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arXiv:0904.0225 · Physical Review A

Demonstrating coherent control in R85b2 using ultrafast laser pulses: A theoretical outline of two experiments

Hugo E. L. Martay, David J. McCabe, Duncan G. England, Melissa E. Friedman, Jovana S. Petrovic, Ian A. Walmsley

Published Sep 3, 2009• 10 citations
arXivHTMLPDF

Abstract

Calculations relating to two experiments that demonstrate coherent control of preformed rubidium-85 molecules in a magneto-optical trap using ultrafast laser pulses are presented. The two experiments are a step toward the stabilization of ultracold rubidium dimers using ultrafast lasers. In the first experiment, it is shown that preassociated molecules in an incoherent mixture of states can be made to oscillate coherently using a single ultrafast pulse. A mechanism that can transfer molecular population to more deeply bound vibrational levels is used in the second. Optimal parameters of the control pulse are presented for the application of the mechanism to molecules in a magneto-optical trap. The calculations make use of an experimental determination of the initial state of molecules photoassociated by the trapping lasers in the magneto-optical trap and use shaped pulses consistent with a standard ultrafast laser system. The experiment's purpose is to demonstrate and evaluate the use of ultrafast shaped pulses to manipulate ultracold rubidium dimers with a view to the eventual stabilization of the molecules.

DOI
10.1103/physreva.80.033403

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Physical Review A•Dec 8, 2009•26 citations
Calculations relating to two experiments that demonstrate coherent control of preformed rubidium-85 molecules in a magneto-optical trap using ultrafast laser pulses are presented. The two experiments are a step toward the stabilization of ultracold rubidium dimers using ultrafast lasers. In the first experiment, it is shown that preassociated molecules in an incoherent mixture of states can be made to oscillate coherently using a single ultrafast pulse. A mechanism that can transfer molecular population to more deeply bound vibrational levels is used in the second. Optimal parameters of the control pulse are presented for the application of the mechanism to molecules in a magneto-optical trap. The calculations make use of an experimental determination of the initial state of molecules photoassociated by the trapping lasers in the magneto-optical trap and use shaped pulses consistent with a standard ultrafast laser system. The experiment's purpose is to demonstrate and evaluate the use of ultrafast shaped pulses to manipulate ultracold rubidium dimers with a view to the eventual stabilization of the molecules.
The establishment of robust laser-cooling techniques for the formation of ultracold atoms has provided a test-bed for low-temperature science, with scattering events changing character from incoherent thermal interactions to coherent quantum mechanical events. A natural extension is the pursuit of ultracold molecules in prescribed low-energy internal states. Atomic cooling techniques, however, do not generalize to the molecular regime due to the complex energy-level structure afforded by its extra degrees of motion. An indirect approach to ultracold molecule formation - photoassociation using ultrafast laser pulses - is the focus of this thesis. A broadband field associates atom pairs into a localized molecular wavepacket that evolves within the attractive excited-state potential. A suitably timed dump pulse may thus be applied to stabilize population into deeply bound ground vibrational states. This strategy may be generalized to any species whose spectroscopy matches the pulse spectrum, and offers a coherent population transfer scheme that does not require precise knowledge of the system. This thesis presents experiments using high-energy photoassociation pulses applied to ultracold rubidium atoms. The pulses quench the background ground-state molecular population but form bound dimers within the excited state. A pump-probe experiment was designed to chart the excited-state dynamics; however, the oscillations predicted by theoretical calculations were not evident in the molecular signal. The nature of the dynamics is expected to be strongly dependent on the initial state of the atom pairs addressed by the ultrafast pulse: a bound molecular population provides an additional candidate to free atoms. A spectroscopic measurement characterizes these bound molecules and identifies their formation mechanism. A subsequent experiment provides evidence that the predominant contributor to the pump-probe signal is the unbound initial population. The consequences with regard to both the observation of excited-state dynamics and the subsequent application of a dump pulse are discussed.
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.
We report on coherent control of excitation processes of translationally ultracold rubidium dimers in a magneto-optical trap by using shaped femtosecond laser pulses. Evolution strategies are applied in a feedback loop in order to optimize the photoexcitation of the Rb2{\mathrm{Rb}}_{2}Rb2​ molecules, which subsequently undergo ionization or fragmentation. A superior performance of the resulting pulses compared to unshaped pulses of the same pulse energy is obtained by distributing the energy among specific spectral components. The demonstration of coherent control to ultracold ensembles opens a path to actively influence fundamental photoinduced processes in molecular quantum gases.
An experimental pump-probe study of the photoassociative creation of translationally ultracold rubidium molecules is presented together with numerical simulations of the process. The formation of loosely bound excited-state dimers is observed as a first step toward a fully coherent pump-dump approach to the stabilization of Rb2{\text{Rb}}_{2}Rb2​ into its lowest ground vibrational states. The population that contributes to the pump-probe process is characterized and found to be distinct from a background population of preassociated molecules.
We experimentally investigate various processes present in the photoassociative interaction of an ultracold atomic sample with shaped femtosecond laser pulses. We demonstrate the photoassociation of pairs of rubidium atoms into electronically excited, bound molecular states using spectrally cut femtosecond laser pulses tuned below the rubidium D1 or D2 asymptote. Time-resolved pump-probe spectra reveal coherent oscillations of the molecular formation rate, which are due to coherent transient dynamics in the electronic excitation. The oscillation frequency corresponds to the detun-ing of the spectral cut position to the asymptotic transition frequency of the rubidium D1 or D2 lines, respectively. Measurements of the molecular photoassociation signal as a function of the pulse energy reveal a non-linear dependence and indicate a non-perturbative excitation process. Chirping the association laser pulse allowed us to change the phase of the coherent transients. Furthermore, a signature for molecules in the electronic ground state is found, which is attributed to molecule formation by femtosecond photoassociation followed by spontaneous decay. In a subsequent article [A. Merli et al., submitted] quantum mechanical calculations are presented, which compare well with the experimental data and reveal further details about the observed coherent transient dynamics.
We experimentally investigate various processes present in the photoassociative interaction of an ultracold atomic sample with shaped femtosecond laser pulses as an detailed extension of previous work [W. Salzmann et al., Phys. Rev. Lett. 100, 233003 (2008)]. We demonstrate the photoassociation of pairs of rubidium atoms into electronically excited, bound molecular states using spectrally cut femtosecond laser pulses tuned below the rubidium D1{D}_{1}D1​ or D2{D}_{2}D2​ asymptote. Time-resolved pump-probe spectra reveal oscillations of the molecular formation rate, which are due to coherent transient dynamics in the electronic excitation. The oscillation frequency corresponds to the detuning of the spectral cut position to the asymptotic transition frequency of the rubidium D1{D}_{1}D1​ or D2{D}_{2}D2​ lines, respectively. Measurements of the molecular photoassociation signal as a function of the pulse energy reveal a nonlinear dependence and indicate a nonperturbative excitation process. Chirping the association laser pulse allowed us to change the phase of the coherent transients. Furthermore, a signature for molecules in the electronic ground state is found, which is attributed to molecule formation by femtosecond photoassociation followed by spontaneous decay. In a subsequent article [A. Merli et al., Phys. Rev. A 80, 063417 (2009)] quantum mechanical calculations are presented, which compare well with the experimental data and reveal further details about the observed coherent transient dynamics.