Reaction rates of ultra-cold 6 Li 2 dimers Quantum state dependent - PowerPoint PPT Presentation

Reaction rates of ultra-cold 6 Li 2 dimers Quantum state dependent chemistry Erik Frieling 1 , Denis Uhland 1 , Gene Polovy 1 , Julian Schmidt 2 , Kirk Madison 1 June 5, 2019 1 University of British Columbia 2 Universit¨ at Freiburg

Table of contents 1. Background and Motivation 2. Making Cold Li2 molecules 3. Transfer to the ground state: STIRAP 4. Modeling Ultracold Reactions 5. Results 6. Conclusion 1

Background and Motivation

Cold Polar molecules Micheli et al. [2006] A toolbox for lattice-spin models with polar molecules 2

Reaction Channels Two possibilities for homonuclear alkali dimers: 3

Reaction Channels Two possibilities for homonuclear alkali dimers: Li 2 ( a 3 Σ + ) + Li 2 ( a 3 Σ + ) → Li 3 + Li ( Trimer formation ) 3

Reaction Channels Two possibilities for homonuclear alkali dimers: Li 2 ( a 3 Σ + ) + Li 2 ( a 3 Σ + ) → Li 3 + Li ( Trimer formation ) Li 2 ( a 3 Σ + ) + Li 2 ( a 3 Σ + ) → Li 2 ( X 1 Σ + ) + Li 2 ( T ) ( triplet to singlet ) 3

Reaction Channels Two possibilities for homonuclear alkali dimers: Li 2 ( a 3 Σ + ) + Li 2 ( a 3 Σ + ) → Li 3 + Li ( Trimer formation ) Li 2 ( a 3 Σ + ) + Li 2 ( a 3 Σ + ) → Li 2 ( X 1 Σ + ) + Li 2 ( T ) ( triplet to singlet ) = ⇒ Trimer Formation expected to dominate 3

Ultracold Collisions- Atoms Closed channel ∆ E ( B ) Entrance channel V bg ∼ C 6 r V ( r ) Separation r 4

Ultracold Collisions- Atoms E kin > U trap Closed channel ∆ E ( B ) Entrance channel V bg ∼ C 6 r V ( r ) 3-body collision Separation r 4

Ultracold Collisions- Molecules Separated E 3 E 2 E 1 = 0 V bg ∼ C 6 r V ( r ) Separation r 5

Ultracold Collisions- Molecules Long-range Separated (elastic collisions) E 3 E 2 E 1 = 0 V bg ∼ C 6 r V ( r ) Separation r 5

Ultracold Collisions- Molecules Short Range Long-range Separated (elastic collisions) (Chemistry) E 3 E 2 E 1 = 0 V bg ∼ C 6 r V ( r ) Separation r 5

Ultracold Collisions- Molecules Short Range Long-range Separated (elastic collisions) (Chemistry) E 3 E 2 E 1 = 0 V bg ∼ C 6 r V ( r ) Separation r 5

Ultracold Collisions- Molecules Short Range Long-range Separated (elastic collisions) (Chemistry) E 3 E 2 E 1 = 0 V bg ∼ C 6 r V ( r ) ¯ R B a Separation r 5

Universal Reaction Rates- Summary Described in Qu´ em´ ener and Julienne [2012], Ultracold Molecules Under Control! • Quantum Langevin Model- every molecule that reaches short range part of potential reacts with unity probability. 6

Universal Reaction Rates- Summary Described in Qu´ em´ ener and Julienne [2012], Ultracold Molecules Under Control! • Quantum Langevin Model- every molecule that reaches short range part of potential reacts with unity probability. • Reaction rate completely determined by long range potential 6

Universal Reaction Rates- Summary Described in Qu´ em´ ener and Julienne [2012], Ultracold Molecules Under Control! • Quantum Langevin Model- every molecule that reaches short range part of potential reacts with unity probability. • Reaction rate completely determined by long range potential • Van der Waals length � 2 µ C 6 � 1 / 4 2 π a = ¯ Γ(1 / 4) 2 � 2 6

Universal Reaction Rates- Summary Described in Qu´ em´ ener and Julienne [2012], Ultracold Molecules Under Control! • Quantum Langevin Model- every molecule that reaches short range part of potential reacts with unity probability. • Reaction rate completely determined by long range potential • Van der Waals length � 2 µ C 6 � 1 / 4 2 π a = ¯ Γ(1 / 4) 2 � 2 • Unitary limit β u = g 4 π � a ≈ 7 . 1 × 10 − 10 cm 3 / s µ ¯ = ⇒ Unless there are deviations from this rate, there is very little you can learn about the reactions 6

