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arXiv:0903.4401 · Physical Review A

Photoassociation and coherent transient dynamics in the interaction of ultracold rubidium atoms with shaped femtosecond pulses. II. Theory

Andrea Merli, Frauke Eimer, Fabian Weise, Albrecht Lindinger, Wenzel Salzmann, Terry Mullins, Simone Götz, Roland Wester, Matthias Weidemüller, Ruzin Ağanoğlu, Christiane P. Koch

Published Dec 8, 2009• 31 citations
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Abstract

Photoassociation of ultracold rubidium atoms with femtosecond laser pulses is studied theoretically. The spectrum of the pulses is cut off in order to suppress pulse amplitude at and close to the atomic resonance frequency. This leads to long tails of the laser pulse as a function of time giving rise to coherent transients in the photoassociation dynamics. They are studied as a function of cut-off position and chirp of the pulse. Molecule formation in the electronically excited state is attributed to off-resonant excitation in the strong-field regime.

DOI
10.1103/physreva.80.063417

Related papers

Photoassociation and coherent transient dynamics in the interaction of ultracold rubidium atoms with shaped femtosecond pulses. I. Experiment

Terry Mullins, Wenzel Salzmann, Simone Götz +10 more

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 ${D}_{1}$ or ${D}_{2}$ 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 ${D}_{1}$ or ${D}_{2}$ 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.

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Photoassociation and coherent transient dynamics in the interaction of ultracold rubidium atoms with shaped femtosecond pulses - I. Experiment

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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.

arXiv:0903.4549•Mar 26, 2009•0 citations

Characteristic oscillations in the coherent transients of ultracold rubidium molecules using red and blue detuned pulses for photoassociation

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We investigate the interaction of femtosecond laser pulses with an ensemble of ultracold rubidium atoms by applying shaped excitation pulses with two different types of spectral filtering. Although the pulses, which are frequency filtered with a high pass, have no spectral overlap with molecular states, we observe coherent molecular transients. Similar transients obtained with nearly transform-limited pulses, where only the atomic resonance is removed, reveal two differing oscillatory components. The resulting transients are compared among themselves and supported with quantum dynamical simulations which indicate a photoassociation process. The effect is due to the strong field interaction of the pulse with the colliding atom pair.

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Coherent Transients in the Femtosecond Photoassociation of Ultracold Molecules

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We demonstrate the photoassociation of ultracold rubidium dimers using coherent femtosecond pulses. Starting from a cloud of ultracold rubidium atoms, electronically excited rubidium molecules are formed with shaped photoassociation pump pulses. The excited state molecules are projected with a time-delayed probe pulse onto molecular ion states which are detected in a mass spectrometer. Coherent transient oscillations of the excited state population are observed in the wings of the pump pulse, in agreement with the time-dependent solution of the Schrödinger equation of the excitation process.

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Coherent control of photoassociation

Ruzin Ağanoğlu

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.

•Jan 1, 2012•0 citations

Suppressing the weakly bound states in the photoassociation dynamics by using a frequency cut-off laser pulse

林峰, 张为, 赵泽宇 +1 more

The photoassociation dynamics of ultracold lithium atoms controlled by a cut-off pulse has been investigated theoretically by solving numerically the time-dependent Schro¨dinger equation using the mapped Fourier grid method. The frequency components of the laser pulse close to the atomic resonance are partly cut off. Compared with the typical Gauss-type pulses, the cut-off pulse is helpful to suppress efficiently the weakly bound states and prepare the associated molecules in the lower vibrational states. Especially, the dependence of photoassociation probability on the cut-off position of the laser pulse is explored.

中国物理B：英文版•Jan 1, 2012•0 citations
Photoassociation of ultracold rubidium atoms with femtosecond laser pulses is studied theoretically. The spectrum of the pulses is cut off in order to suppress pulse amplitude at and close to the atomic resonance frequency. This leads to long tails of the laser pulse as a function of time giving rise to coherent transients in the photoassociation dynamics. They are studied as a function of cut-off position and chirp of the pulse. Molecule formation in the electronically excited state is attributed to off-resonant excitation in the strong-field regime.
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.
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 investigate the interaction of femtosecond laser pulses with an ensemble of ultracold rubidium atoms by applying shaped excitation pulses with two different types of spectral filtering. Although the pulses, which are frequency filtered with a high pass, have no spectral overlap with molecular states, we observe coherent molecular transients. Similar transients obtained with nearly transform-limited pulses, where only the atomic resonance is removed, reveal two differing oscillatory components. The resulting transients are compared among themselves and supported with quantum dynamical simulations which indicate a photoassociation process. The effect is due to the strong field interaction of the pulse with the colliding atom pair.
We demonstrate the photoassociation of ultracold rubidium dimers using coherent femtosecond pulses. Starting from a cloud of ultracold rubidium atoms, electronically excited rubidium molecules are formed with shaped photoassociation pump pulses. The excited state molecules are projected with a time-delayed probe pulse onto molecular ion states which are detected in a mass spectrometer. Coherent transient oscillations of the excited state population are observed in the wings of the pump pulse, in agreement with the time-dependent solution of the Schrödinger equation of the excitation process.
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.
The photoassociation dynamics of ultracold lithium atoms controlled by a cut-off pulse has been investigated theoretically by solving numerically the time-dependent Schro¨dinger equation using the mapped Fourier grid method. The frequency components of the laser pulse close to the atomic resonance are partly cut off. Compared with the typical Gauss-type pulses, the cut-off pulse is helpful to suppress efficiently the weakly bound states and prepare the associated molecules in the lower vibrational states. Especially, the dependence of photoassociation probability on the cut-off position of the laser pulse is explored.