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Physical Review A

Laser-controlled rotational cooling of Na2 based on exceptional points

Viatcheslav Kokoouline, Adam Wearne, R. Lefèbvre, Osman Atabek

Published Sep 6, 2013• 6 citations
Publisher

Abstract

Exceptional points (EPs) corresponding to resonance coalescence (i.e., complex energy degeneracy and identical wave functions) occur in many areas of non-Hermitian physics and, in particular, in laser-induced molecular dynamics for specific choices of two control parameters. We have previously shown [Atabek, et al., Phys. Rev. Lett. 106, 173002 (2011)] how these control parameters, namely, the wavelength and the intensity of the external field, have to be tuned to take advantage of EPs for selective vibrational transfers within a reduced one-dimensional model describing a diatomic molecule with frozen rotation. Moreover, the possibility offered by such transfers to adiabatically transport all the vibrational population to the ground $v=0$ level has been presented as a realistic vibrational cooling strategy with an entropy flow toward the field-induced dissociative channel. The purpose of the present article is twofold: (i) Extend the model to a full three-dimensional quantum description of the rotating molecule and discuss the existence, determination, and role of EPs involving rovibrational resonances; (ii) examine the possibility for a further challenging step in obtaining ultracold molecules through combined vibrational and rotational laser control dynamics, aiming at total purification for reaching the ground ($v=J=0$) rovibrational level. The illustrative example is the ${\mathrm{Na}}_{2}$ molecule for which translationally cold species have experimentally been obtained.

