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arXiv:1812.11682 · Physical Review A

High-intensity two-frequency photoassociation spectroscopy of a weakly bound molecular state: Theory and experiment

Wen Yu Kon, J. A. Aman, Joshua C. Hill, T. C. Killian, Kaden R. A. Hazzard

Published Jul 15, 2019• 4 citations
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Abstract

We investigate two-frequency photoassociation of a weakly bound molecular state, focusing on a regime where the AC Stark shift is comparable to the halo-state energy. In this ``high-intensity'' regime, we observe features absent in low-intensity two-frequency photoassociation. We experimentally measure the spectra of $^{86}\mathrm{Sr}$ atoms coupled to the least bound state of the $^{86}\mathrm{Sr}_{2}$ ground electronic channel through an intermediate electronically excited molecular state. We compare the spectra to a simple three-level model that includes a two-frequency drive on each leg of the transition. With numerical solution of the time-dependent Schr\"odinger equation, we show that this model accurately captures (1) the existence of experimentally observed satellite peaks that arise from nonlinear processes, (2) the locations of the two-photon peak in the spectrum, including AC Stark shifts, and (3) in some cases, spectral line shapes. To better understand these numerical results, we develop an approximate treatment of this model, based on Floquet and perturbation theory, that gives simple formulas that accurately capture the halo-state energies. We expect these expressions to be valuable tools to analyze and guide future two-frequency photoassociation experiments.

DOI
10.1103/physreva.100.013408

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We investigate two-frequency photoassociation of a weakly bound molecular state, focusing on a regime where the AC Stark shift is comparable to the halo-state energy. In this ``high-intensity'' regime, we observe features absent in low-intensity two-frequency photoassociation. We experimentally measure the spectra of 86Sr^{86}\mathrm{Sr}86Sr atoms coupled to the least bound state of the 86Sr2^{86}\mathrm{Sr}_{2}86Sr2​ ground electronic channel through an intermediate electronically excited molecular state. We compare the spectra to a simple three-level model that includes a two-frequency drive on each leg of the transition. With numerical solution of the time-dependent Schr"odinger equation, we show that this model accurately captures (1) the existence of experimentally observed satellite peaks that arise from nonlinear processes, (2) the locations of the two-photon peak in the spectrum, including AC Stark shifts, and (3) in some cases, spectral line shapes. To better understand these numerical results, we develop an approximate treatment of this model, based on Floquet and perturbation theory, that gives simple formulas that accurately capture the halo-state energies. We expect these expressions to be valuable tools to analyze and guide future two-frequency photoassociation experiments.
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We experimentally investigate various processes present in the photoassociative interaction of an ultracold atomic sample with shaped femtosecond laser pulses. We demonstrate the photoassociation of pairs of rubidium atoms into electronically excited, bound molecular states using spectrally cut femtosecond laser pulses tuned below the rubidium D1 or D2 asymptote. Time-resolved pump-probe spectra reveal coherent oscillations of the molecular formation rate, which are due to coherent transient dynamics in the electronic excitation. The oscillation frequency corresponds to the detun-ing of the spectral cut position to the asymptotic transition frequency of the rubidium D1 or D2 lines, respectively. Measurements of the molecular photoassociation signal as a function of the pulse energy reveal a non-linear dependence and indicate a non-perturbative excitation process. Chirping the association laser pulse allowed us to change the phase of the coherent transients. Furthermore, a signature for molecules in the electronic ground state is found, which is attributed to molecule formation by femtosecond photoassociation followed by spontaneous decay. In a subsequent article [A. Merli et al., submitted] quantum mechanical calculations are presented, which compare well with the experimental data and reveal further details about the observed coherent transient dynamics.
Creation and precise spectroscopy of 86^{86}86Sr2_22​ halo molecules
We report on the creation of 86^{86}86Sr2_22​ molecules in the halo state and neighboring weakly bound states. Efficient molecule production via one-photon photoassociation relies on sufficient wavefunction overlap between the target vibrational states in the electronic excited- and ground-state potentials. Using Autler-Townes spectroscopy, transition strengths are measured to identify optimal pathways for production of weakly bound molecules. Vibrational splittings for the three least-bound vibrational states are measured, and dominant systematic uncertainties are evaluated with uncertainties below 100 Hz. From these splittings, absolute binding energies for these weakly bound vibrational states are determined. The results pave the way to a molecular isotope shift measurement with Sr2_22​.
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Photoassociation with short laser pulses has been proposed as a technique to create ultracold ground state molecules. A broad-band excitation seems the natural choice to drive the series of excitation and deexcitation steps required to form a molecule in its vibronic ground state from two scattering atoms. First attempts at femtosecond photoassociation were, however, hampered by the requirement to eliminate the atomic excitation leading to trap depletion. On the other hand, molecular levels very close to the atomic transition are to be excited. The broad bandwidth of a femtosecond laser then appears to be rather an obstacle. To overcome the ostensible conflict of driving a narrow transition by a broad-band laser, we suggest a two-photon photoassociation scheme. In the weak-field regime, a spectral phase pattern can be employed to eliminate the atomic line. When the excitation is carried out by more than one photon, different pathways in the field can be interfered constructively or destructively. In the strong-field regime, a temporal phase can be applied to control dynamic Stark shifts. The atomic transition is suppressed by choosing a phase which keeps the levels out of resonance. We derive analytical solutions for atomic two-photon dark states in both the weak-field and strong-field regime. Two-photon excitation may thus pave the way toward coherent control of photoassociation. Ultimately, the success of such a scheme will depend on the details of the excited electronic states and transition dipole moments. We explore the possibility of two-photon femtosecond photoassociation for alkali and alkaline-earth metal dimers and present a detailed study for the example of calcium.