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arXiv:1301.1143 · Physical Review A

Enhancing photoassociation rates by nonresonant-light control of shape resonances

Rosario González‐Férez, Christiane P. Koch

Published Dec 26, 2012• 27 citations
arXivHTMLPDF

Abstract

Photoassociation, assembling molecules from atoms using laser light, is limited by the low density of atom pairs at sufficiently short interatomic separations. Here we show that nonresonant light with intensities of the order of ${10}^{10}\phantom{\rule{0.16em}{0ex}}$W/cm${}^{2}$ modifies the thermal cloud of atoms, enhancing the Boltzmann weight of shape resonances and pushing scattering states below the dissociation limit. This leads to an enhancement of photoassociation rates by several orders of magnitude and opens the way to significantly larger numbers of ground-state molecules in a thermal ensemble than achieved so far.

DOI
10.1103/physreva.86.063420

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Photoassociation, assembling molecules from atoms using laser light, is limited by the low density of atom pairs at sufficiently short interatomic separations. Here we show that nonresonant light with intensities of the order of 1010{10}^{10}\phantom{\rule{0.16em}{0ex}}1010W/cm2{}^{2}2 modifies the thermal cloud of atoms, enhancing the Boltzmann weight of shape resonances and pushing scattering states below the dissociation limit. This leads to an enhancement of photoassociation rates by several orders of magnitude and opens the way to significantly larger numbers of ground-state molecules in a thermal ensemble than achieved so far.
A (diatomic) shape resonance is a metastable state of a pair of colliding atoms quasi-bound by the centrifugal barrier imposed by the angular momentum involved in the collision. The temporary trapping of the atoms' scattering wavefunction corresponds to an enhanced atom pair density at low interatomic separations. This leads to larger overlap of the wavefunctions involved in a molecule formation process such as photoassociation, rendering the process more efficient. However, for an ensemble of atoms, the atom pair density will only be enhanced if the energy of the resonance comes close to the temperature of the atomic ensemble. Herein we explore the possibility of controlling the energy of a shape resonance by shifting it toward the temperature of atoms confined in a trap. The shifts are imparted by the interaction of non-resonant light with the anisotropic polarizability of the atom pair, which affects both the centrifugal barrier and the pair's rotational and vibrational levels. We find that at laser intensities of up to 5×1095\times 10^{9}5×109 W/cm2^22 the pair density is increased by one order of magnitude for 87^{87}87Rb atoms at 100μ100 μ100μK and by two orders of magnitude for 88^{88}88Sr atoms at 20μ20 μ20μK.
In this work, the coherence properties of the matter is studied in the frame of photoassociation of ultracold alkali atoms by using short and ultrashort laser pulses. Ultracold can be described with temperatures below 100 microK. When energy approaches the ultracold regime, quantum properties of matter becomes visible. In this regime matter such as atoms and molecules show wave properties. Coherent control employs the wave properties of matter to steer a physical process toward a desired target. It can be implemented with coherent radiation such as laser light. In particular, femtosecond laser pulses can be shaped. They thus have become a standard tool for coherent control. Since matter shows its wave properties most clearly at ultralow temperatures, ultracold matter represents the perfect object for coherent control. In the other hand using incoherent fields on ultracold matter does not give us good opportunities to drive quantum properties of it. In this work, it is aimed to bring together ultracold and ultrafast regimes in the frame of photoassociation. Photoassociation, excitation of two colliding atoms by laser light creates very weakly bound molecules. In the first part of this study, femtosecond photoassociation experiments are simulated. In these experiments and simulations, the broad spectrum of the femtosecond pulses addressing both atomic and molecular transitions is manipulated in a way to prevent the atomic transitions and to promote the molecular transitions. Then the effect of chirp and the effect of additional phase to the pulse are examined. Excited and ground state population are monitored by carrying out quantum dynamical simulations. The driving ultrafast dipole dynamics are presented. The photoassociation rate is limited by the low initial atomic pair density at inter-nuclear separations where photoassociation is feasible. In the second part of this study, a new scheme is proposed in order to manage this low pair density by manipulating the shape resonances of the initial atom pair. A shape resonance which is a metastable state occurs when some part of the wavefunction of partial waves with J > 0 trapped by a rotational barrier shows a bound structure in the closer internuclear distances where the rest of it shows a scattering wavefunction behavior. Most of the shape resonances in alkaline and alkaline earth metals occur typically at temperatures of a few milli-Kelvin. Therefore, the thermal weight of a shape resonance at photoassociation temperatures is quite small. By applying a non-resonant laser to the system the energy of the resonant state is brought close to the energies those corresponding to the photoassociation temperatures. Thus, the thermal weight of a shape resonance is amplified and initial pair density is enhanced. This effect is studied in both adiabatic and non-adiabatic time scales with respect to the rotational period of the system, intensity effects on the resonance energy and lifetime are presented.