DOI
10.1103/physreva.88.033408

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The Journal of Chemical Physics•Jun 22, 1996•184 citations
Exceptional points (EPs) corresponding to resonance coalescence (i.e., complex energy degeneracy and identical wave functions) occur in many areas of non-Hermitian physics and, in particular, in laser-induced molecular dynamics for specific choices of two control parameters. We have previously shown [Atabek, et al., Phys. Rev. Lett. 106, 173002 (2011)] how these control parameters, namely, the wavelength and the intensity of the external field, have to be tuned to take advantage of EPs for selective vibrational transfers within a reduced one-dimensional model describing a diatomic molecule with frozen rotation. Moreover, the possibility offered by such transfers to adiabatically transport all the vibrational population to the ground v=0v=0v=0 level has been presented as a realistic vibrational cooling strategy with an entropy flow toward the field-induced dissociative channel. The purpose of the present article is twofold: (i) Extend the model to a full three-dimensional quantum description of the rotating molecule and discuss the existence, determination, and role of EPs involving rovibrational resonances; (ii) examine the possibility for a further challenging step in obtaining ultracold molecules through combined vibrational and rotational laser control dynamics, aiming at total purification for reaching the ground (v=J=0v=J=0v=J=0) rovibrational level. The illustrative example is the Na2{\mathrm{Na}}_{2}Na2​ molecule for which translationally cold species have experimentally been obtained.
With a specific choice of laser parameters resulting in a so-called exceptional point (EP) in the wavelength-intensity parameter plane, it is possible to produce the coalescence of two Floquet resonances describing the photodissociation of the Na(2) molecule, which is one of the candidates for the formation of samples of translationally cold molecules. By appropriately tuning laser parameters along a contour encircling the exceptional point, the resonances exchange their quantum nature. Thus a laser-controlled transfer of the probability density from one field-free vibrational level to another is achieved through adiabatic transport involving these resonances. We propose an efficient scenario for vibrational cooling of Na(2) referring to cascade transfers involving multiple EPs and predicted to be robust up to a 78% rate against laser-induced dissociation.
Laser control of complete vibrational transfer in Na2_22​ using resonance coalescence
With a specific choice of laser parameters resulting into a so-called exceptional point in the wavelength-intensity plane, it is possible to produce the coalescence of two Floquet resonances describing the photodissociation of the molecule Na2_22​, which is one of the candidates for molecular cooling. Appropriately tuning laser parameters, following a contour around the exceptional point, the resonances exchange their labels. This represents a laser control of the vibrational transfer from one field-free state to another, through an adiabatic transport involving these resonances. The proportion of undissociated molecules at the end of the pulse is checked through Floquet adiabatic theory. A vibrational cooling scenario can be proposed based on a complete vibrational transfer which is predicted, with only 20 percent of molecules undergoing dissociation.
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).
Feshbach resonances play a major role in translationally cold-molecule preparation. In this context, their laser control is of crucial importance. This work is devoted to the depiction of some basic mechanisms of such a control using intense, short laser pulses and referring to nonlinear multiphoton processes. Our goal is to adiabatically transport a Feshbach resonance onto a zero-width resonance, the characteristics of which have already been discussed in the literature. Three processes are then addressed: (i) during the rise of the pulse and its plateau, the preparation of a so-called laser bound molecule (LBM) still stable, but structurally different from the standard chemically bound molecule; (ii) during the pulse switching off, an adiabatic transport of this LBM on a very few excited vibrational levels, and (iii) concomitantly, a filtration strategy to photodissociate all these levels except one, giving thus rise to but a single field-free excited vibrational state. With or without an eventual stimulated Raman adiabatic passage technique to bring all the population to the ground rovibrational state, this opens an alternate for a full optical control of ultracold-molecule formation. The illustrative example, offering the potentiality to be transposed to other diatomics, is H2+{\mathrm{H}}_{2}^{+}H2+​.
In molecular photodissociation, some specific combinations of laser parameters (wavelength and intensity) lead to unexpected zero-width resonances (ZWRs) with, in principle, infinite lifetimes. Their potential to induce basic quenching mechanisms has recently been devised in the laser control of vibrational cooling through filtration strategies [O. Atabek et al., Phys. Rev. A 87, 031403(R) (2013)]. A full quantum adiabatic control theory based on the adiabatic Floquet Hamiltonian is developed to show how a laser pulse could be envelope-shaped and frequency-chirped so as to protect a given initial vibrational state against dissociation, taking advantage of its continuous transport on the corresponding ZWR all along the pulse duration. As compared with previous control scenarios that actually suffered from nonadiabatic contamination, drastically different and much more efficient filtration goals are achieved. A semiclassical analysis helps us to find and interpret a complete map of ZWRs in the laser parameter plane. In addition, the choice of a given ZWR path, among the complete series identified by the semiclassical approach, turns out to be crucial for the cooling scheme, targeting a single vibrational state population left at the end of the pulse, while all others have almost completely decayed. The illustrative example, which has the potential to be transposed to other diatomics, is Na2{\mathrm{Na}}_{2}Na2​ prepared by photoassociation in vibrationally hot but translationally and rotationally cold states.
A novel scheme is proposed for sequential cooling of rotation, translation, and vibration of molecules. More generally, this scheme manipulates and controls the states and energies of molecules. The scheme, while somewhat complex, is simpler and more feasible than simply providing a large number of synchronously but independently tunable lasers. The key component is a multiple single frequency laser (MSFL) in which a single narrow band pump laser generates an ensemble of resonant ‘‘stimulated Raman’’ (RSR) sidebands (subsequently amplified and selected) in a sample of the molecules to be cooled. Starting with a relatively cold molecular sample (e.g., a supersonic beam of Cs2), the rotation of molecules is cooled by sequential application of P branch electronic transition frequencies transverse to the molecular beam beginning at higher rotational angular momentum J. Then translation of molecules is cooled by application of multiple low J, P, and R branch transition frequencies which counterpropagate with the molecular beam and are synchronously chirped over their Doppler profiles. Finally, vibration of molecules is cooled by blocking the R(0) line of the 0–0 band. Only this specific order of rotation–translation–vibration appears feasible (using molecules produced by photoassociation of ultracold atoms avoids the requirement for translational cooling). Each step employs true dissipative cooling (i.e., reduction of system entropy in three degrees of freedom) by spontaneous emission and should yield a large translationally cold sample of molecules in the lowest (v=0, J=0) level of the ground electronic state, suitable for studies such as molecule trapping, ‘‘molecule optics,’’ or long range intermolecular states.