two different trap frequencies are compared with the adiabaticity constraint better fulfilled for the tighter trap.

Figure 5

(Color online) Light shift: binding energy of the least bound dressed state levels as a function of intensity for the laser tuned close to the second to last excited state level ${\widehat{\mathsf{H}}}^{IC}$ (last level, black circles; second to last level, red squares; third to last level, blue diamonds; fourth to last level, green triangles). The upper panel shows the behavior of the last level near zero laser intensity and near the resonance.

Figure 6

(Color online) Same as Fig. 5, but for the laser tuned close to the fourth to last excited-state level of ${\widehat{\mathsf{H}}}^{IC}$.

Figure 7

(Color online) Excited-state population (solid circles) and population in bound excited-state molecular levels (open triangles) after the photoassociation pump pulse as a function of pulse energy for three different photoassociation pump pulse detunings ${\Delta }_{PA}$. The populations undergo Rabi oscillations as the pulse energy is increased.

Figure 8

Time-dependent projection of the excited-state wave packet onto ground-state vibrational levels for a photoassociation detuning of $-4{\mathrm{cm}}^{-1}$ and a pump pulse energy of $1\mathrm{nJ}$. The upper panel shows the photoassociation pump pulse.

Figure 9

Same as Fig. 8, but for a photoassociation detuning of $-19{\mathrm{cm}}^{-1}$ and a pump pulse energy of $3\mathrm{nJ}$.