Formation of Slow Molecules in Chemical Reactions in Crossed Molecular Beams

PHYSICAL REVIEW A 78, 022705 ͑2008͒ Formation of slow molecules in chemical reactions in crossed molecular beams T. V. Tscherbul,1 Ğ Barinovs,1,2 J. Kłos,3 and R. V. Krems1 1Department of Chemistry, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1 2Department of Theoretical Physics, Institute of Chemical Physics, University of Latvia, Riga, Latvia 3Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA ͑Received 13 January 2008; revised manuscript received 29 May 2008; published 8 August 2008͒ We demonstrate that chemical reactions in collisions of molecular beams can generally produce low-velocity molecules in the laboratory-fixed frame. Our analysis shows that collisions of beams may simultaneously yield slow reactant molecules and slow products. The reaction products are formed in selected rovibrational states and scattered in a specific direction, which can be controlled by tuning the kinetic energies of the incident beams and the angle between the beams. Our calculations indicate that chemical reactions of polar alkali-metal dimers are barrierless and we suggest that chemical reactions involving alkali-metal dimers may be particularly suitable for producing slow molecules in crossed beams. DOI: 10.1103/PhysRevA.78.022705 PACS number͑s͒: 34.20.Ϫb, 37.10.Mn I. INTRODUCTION the rovibrationally ground state ͓17͔. Decelerated molecular beams can be injected in a molecular synchrotron to produce The creation of ultracold molecules is predicted to have a packets of molecules with well defined and tunable kinetic significant impact on atomic and molecular physics ͓1͔, energies ͓18͔. External electric fields can be used to bunch condensed-matter physics ͓2͔, quantum-information science the molecular packets together or spread them apart. Electro- ͓3͔, physics of elementary particles ͓4͔, and chemistry ͓5͔.A static guiding can be used to deflect slow molecular beams major goal of current research in molecular physics is there- and collide them at a particular angle. Low-energy molecular beams can also be collided with trapped atoms or molecules fore to produce ensembles of ultracold molecules with a ͓ ͔ wide range of properties. This goal stimulated the develop- 19 . Chemical reactions in collisions of molecular beams thus produced may potentially yield a great variety of mo- ment of experimental techniques based on Stark deceleration lecular species for studies of low temperature physics and of molecular beams ͓6͔, photoassociation of ultracold atoms ͓ ͔ ͓ ͔ chemistry. It is therefore important to extend the method of 7 , and cryogenic cooling using He buffer gas 5,8 . Chan- Chandler and co-workers ͓9,10͔ to reactive collisions. dler and co-workers have recently demonstrated the possibil- A major thrust of recent experimental work has been to ity of slowing molecules by colliding two molecular beams create ultracold polar molecules, as ultracold dipolar gases ͓ ͔ 9,10 . Their experiment showed that certain configurations offer exciting opportunities for new fundamental discoveries of crossed molecular beams allow for inelastic scattering that ͓4͔. Many research groups demonstrated the possibility of cancels out the translational energy of molecules in the labo- creating ultracold polar molecules by photoassociation of ul- ratory fixed ͑LF͒ frame. Liu and Loesch proposed an alter- tracold alkali-metal atoms ͓7͔. Alkali-metal dimers have thus native method based on chemical reactions in molecular become paradigm systems for studies of molecular physics at beams producing heavy molecules and light atoms ͓11͔. ultracold temperatures ͓20͔. Although photoassociation usu- They showed that the chemical reaction K+HBr→KBr+H ally yields ultracold molecules in vibrationally excited states, may produce slow KBr molecules, as most of the product Sage and co-workers have recently reported the creation of recoil energy is carried away by light hydrogen atoms. Here, ultracold RbCs molecules in the vibronic ground state ͓21͔. we generalize the method of Chandler and co-workers ͓9,10͔ The stability of ultracold molecules in dense gases is deter- and Liu and Loesch ͓11͔ to show that molecules with zero mined by their collision properties. For example, vibra- velocity in the LF frame can be produced in reactive colli- tionally inelastic collisions limit the lifetime of vibrationally sions of molecular beams with arbitrary mass compositions excited ultracold dimers ͓20͔. Collisions of polar molecules of the reactants and products. in the rovibrational ground state may lead to chemical reac- While the technique of producing slow molecules based tions resulting in