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Physical Review A

Momentum control in photoassociation of ultracold atoms

Shimshon Kallush, Ronnie Kosloff

Published Nov 12, 2007• 15 citations
Publisher

Abstract

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 ${10}^{14}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$ and pulse duration of $10\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$.

DOI
10.1103/physreva.76.053408

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Physical Review A•Dec 12, 2000•107 citations
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{R}^{\ensuremath{-}6}R\ensuremath−6 the acceleration becomes negligible. The electronic excited state potentials scale for homonuclear S\ensuremath→PS\ensuremath{\rightarrow}PS\ensuremath→P transitions more favorably as R\ensuremath−3{R}^{\ensuremath{-}3}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.
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.
Bound-state molecules can be photoassociated directly from ultracold free-atom pairs by excitation to a purely repulsive electronic state. The process is explained on the basis of quantum unitarity: the initially free-scattering state is transformed by an impulsive light pulse to a deformed superposition which contains bound-state components. For pulse durations which are short compared to the ultracold dynamics, the maximal rate of photoassociation was found to be determined by the initial stationary distribution of scattering states of the atom pairs. The process was simulated for an ultracold gas of 87Rb^{87}\text{R}\text{b}87Rb with a temperature of $T=44\text{ }\ensuremath{\mu}\text{K}$ and a density of $\ensuremath{\approx}{10}^{11}\text{ }{\text{cm}}^{\ensuremath{-}3}$. Transform-limited pulses maximize the photoassociation, yielding $\ensuremath{\sim}1$ bound molecule per pulse. Coherent control calculated by a local control scheme can increase the photoassociation yield by two orders of magnitude.
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 the ultracold regime, where the interactions between atoms become quantum mechanical in nature, we can investigate the fundamental properties of matter. A natural progression from the catalogue of pioneering experiments using ultracold atoms is to extend the size of our quantum system by producing ultracold molecules in prescribed low-energy internal states. Techniques for cold molecule production are split into two methods: direct and indirect cooling. While direct cooling methods have yet to realize ultracold temperatures, collisional relaxation in the molecules leads to low internal energy states. By contrast, indirect cooling — the association of molecules from pre-cooled atoms—has produced a range of molecules at ultracold temperatures; the challenge with this technique is to control the internal state.This thesis concentrates on a technique that is complementary to those already in existence: ultrafast photoassociation. Key to this technique is the formation of time non-stationary wavepackets in the excited-state in order to improve FranckCondon overlap of the excited state with deeply bound ground-state vibrational levels. A pump-probe experiment was designed and built to demonstrate the formation of bound excited-state dimers. In this work we show that the initial state from which the wavepacket originates is of critical importance to the evolution of excited-state population. We find that the internuclear separation of the wavepacket produced in a rubidium magneto-optical trap is too large to observe coherent oscillations in the excited state. The implications of this are discussed along with recommendations for future ultrafast photoassociation experiments. Consequently, a new ultracold atom apparatus was built utilizing magnetic and dipole-force trapping to increase the density of the atomic sample; this apparatus will enable future experiments combining the exciting fields of ultracold matter and ultrafast light.
We theoretically explore photoassociation by adiabatic passage of two colliding cold 85Rb^{85}\mathrm{Rb}85Rb atoms in an atomic trap to form an ultracold Rb2{\mathrm{Rb}}_{2}Rb2​ molecule. We consider the incoherent thermal nature of the scattering process in a trap and show that coherent manipulations of the atomic ensemble, such as adiabatic passage, are feasible if performed within the coherence time window dictated by the temperature, which is relatively long for cold atoms. We show that a sequence of $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{7}$ pulses of moderate intensities, each lasting $\ensuremath{\sim}750\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$, can photoassociate a large fraction of the atomic ensemble at temperature of $100\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}$ and density of 1011atoms∕cm3{10}^{11}\phantom{\rule{0.3em}{0ex}}\text{atoms}∕{\mathrm{cm}}^{3}1011atoms∕cm3. Use of multiple pulse sequences makes it possible to populate the ground vibrational state. Employing spontaneous decay from a selected excited state, one can accumulate the molecules in a narrow distribution of vibrational states in the ground electronic potential. Alternatively, by removing the created molecules from the beam path between pulse sets, one can create a low-density ensemble of molecules in their ground rovibrational state.
Enhancement of the production of cold molecules via photoassociation is considered for the Cs2{\mathrm{Cs}}_{2}Cs2​ system. The employment of chirped picosecond pulses is proposed and studied theoretically. The analysis is based on the ability to achieve impulsive excitation which is given by the ultracold initial conditions where the nuclei are effectively stationary during the interaction with a field. The appropriate theoretical framework is the coordinate-dependent two-level system. Matching the pulse parameters to the potentials and initial conditions results in full Rabi cycling between the electronic potentials. By chirping the laser pulse, adiabatic transfer leading to the population inversion from the ground to the excited state is possible in a broad and tunable range of internuclear distance. Numerical simulations based on solving the time-dependent Schr\"odinger equation (TDSE) were performed. The simulation of the photoassociation of Cs2{\mathrm{Cs}}_{2}Cs2​ from the ground ${}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ to the excited ${0}_{g}^{\ensuremath{-}}$ state under ultracold conditions verifies the qualitative picture. The ability to control the population transfer is employed to optimize molecular formation. Transfer of population to the excited ${0}_{g}^{\ensuremath{-}}$ surface leaves a void in the nuclear density of the ground ${}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ surface. This void is either filled by thermal motion or by quantum ``pressure'' and it is the rate-determining step in the photoassociation. The spontaneous-emission process leading to cold-molecules is simulated by including an optical potential in the TDSE. Consequently, the rate of cold molecule formation in a pulsed mode is found to be larger than that obtained in a continuous-wave mode.