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Optics Express

Complete population transfer to and from a continuum and the radiative association of cold Na atoms to produce translationally cold Na2 molecules in specific vib-rotational states

Amichay Vardi, M. Shapiro, Klaas Bergmann

Published Jan 18, 1999• 33 citations
Publisher

Abstract

We demonstrate the feasibility of a laser induced complete population transfer to and from a continuum of states. We study the two-photon dissociation of v = 28; J = 1,...,10 sodium dimers. We demonstrate that using just a pair of "counter intuitively" ordered pulses we can dissociate 100% of the molecules in an ensemble. The scheme is shown to be stable with respect to the initial choice of rotational level and to fluctuations in the laser frequency and intensity. We also study the reverse phenomenon of complete population transfer from the continuum. We perform calculations on the radiative association of Na atoms to form the Na2 molecule in specific vib-rotational states. It is shown that two pulses of 20 nsec duration and as little as 6 MW/cm 2 peak power can photo-associate more than 98% of the atoms within a (pulse and velocity determined) relative effective distance, to yield Na2 molecules in the chosen v = 28; J = 10 vib-rotational state. This means that given a density of 10 16 atoms/cm 3 and a temperature of 7K, a 10Hz pulsed laser source of the above parameters can con- vert half of all the Na atoms in the ensemble to v = 28; J = 10 Na2 molecules within 15 seconds of operation.

DOI
10.1364/oe.4.000091

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arXiv:quant-ph/0302021•Feb 3, 2003•0 citations
We demonstrate the feasibility of a laser induced complete population transfer to and from a continuum of states. We study the two-photon dissociation of v = 28; J = 1,...,10 sodium dimers. We demonstrate that using just a pair of "counter intuitively" ordered pulses we can dissociate 100% of the molecules in an ensemble. The scheme is shown to be stable with respect to the initial choice of rotational level and to fluctuations in the laser frequency and intensity. We also study the reverse phenomenon of complete population transfer from the continuum. We perform calculations on the radiative association of Na atoms to form the Na2 molecule in specific vib-rotational states. It is shown that two pulses of 20 nsec duration and as little as 6 MW/cm 2 peak power can photo-associate more than 98% of the atoms within a (pulse and velocity determined) relative effective distance, to yield Na2 molecules in the chosen v = 28; J = 10 vib-rotational state. This means that given a density of 10 16 atoms/cm 3 and a temperature of 7K, a 10Hz pulsed laser source of the above parameters can con- vert half of all the Na atoms in the ensemble to v = 28; J = 10 Na2 molecules within 15 seconds of operation.
A time dependent theory for radiative recombination induced by strong pulses is presented. Analytic solutions in the adiabatic limit are derived and found to be in excellent agreement with exact numerical solutions. Both the pump-before-dump “intuitive” and dump-before-pump “counter-intuitive” schemes are considered. Resonantly enhanced two-photon recombination of ultracold atoms is shown to be an efficient mechanism for the production of ultracold molecules. We have performed detailed calculations on the radiative recombination of cold Na atoms by short laser pulses. Our calculations show that, per pulse, it is possible for up to 97% of all head-on Na-Na colliding pairs to end up as v=0, J=0 translationally cold Na2 molecules. We show that these findings, translated to thermally cooled ensemble conditions, mean that the fraction of Na atoms at μKelvin which can be recombined by a pulse of 20 ns duration and 108 W/cm2 peak intensity, to form J=0 molecules is 6×10−6 per pulse. With the above parameters, a laser operating at 100 Hz can convert half of an ensemble of cold atoms to cold molecules in ∼25 min. The efficiency of the process can be increased by going to longer pulses of lower intensity, by going to lower temperatures or by increasing the density of the ensemble. In particular, the “counter-intuitive” scheme which allows for use of longer pulses of lower intensities, with no spontaneous emission losses, considerably increases the yield.
Abstract By utilizing the time-dependent wavepacket method, we studied the population transfer between the electronic states of the Na 2 molecule driven by femtosecond laser pulses. Three electronic states, X 1 Σ g + , A 1 Σ u + and 2 1 Π g , are taken to be the initial, the intermediate and the target states, respectively. Two classes of calculations are performed for comparison: one is to invoke the rotating wave approximation (RWA), and the other is more accurate calculations without consideration of RWA (non-RWA). It is found that for this three-state-model, the RWA fails to describe the accurate population transfer process in femtosecond-pulse fields and that the adiabatic passage is hard to be constructed in the non-RWA calculations. Based on the non-RWA calculations, we determined a set of laser parameters, including the peak intensity, detuning, pulse duration and time delay, for efficient population transfer.
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.
A theory is developed and applied to the study of opportunities and specific features of coherent control of four-wave mixing as well as of the accompanying processes in the continuous-wave regime, which involve transitions between bound and free quantum states. Such opportunities become feasible through constructive and destructive interference of quantum pathways. Two coupling schemes of practical importance are investigated. In the first, a ladder energy level scheme, fully-resonant sum-frequency nonlinear-optical generation of short-wavelength radiation driven by several strong fields is investigated. The relaxation processes as well as absorption of the fundamental and generated radiations, which play an important role, are taken into consideration. It is shown that the generation output can be considerably increased through the appropriate adjustment of several laser-induced continuum structures. In the second, a folded scheme, a possible control of two-photon dissociation (Lambda-scheme) using auxiliary laser radiation applied to the adjacent bound-free transition (V-configuration) is investigated. Besides dissociation, the proposed method enables one to control population transfer between two upper discreet levels via the lower-energy dissociation continuum, while direct transition between these states is not allowed. The opportunities of manipulating these processes as well as of four-wave-mixing-based spectroscopy are explored both analytically and through a numerical simulation for Na_2 dimers.