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arXiv:physics/0406100 · Physical Review A

Rotational cooling of heteronuclear molecular ions with Σ1 , Σ2 , Σ3 , and Π2 electronic ground states

Ivan R. Vogelius, Lars Bojer Madsen, Michael Drewsen

Published Nov 24, 2004• 43 citations
arXivHTMLPDF

Abstract

The translational motion of molecular ions can be effectively cooled sympathetically to translational temperatures below $100\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ in ion traps through Coulomb interactions with laser-cooled atomic ions. The rovibrational degrees of freedom, however, are expected to be largely unaffected during translational cooling. We have previously proposed schemes for cooling of the internal degrees of freedom of such translationally cold but internally hot heteronuclear diatomic ions in the simplest case of $^{1}\ensuremath{\Sigma}$ electronic ground-state molecules. Here we present a significant simplification of these schemes and make a generalization to the most frequently encountered electronic ground states of heteronuclear molecular ions: $^{1}\ensuremath{\Sigma}$, $^{2}\ensuremath{\Sigma}$, $^{3}\ensuremath{\Sigma}$, and $^{2}\ensuremath{\Pi}$. The schemes are relying on one or two laser-driven transitions with the possible inclusion of a tailored incoherent far-infrared radiation field.

DOI
10.1103/physreva.70.053412

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The translational motion of molecular ions can be effectively cooled sympathetically to translational temperatures below 100mK100\phantom{\rule{0.3em}{0ex}}\mathrm{mK}100mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The rovibrational degrees of freedom, however, are expected to be largely unaffected during translational cooling. We have previously proposed schemes for cooling of the internal degrees of freedom of such translationally cold but internally hot heteronuclear diatomic ions in the simplest case of 1\ensuremathΣ^{1}\ensuremath{\Sigma}1\ensuremathΣ electronic ground-state molecules. Here we present a significant simplification of these schemes and make a generalization to the most frequently encountered electronic ground states of heteronuclear molecular ions: 1\ensuremathΣ^{1}\ensuremath{\Sigma}1\ensuremathΣ, 2\ensuremathΣ^{2}\ensuremath{\Sigma}2\ensuremathΣ, 3\ensuremathΣ^{3}\ensuremath{\Sigma}3\ensuremathΣ, and 2\ensuremathΠ^{2}\ensuremath{\Pi}2\ensuremathΠ. The schemes are relying on one or two laser-driven transitions with the possible inclusion of a tailored incoherent far-infrared radiation field.
The translational motion of molecular ions can be effectively cooled sympathetically to temperatures below 100 mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The distribution of internal rovibrational states, however, gets in thermal equilibrium with the typically much higher temperature of the environment within tens of seconds. We consider a concept for rotational cooling of such internally hot, but translationally cold, heteronuclear diatomic molecular ions. The scheme relies on a combination of optical pumping from a few specific rotational levels into a "dark state" with redistribution of rotational populations mediated by blackbody radiation.
Working with MgH+molecular ions in a linear Paul trap, we routinely cool their translational degrees of freedom by sympathetic cooling with Doppler laser cooled Mg+ions. Giving the time for the molecules to equilibrate internally to room temperature blackbody radiation, the vibrational degree of freedom is frozen out, leaving only the rotational degree of freedom to be cooled. We have implemented a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ions, using a scheme based on excitation of a single rovibrational transition. This technique is generalizable to any diatomic polar molecular ion, given an appropriate mid-infrared laser source such as a quantum cascade laser.
Stationary molecules in well-defined internal states are of broad interest in both physics and chemistry. Through high-resolution spectroscopy, fundamental physics can be tested and lead to, e.g., improved values of the electron-to-proton mass ratio [1], new boundaries on the electron electric dipole moment [2] and observation of the potential evolution of the fine structure constant over time [3]. Translationally and internally cold molecules have as well been considered promising candidates for qubits in new quantum computing senarios [4], and molecular ions could in the future likely become an excellent alternative to atomic qubits in the realization of a practical ion trap based quantum computer due to favourable internal state decoherence rates. In chemistry, state prepared molecular targets are an ideal starting point for uni-molecular reactions, including coherent control of photofragmentation through the application