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Physical Review A

Laser cooling of internal molecular degrees of freedom for vibrationally hot molecules

S. G. Schirmer

Published Dec 5, 2000• 30 citations
Publisher

Abstract

We present an approach to laser cooling of internal molecular degrees of freedom for vibrationally hot molecules using a sequence of ultrashort laser pulses. It is assumed that the molecules initially occupy different vibrational states with a substantial portion of the molecules being in excited vibrational states. We show that the ultimate aim of increasing the vibrational ground-state population through a reduction of the system's entropy can be achieved through a multistep process. In the first step, we design an ultrashort laser pulse that selectively transfers most of the population of the excited vibrational states to an excited electronic surface; then the field is switched off and the system allowed to relax until most of the excited electronic state population has decayed due to spontaneous emission. By repeating this procedure a few times, the entropy of the system can be substantially reduced and the population of the vibrational ground state increased considerably, even if the lifetimes of the excited electronic states are much greater than the length of a control pulse, i.e., if dissipative effects are negligiable on the time scales of coherent control.

DOI
10.1103/physreva.63.013407

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Molecular vibrational cooling by Optical Pumping with shaped femtosecond pulses

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Abstract. Some of us have recently reported in Science [1] vibrational cooling of translationally cold Cs2 molecules into the lowest vibrational level v = 0 of the singlet X1Σg ground electronic state. Starting from a sample of cold molecules produced in a collection of vibrational levels of the ground state, our method was based on repeated optical pumping by laser light with a spectrum broad enough to excite all populated vibrational levels but frequency-limited in such a way to eliminate transitions from v = 0 level, in which molecules accumulate. In this paper this method is generalized to accumulate molecules into an arbitrary selected ”target ” vibrational level. It is implemented by using ultrashort pulse shaping techniques based on Liquid Crystal spatial light modulator. In particular a large fraction of the initially present molecule is transferred into a selected vibrational level such as v = 1, 2 and 7. Limitations of the method as well as the possible extension to rotational cooling are also discussed. PACS numbers: 06.60.Jn; 32.80.Qk; 33.20.Tp; 37.10.Mn; 42.65.Re; 42.79.Kr 1.

