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arXiv:1003.1757 · Physical Review A

Creating a quantum degenerate gas of stable molecules via weak photoassociation

Matt Mackie, Pierre Phou

Published Jul 27, 2010• 1 citation
arXivHTMLPDF

Abstract

Quantum degenerate molecules represent a new paradigm for fundamental studies and practical applications. Association of already quantum degenerate atoms into molecules provides a crucial shortcut around the difficulty of cooling molecules to ultracold temperatures. Whereas association can be induced with either laser or magnetic fields, photoassociation requires impractical laser intensity to overcome poor overlap between the atom pair and molecular wave functions, and experiments are currently restricted to magnetoassociation. Here we model realistic production of a quantum degenerate gas of stable molecules via two-photon photoassociation of Bose-condensed atoms. An adiabatic change of the laser frequency converts the initial atomic condensate almost entirely into stable molecular condensate, even for low-intensity lasers. Results for dipolar LiNa provide an upper bound on the necessary photoassociation laser intensity for alkali-metal atoms $~$$30$ W/cm${}^{2}$, indicating a feasible path to quantum degenerate molecules beyond magnetoassociation.

DOI
10.1103/physreva.82.011609

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Quantum degenerate molecules represent a new paradigm for fundamental studies and practical applications. Association of already quantum degenerate atoms into molecules provides a crucial shortcut around the difficulty of cooling molecules to ultracold temperatures. Whereas association can be induced with either laser or magnetic fields, photoassociation requires impractical laser intensity to overcome poor overlap between the atom pair and molecular wave functions, and experiments are currently restricted to magnetoassociation. Here we model realistic production of a quantum degenerate gas of stable molecules via two-photon photoassociation of Bose-condensed atoms. An adiabatic change of the laser frequency converts the initial atomic condensate almost entirely into stable molecular condensate, even for low-intensity lasers. Results for dipolar LiNa provide an upper bound on the necessary photoassociation laser intensity for alkali-metal atoms ~$$30 W/cm2{}^{2}2, indicating a feasible path to quantum degenerate molecules beyond magnetoassociation.
Quantum degenerate molecular gases are of interest for the unique level of control they offer over chemical interactions and processes. To reach the quantum degenerate regime, these molecular gases must be cooled to ultracold temperatures, typically on the order of 100 nanoKelvins. Unlike atoms, with a few-level system that facilitates cooling, molecules represent a many-level system, which makes these temperatures experimentally difficult to achieve. As a result, experiments have turned to photoassociation and Feshbach resonance as shortcuts to form ultracold molecules from already ultracold atoms. Photoassociation and Feshbach resonance have been utilized to successfully create stable quantum degenerate molecules, but not on a routine basis, and only for a small range of molecular species. The primary focus of this thesis will be to study photoassociation and Feshbach resonance, and investigate possible routes to more efficient long-lived quantum degenerate molecule formation. We will also investigate realistic limiting conditions to open the possibility to more routine molecules, and to molecular species that are currently inaccessible. Overall, we find combined photoassociation and Feshbach resonance are viable schemes for efficiently creating quantum degenerate molecules, under realistic restrictions such as low laser intensity, narrow Feshbach resonance, and strong elastic collisions. As the techniques to create quantum degenerate molecules become more robust and experimentally available, the creation of colder, larger, and more long-lived samples will facilitate study of these molecules, and spur development into new applications.
Photoassociation and the Feshbach resonance are, in principle, feasible means for creating a molecular Bose-Einstein condensate from an already-quantum-degenerate gas of atoms; however, mean-field shifts and irreversible decay place practical constraints on the efficient delivery of stable molecules using either mechanism alone. We therefore propose Feshbach-stimulated Raman photoproduction, i.e., a combination of magnetic and optical methods, as a means to collectively convert degenerate atoms into a stable molecular condensate with near-unit efficiency.
We consider two-color heteronuclear photoassociation of a dual-species Bose-Einstein condensate into a Bose-Einstein condensate of dipolar molecules in the J=1J=1J=1 vibronic ground state, where a free-ground laser couples atoms directly to the ground state and a free-bound laser couples the atoms to an electronically excited state. This problem raises an interest because heteronuclear photoassociation from atoms to near-ground-state molecules is limited by the small size of the target state. Nevertheless, the addition of the electronically excited state creates a second pathway for creating molecules in the vibronic ground state, leading to quantum interference between direct photoassociation and photoassociation via the excited molecular state, as well as a dispersivelike shift of the free-ground resonance position. Using LiNa as an example, these results are shown to depend on the detuning and intensity of the free-bound laser, as well as the semiclassical size of both molecular states. Whereas strong enhancement enables saturation of the free-ground transition, coherent conversion from a two-species condensate of atoms to a condensate of dipolar molecules in the vibronic ground state is only possible for a limited range of free-bound detunings near resonance.
Although photoassociation and the Feshbach resonance are feasible means in principle for creating a molecular Bose–Einstein condensate (MBEC) from an already quantum-degenerate gas of atoms, collision-induced mean-field shifts and irreversible decay place practical constraints on the efficient Raman delivery of stable molecules. Focusing on stimulated Raman adiabatic passage, we propose that the efficiency of both mechanisms for producing a stable MBEC can be improved by treating the density of the initial atom condensate as an optimization parameter.
Photoassociation is a process by which two cold, trapped atoms can be optically excited during a collision to make a vibrational level of an excited electronic state of a molecular dimer. High-resolution photoassociation spectra are now well-known for most alkali dimers. The upper level normally decays by spontaneous emission to a number of final molecular levels, bound and unbound. A laser of a second color can be used to stimulate a transition from the upper level to a particular ground state vibrational level. Such a Raman photoassociation process can be used to form translationally cold molecules in a cold atomic gas or a Bose-Einstein condensate. Coupled channels scattering calculations show that the collisional rate coefficient for coherent production of molecules in specific target states, >10−10cm3/s,> 10^{-10} cm^{3}/s,>10−10cm3/s, can greatly exceed the rate coefficient for forming products due to excited state spontaneous decay. This implies the feasibility of rapid coherent conversion of atom pairs in a condensate to molecules on a time scale short compared to the trap oscillation time. The untrapped molecules can form a coherent molecular beam. We will examine the prospects for the experimental realization of photoassociative molecule formation in cold alkali gases or condensates.
Summary form only given. Laser cooling and trapping of atoms has enabled some of the most exciting recent advances in atomic physics, including the achievement of Bose-Einstein condensation (BEC). Efforts are now underway to trap ultracold molecules in order to study chemical reactions and to investigate BEC of larger particles. In the atomic BEC experiments, the atoms are cooled to sub-/spl mu/K temperatures so the energy spread of the atoms which are not in the condensate is small (/spl les/20 kHz) and that of the condensate itself is zero. Therefore, a quantum degenerate gas enables an unprecedented level of spectroscopic precision. We report two-photon photoassociation of quantum degenerate /sup 7/Li atoms into the least-bound vibrational level of the ground-state triplet potential of /sup 7/Li/sub 2/. These molecules are magnetically trappable by virtue of their electronic magnetic moment.