of various laser sources [5,6]. In cold bi-molecular reactions, where the effect of even tiny potential barriers becomes significant, experiments with state prepared molecules can yield important information on the details of the potential curves of the molecular complexes [7,8,9]. Furthermore, in order to learn more about the chemistry in interstellar clouds, astrochemists can benefit greatly from direct measurements on cold reactions in laboratories [9]. Working with MgH+ molecular ions in a linear Paul trap, we routinely cool their translational degree of freedom by sympathetic cooling with Doppler laser cooled Mg+ ions. Giving the time for the molecules to equilibrate internally to the room temperature blackbody radiation, the vibrational degree of freedom will freeze out, leaving only the rotational degree of freedom to be cooled. We report here on the implementation of a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ ions [10]. The scheme is based on excitation of a single rovibrational transition [11], and it should be generalizable to any diatomic polar molecular ion, given appropriate mid-infrared laser sources such as a quantum cascade laser are available. In recent experiments, a nearly 15-fold increase in the rotational ground-state population was obtained, with the resulting ground-state population of 36,7±1,2 %, equivalent to that of a thermal distribution at about 20 K. The obtained cooling results imply that, through this technique, cold molecular-ion experiments can now be carried out at cryogenic temperatures in room-temperature set-ups. References [1] Koelemeij, J. C. J., Roth, B., Wicht, A., Ernsting, I. and Schiller, S., Phys. Rev. Lett. 98, 173002 (2007). [2] Hudson, J. J., Sauer, B. E., Tarbutt, M. R. and Hinds, E. A., Phys. Rev. Lett. 89, 023003 (2002). [3] Hudson, E. R., Lewandowski, H. J., Sawyer, B. C. and Ye, J, Phys. Rev. Lett. 96, 143004 (2006). [4] DeMille, D, Phys. Rev. Lett. 88, 067901 (2002). [5] Rice, S. A. and Zaho, M. Optical control of molecular dynamics (Wiley, New York, 2000). [6] Shapiro, M. and Brumer, P. W. Principles of the Quantum Control of Molecular Processes (Wiley, New York, 2003). [7] Willitsch, S., Bell, M. T., Gingell, A. D. and Softley, T. P., Phys. Chem. Chem. Phys. 10, 7200 ( 2008). [8] Krems, R. V., Phys. Chem. Chem. Phys. 10, 4079 (2008). [9] Smith, I. W. M., Low temperatures and cold molecules (Imperial College Press, London, 2008). [10] Staanum, P. F., Højbjerre, K., Skyt, P.S., Hansen, A. K. and Drewsen, M., Nat. Phys. 6, 271 (2010). [11] Vogelius, I. S., Madsen, L. B. and Drewsen, M., Phys. Rev. Lett. 89, 173003 (2002).
Ensembles of ultra-cold atoms, molecules and ions (both atomic and molecular) can be held in traps for increasingly long periods of time. While these trapped species remain translationally cold, for molecules the absorption of ambient black-body radiation can result in rapid thermalisation of the rotational (and vibrational) degrees of freedom. At 300 K, internal state purity is lost typically on the order of tens of seconds, inhibiting the study of quantum state selected reactions. In this paper a theoretical model is used to investigate laser-driven, blackbody-mediated, rotational cooling schemes for several (1)Σ and (2)Π diatomic species. The rotational cooling is particularly effective for DCl(+) and HCl(+), for which 92% and >99% (respectively) of the population can be driven into the rovibrational ground state. For the other systems a broadband optical pumping source (simultaneously exciting up to four transitions) is found to enhance the population that can be accumulated in the rovibrational ground state by up to 29% over that achieved when exciting a single transition. The influence of the rotational constant, dipole moments and electronic state of the diatomics on the rotational cooling achievable is also considered. An extension to polyatomic species is discussed and a combination of cold trap environments (at 77 K) and optical pumping schemes is proposed.
Sympathetic cooling of molecular ions through the Coulomb interaction with laser-cooled atomic ions is an efficient tool to prepare translationally cold molecules without, ideally, affecting the internal state of the molecular ions. However, the electric field due to the Coulomb interaction may induce rotational transitions that change the purity of initially quantum state prepared molecules. Here, we use estimates of rotational state changes in single collisions of diatomic ions with atomic ions [J. M. Berglund, M. Drewsen, and C. P. Koch, ] to determine the overall rotational excitation accumulated over the sympathetic cooling. Considering two different experimental scenarios, that of a molecular ion cotrapped with a single atomic ion and a molecular ion immersed in a Coulomb crystal of atomic ions, we also estimate the cooling time.