•Nov 20, 2012•24 citations
We present an approach to laser cooling of internal molecular degrees of freedom for vibrationally hot molecules using a sequence of ultrashort laser pulses. It is assumed that the molecules initially occupy different vibrational states with a substantial portion of the molecules being in excited vibrational states. We show that the ultimate aim of increasing the vibrational ground-state population through a reduction of the system's entropy can be achieved through a multistep process. In the first step, we design an ultrashort laser pulse that selectively transfers most of the population of the excited vibrational states to an excited electronic surface; then the field is switched off and the system allowed to relax until most of the excited electronic state population has decayed due to spontaneous emission. By repeating this procedure a few times, the entropy of the system can be substantially reduced and the population of the vibrational ground state increased considerably, even if the lifetimes of the excited electronic states are much greater than the length of a control pulse, i.e., if dissipative effects are negligiable on the time scales of coherent control.
Optimal control theory is applied to laser cooling of molecules. The objective is to cool vibrations, using shaped pulses synchronized with the spontaneous emission. The optimal mechanism is found to operate by a “vibrationally selective coherent population trapping”. The trapping condition is that the instantaneous phase of the laser is locked to the phase of the transition dipole moment of v=0 with the excited population. The molecules that reach v=0 by spontaneous emission are then trapped, while the others are continually repumped.
Theoretical progress in the cooling of internal degrees of freedom of molecules using shaped laser pulses is reported. The emphasis is on general concepts and universal constraints. Several alternative definitions of cooling are considered, including reduction of the von Neumann entropy, −tr{ρ̂logρ̂} and increase of the Renyi entropy, tr{ρ̂2}. A distinction between intensive and extensive considerations is used to analyse the cooling process in open systems. It is shown that the Renyi entropy increase is consistent with an increase in the system phase space density and an increase in the absolute population in the ground state. The limitations on cooling processes imposed by Hamiltonian generated unitary transformations are analyzed. For a single mode system with a ground and excited electronic surfaces driven by an external field it is shown that it is impossible to increase the ground state population beyond its initial value. A numerical example based on optimal control theory demonstrates this result. For this model only intensive cooling is possible which can be classified as evaporative cooling. To overcome this constraint, a single bath degree of freedom is added to the model. This allows a heat pump mechanism in which entropy is pumped by the radiation from the primary degree of freedom to the bath mode, resulting in extensive cooling.
Some of us have recently reported (Viteau et al 2008 Science 321 232–4) vibrational cooling of translationally cold Cs 2 molecules into the lowest vibrational level v =0 of the singlet X 1 Σ g ground electronic state. Starting from a sample of cold molecules produced in a collection of vibrational levels of the ground state, our method was based on repeated optical pumping by laser light with a spectrum broad enough to excite all populated vibrational levels but frequency-limited in such a way to eliminate transitions from v =0 level, in which molecules accumulate. In this paper, this method is generalized to accumulate molecules into an arbitrary selected 'target' vibrational level. It is implemented by using ultrashort pulse shaping techniques based on liquid crystal spatial light modulator. In particular, a large fraction of the initially present molecules is transferred into a selected vibrational level such as v =1, 2 and 7. Limitations of the method as well as the possible extension to rotational cooling are also discussed.
The methods producing cold molecules from cold atoms tend to leave molecular ensembles with substantial residual internal energy. For instance, cesium molecules initially formed via photoassociation of cold cesium atoms are in several vibrational levels nu of the electronic ground state. We applied a broadband femtosecond laser that redistributes the vibrational population in the ground state via a few electronic excitation/spontaneous emission cycles. The laser pulses are shaped to remove the excitation frequency band of the nu = 0 level, preventing re-excitation from that state. We observed a fast and efficient accumulation ( approximately 70% of the initially detected molecules) in the lowest vibrational level, nu = 0, of the singlet electronic state. The validity of this incoherent depopulation pumping method is very general and opens exciting prospects for laser cooling and manipulation of molecules.
In the last several years we have discovered a variety of remarkable pulse strategies for manipulating molecular motion by employing a design strategy we call “local optimization.'' Here we review the concept of local optimization and contrast it with optimal control theory. By way of background, we give highlights from two recent examples of the method: (1) a strategy for eliminating population transfer to one or many excited electronic states during strong field excitation, an effect we call ‘optical paralysis’; (2) a generalization of the counterintuitive STIRAP (stimulated Raman adiabatic passage) pulse sequence from three levels to N levels, a strategy we call ‘straddling STIRAP.' We then turn to a third example, which is the main subject of this paper: laser cooling of molecular internal degrees of freedom. We study a model that includes both coherent interaction with the radiation field and spontaneous emission; the latter is necessary to carry away the entropy from the molecule. An optimal control calculation was performed first and succeeded in producing vibrational cooling, but the resulting pulse sequence was difficult to interpret. Local optimization subsequently revealed the cooling mechanism: the instantaneous phase of the laser is locked to the phase of the transition dipole moment between the excited state amplitude and v=0 of the ground state. Thus, the molecules that reach v=0 by spontaneous emission become decoupled from the field, and no longer absorb, while molecules in all other states are continually repumped. The mechanism could be called “vibrationally selective coherent population trapping,'' in analogy to the corresponding mechanism of velocity selective coherent population trapping in atoms for sub-Doppler cooling of translations.
Abstract. Some of us have recently reported in Science [1] vibrational cooling of translationally cold Cs2 molecules into the lowest vibrational level v = 0 of the singlet X1Σg ground electronic state. Starting from a sample of cold molecules produced in a collection of vibrational levels of the ground state, our method was based on repeated optical pumping by laser light with a spectrum broad enough to excite all populated vibrational levels but frequency-limited in such a way to eliminate transitions from v = 0 level, in which molecules accumulate. In this paper this method is generalized to accumulate molecules into an arbitrary selected ”target ” vibrational level. It is implemented by using ultrashort pulse shaping techniques based on Liquid Crystal spatial light modulator. In particular a large fraction of the initially present molecule is transferred into a selected vibrational level such as v = 1, 2 and 7. Limitations of the method as well as the possible extension to rotational cooling are also discussed. PACS numbers: 06.60.Jn; 32.80.Qk; 33.20.Tp; 37.10.Mn; 42.65.Re; 42.79.Kr 1.