exchange of atoms. Chemical reactions at on collisions of thermal beams is very general, it is limited ultracold temperatures should be suppressed by reaction ac- by the velocity spread of colliding beams which broadens the tivation barriers ͓22͔. However, many chemical reactions of energy distribution of scattered molecules. Recent experi- alkali metal dimers do not require activation energy. For ex- ͓ ͔ ͓ ͔ mental work on Stark 6 and Zeeman 12–14 deceleration ample, the reactions of K atoms with K2 molecules, Na at- ͓ ͔ of molecular beams, buffer gas cooling of molecules 15 , oms with Na2 molecules, and Li atoms with Li2 molecules and electromagnetic guiding of atoms and molecules ͓16͔ have been found to be barrierless and very efficient at ultra- has lead to the development of new technologies that allow cold temperatures ͓23͔. In this work, we examine the inter- for the production of molecular beams with extremely nar- action energies of two RbCs molecules and the RbCs-Rb row energy distributions and relatively low forward veloci- reaction complex. Our calculation demonstrates that chemi- ties. For example, molecules cooled in a He buffer gas to cal reactions of alkali-metal dimers in molecule-molecule temperatures of a few Kelvin can be guided out of the buffer collisions are barrierless. Based on this calculation, we sug- → gas cell, yielding a low-temperature beam of molecules in gest that chemical reactions of the type Rb2 +Cs RbCs 1050-2947/2008/78͑2͒/022705͑7͒ 022705-1 ©2008 The American Physical Society TSCHERBUL et al. PHYSICAL REVIEW A 78, 022705 ͑2008͒ ͑ ͒ ui = vi − vc.m.. 3 Figure 1 shows the vectors for a particular configuration of ␪ two beams intersecting at the angle AB. The reaction prod- ͑ ͒ ucts depart with the velocities vX and vY. Using Eq. 3 ,we find that if ͑ ͒ uX =−vc.m., 4 the product X has zero velocity in the LF coordinate system. Equation ͑3͒ can be rewritten for the reaction products as m −1 ͩ X ͪ Ј ͑ ͒ uX = 1+ vr . 5 mY Squaring the vectors in Eqs. ͑3͒ and ͑4͒ and using Eq. ͑5͒ to FIG. 1. ͑Color online͒ Vector diagram illustrating the kinematics transform the vectors uX and uA, we obtain the scalar part of of a molecular beam reactive scattering experiment. the cancellation relation m −2 m −2 +Rb may be used to produce cold polar molecules and sug- ͩ A ͪ 2 2 ͑ ͒ ͩ X ͪ Ј2 ͑ ͒ 1+ vr − vA +2 vA · vc.m. = 1+ vr . 6 gest optimal conditions for molecular beam collisions that mB mY maximize the yield of cold RbCs molecules. The scalar product of vectors vA and vc.m. can be evaluated ͑ ͒ using the vector diagram in Fig. 1 to give vA ·vc.m. ͑ 2 ␪ ͒/͑ ͒ ␪ II. THEORY = mAvA +mBvAvB cos AB mA +mB , where the angle AB is shown in Fig. 1. Substituting this into Eq. ͑6͒ allows us to A. Slowing molecules by reactive collisions use the energy balance ͑2͒ to obtain after some algebra Consider a chemical reaction m m Ј ⌬ ͩ A ͪ ͩ B ͪ A + B → X + Y, ͑1͒ Eint − E0 = 1− EA + 1− EB mY mY where A and B can be molecules, atoms or ions. We assume m m 1/2 ␪ ͩ A B ͪ ͱ ͑ ͒ that reaction ͑18͒ occurs in a crossed molecular beam appa- − 2 cos AB 2 EAEB, 7 ͑ mY ratus so that the velocities of the reactants A and B vA and ͒ vB are well defined in the laboratory frame. The velocity of where EA and EB are the kinetic energies of the reactant the center of mass ͑c.m.͒ of the collision complex is given by beams in the LF frame. When the reactants and products are ͑ ͒/͑ ͒ ͑␪ ␲/ ͒ vc.m.= mAvA +mBvB mA +mB , where mi is the mass of spe- identical and the beams are perpendicular AB= 2 , this cies i. The relative velocities of the reactants ͑unprimed͒ and result reduces to the expression of Chandler and co-workers ͑ ͒ Ј ͓ ͔ products primed are defined by vr =vA −vB and vr =vX for inelastic scattering of molecules 9,10 . Unlike their re- ͓ ͔ −vY, and the energy conservation requirement yields 24 sult, however, the cancellation relation for reactive scattering ͑7͒ depends on both E and E . 1 ␮ 2 1 ␮ Ј2 Ј ⌬ ͑ ͒ A B 2 ABvr = 2 XYvr + Eint − E0, 2 To obtain the angular part of the cancellation relation ͑4͒, ␮ ␮ we project it onto the vector v and use Eq. ͑5͒. This gives where AB and XY denote the reduced masses of the reac- r tants and products, EЈ is the energy deposited into internal −1 int mX modes of the products ͑vibration and rotation͒, and ⌬E is ͩ1+ ͪ vЈv cos ␪ = ͑v · v ͒ − ͑v · v ͒, ͑8͒ 0 m r r B c.m. A c.m. the difference between the total ͑electronic+rovibrational͒ Y internal energy of the reactants and the electronic energy of where ␪ is the c.m. scattering angle. Evaluating the right- the products. hand side of Eq. ͑8͒ using Fig. 1 and using Eq. ͑7͒, we obtain In the c.m.

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