Ultracold photoassociation is a process in which two cold atoms combine to form a molecule. This process is crucially dependent on the atom pair density at close distance termed the photoassociation window. We explore the possibilities for increasing the pair density at the photoassociation window by using a prepulse to accelerate the pairs of atoms at large interatomic separation toward each other. We show that the signal of a subsequent photoassociation pulse could be enhanced by a factor of one to two orders of magnitude with respect to the conventional continuous wave experiment. For neutral encounters on the ground potential surface which scales as ${R}^{\ensuremath{-}6}$ the acceleration becomes negligible. The electronic excited state potentials scale for homonuclear $S\ensuremath{\rightarrow}P$ transitions more favorably as ${R}^{\ensuremath{-}3}$. A possible pump-dump mechanism for acceleration, excites a pair of atoms at large distance employing the natural acceleration on the excited state. Then a dump pulse moves the population back to the ground surface. By controlling the phase and the amplitude of the light field this scenario can be optimized. In addition the momentum partitioned between the ground and excited surfaces can also be controlled. The possibility for pure quantum light-induced acceleration due to a gradient of the transition dipole is analyzed. Significant acceleration can be obtained only for pulses with intensities above 1014W∕cm2{10}^{14}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}1014W∕cm2 and pulse duration of 10ps10\phantom{\rule{0.3em}{0ex}}\mathrm{ps}10ps.
We investigate theoretically the molecular yield in photoassociation of Bose-Einstein condensed sodium atoms for light intensities of the order of and above those applied in a recent experiment. Our results show that the rate at which ground-state molecules may be formed saturates at high light intensities whereas the loss rate of condensate atoms does not. This is caused by the opposing roles of the short- and long-range pair correlations present near resonance under the influence of the laser and is crucial for the development of efficient photoassociation procedures in a condensate.
In this thesis I present the results of photoassociation measurements in ensembles of atomic calcium over an intensity range of below 1 W/cm2 up to 600 W/cm2. The temperature of the atoms was reduced to 1 μK by laser and evaporative cooling. Afterwards the two most-weakly bound states in the excited molecular potentials that dissociate to the asymtote 3P1+1S0 have been investigated regarding the shape and absolute rate of the resonances. The investigation showed that the measured rates differ by more than an order of magnitude compared to theoretical calculations. The predictions are based on a scattering formalism by Bohn & Julienne and wave functions derived from coupled-channel calculations. The shape of the resonances, the width in particular, agrees well with the numerical calculations. Especially the power broadening at high intensity is reproduced by the experiment. Further the light shift introduced by the photoassociation laser has been measured which also differs from the predictions. In the further course of the thesis the numerical simulations were improved by considering additional influences like the exact dependence of the Franck-Condon density and the light shift of the photoassociation laser as a function of the collision energy. Additionally the modeling of the experimental setup with a special emphasis on the volume of the optical trap and thus the density of the atomic ensemble was improved and the influence of varying trap depth and photoassociation duration has been studied. Investigating possible explanations for the discrepancy of the measured rates compared to theory, I show that by a modification of the coupling parameter and the spontaneous decay rate of the molecular state the rates measured in the experiment can be reproduced theoretically, with the restriction that at high intensity the calculated line shape no longer agrees with the measurement. In the last chapter an improved experimental apparatus is presented that by using an optical lattice suppresses thermal broadening and thus simplifies the analysis substantially.
We derive ultracold atom-atom photoassociation line shapes valid for intense light fields and investigate laser power effects in sodium and rubidium photoassociation to the purely long-range ${0}_{g}^{\ensuremath{-}}$ symmetry state. We consider intensities up to a few hundreds W/cm2,{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2},W/cm2, a strongly saturating intensity for typical transitions of experimental interest. For these intensities the ${0}_{g}^{\ensuremath{-}}$ rotational spectrum is still well resolved; however, it is essential to couple the photoassociation resonance to both s- and d-wave ground-state channels. A low-energy d-wave shape resonance can have a profound effect on the line shape. Understanding the line shape is essential for precision spectroscopic analysis and could improve the extraction of ground-state scattering properties such as scattering lengths.