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arXiv:0903.0811 · Physical Review Letters

Probing Weakly Bound Molecules with Nonresonant Light

Mikhail Lemeshko, Břetislav Friedrich

Published Jul 31, 2009• 19 citations
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Abstract

We show that weakly bound molecules can be probed by "shaking" in a pulsed nonresonant laser field. The field introduces a centrifugal term which expels the highest vibrational level from the potential that binds it. Our numerical simulations applied to the Rb(2) and KRb Feshbach molecules indicate that shaking by feasible laser pulses can be used to accurately recover the square of the vibrational wave function and, by inversion, also the long-range part of the molecular potential.

DOI
10.1103/physrevlett.103.053003

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We show that weakly bound molecules can be probed by "shaking" in a pulsed nonresonant laser field. The field introduces a centrifugal term which expels the highest vibrational level from the potential that binds it. Our numerical simulations applied to the Rb(2) and KRb Feshbach molecules indicate that shaking by feasible laser pulses can be used to accurately recover the square of the vibrational wave function and, by inversion, also the long-range part of the molecular potential.
We evaluate the shifts imparted to vibrational and rotational levels of a linear molecule by a nonresonant laser field at intensities of up to 10(12) W/cm(2). Both types of shift are found to be either positive or negative, depending on the initial rotational state acted upon by the field. An adiabatic field-molecule interaction imparts a rotational energy shift which is negative and exceeds the concomitant positive vibrational shift by a few orders of magnitude. The rovibrational states are thus pushed downward in such a field. A nonresonant pulsed laser field that interacts nonadiabatically with the molecule is found to impart rotational and vibrational shifts of the same order of magnitude. The nonadiabatic energy transfer occurs most readily at a pulse duration which amounts to about a tenth of the molecule's rotational period and vanishes when the sudden regime is attained for shorter pulses. We applied our treatment to the much-studied (87)Rb(2) molecule in the last bound vibrational levels of its lowest singlet and triplet electronic states. Our calculations indicate that 15 and 1.5 ns laser pulses of an intensity in excess of 5 x 10(9) W/cm(2) are capable of dissociating the molecule due to the vibrational shift. Lesser shifts can be used to fine-tune the rovibrational levels and thereby affect collisional resonances by the nonresonant light. The energy shifts due to laser intensities of 10(9) W/cm(2) may be discernible spectroscopically, with a 10 MHz resolution.
By making use of the quantization rule of Raab and Friedrich [Phys. Rev. A 78, 022707 (2008)], we derive simple and accurate formulae for the number of rotational states supported by a weakly bound vibrational level of a diatomic molecule and the rotational constants of any such levels up to the threshold, and provide a criterion for determining whether a given weakly bound vibrational level is rotationless. The results depend solely on the long-range part of the molecular potential and are applicable to halo molecules.
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+​.
We perform a detailed quantum study of forced molecular rotation in an optical centrifuge, recently proposed by J. Karczmarek [Phys, Rev. Lett. 82, 3420 (1999)]. The approach uses strong nonresonant laser fields with chirped frequency to induce efficient rotational excitation of anisotropic molecules via a sequence of Raman transitions. Quantum calculations firstly of angular confinement (angular trapping) of a molecule in the early stages of the centrifuge evolution and secondly of the resulting rotational dissociation process are carried out herein. The trapping calculations include both angular degrees of freedom while the dissociation calculations include one vibrational and one rotation degree of freedom. Diatomic Cl2 is used as a test case. An extension of the scheme outlined by Karczmarek et al. is proposed as a method of producing molecules in a single selected J=Jz level.