Literature Review Dimer-dimer collisions: • Ospelkaus et al. [2010]: KRb Universal + state-dependent (Pauli suppression) 7

Literature Review Dimer-dimer collisions: • Ospelkaus et al. [2010]: KRb Universal + state-dependent (Pauli suppression) • Takekoshi et al. [2014]: RbCs chemically stable, non-univeral loss, magnetic field dependent 7

Literature Review Dimer-dimer collisions: • Ospelkaus et al. [2010]: KRb Universal + state-dependent (Pauli suppression) • Takekoshi et al. [2014]: RbCs chemically stable, non-univeral loss, magnetic field dependent • Drews et al. [2017]: Rb 2 • Rvachov et al. [2017]: NaLi 7

Literature Review Dimer-dimer collisions: • Ospelkaus et al. [2010]: KRb Universal + state-dependent (Pauli suppression) • Takekoshi et al. [2014]: RbCs chemically stable, non-univeral loss, magnetic field dependent • Drews et al. [2017]: Rb 2 • Rvachov et al. [2017]: NaLi • Ye et al. [2018]: NaRb Universal, even for chemically stable ground state 7

Literature Review Dimer-dimer collisions: • Ospelkaus et al. [2010]: KRb Universal + state-dependent (Pauli suppression) • Takekoshi et al. [2014]: RbCs chemically stable, non-univeral loss, magnetic field dependent • Drews et al. [2017]: Rb 2 • Rvachov et al. [2017]: NaLi • Ye et al. [2018]: NaRb Universal, even for chemically stable ground state • Guo et al. [2018] NaRb β > β u , electric field dependent 7

Literature Review Dimer-dimer collisions: • Ospelkaus et al. [2010]: KRb Universal + state-dependent (Pauli suppression) • Takekoshi et al. [2014]: RbCs chemically stable, non-univeral loss, magnetic field dependent • Drews et al. [2017]: Rb 2 • Rvachov et al. [2017]: NaLi • Ye et al. [2018]: NaRb Universal, even for chemically stable ground state • Guo et al. [2018] NaRb β > β u , electric field dependent Dimer-atom collisions: • Zahzam et al. [2006]: Cs+Cs 2 • Hudson et al. [2008]: RbCs+Cs & RbCs+Rb • Deiglmayr et al. [2011]: LiCs + Cs 7

Literature Review Dimer-dimer collisions: • Ospelkaus et al. [2010]: KRb Universal + state-dependent (Pauli suppression) • Takekoshi et al. [2014]: RbCs chemically stable, non-univeral loss, magnetic field dependent • Drews et al. [2017]: Rb 2 • Rvachov et al. [2017]: NaLi • Ye et al. [2018]: NaRb Universal, even for chemically stable ground state • Guo et al. [2018] NaRb β > β u , electric field dependent Dimer-atom collisions: • Zahzam et al. [2006]: Cs+Cs 2 • Hudson et al. [2008]: RbCs+Cs & RbCs+Rb • Deiglmayr et al. [2011]: LiCs + Cs • Yang et al. [2019]: NaK + K ⇒ Magnetically tunable resonances 7

Experimental Questions 1. Is the triplet ground state stable? 8

Experimental Questions 1. Is the triplet ground state stable? 2. Do we observe non-universal reaction rates? 8

Experimental Questions 1. Is the triplet ground state stable? 2. Do we observe non-universal reaction rates? 3. Is there a magnetic field dependence? 8

Making Cold Li2 molecules

Li MOT ∼ 10 million atoms at ∼ 10mK 9

Crossed Optical Diple Trap (cODT) 10

Feshbach molecules 11

Transfer to the ground state: STIRAP

Stimulated Raman Adiabatic Passage (STIRAP) = Ω 1 | g � − Ω 2 | a � � � a 0 � � Ω 2 1 + Ω 2 2 12

Procedure 13

STIRAP Lineshape Figure 1: Feshbach molecule number after a forward and reverse STIRAP sequence to the v ′′ = 9 level as a function of the probe laser’s frequency. The 14 stokes laser’s frequency is fixed close to the resonance of the | g � − | a �

Modeling Ultracold Reactions

Cloud Density Assuming a thermal cloud: n ( r , t ) = n peak ( t ) e − x 2 / 2 σ 2 x e − y 2 / 2 σ 2 y e − z 2 / 2 σ 2 (1) z 15

Cloud Density Assuming a thermal cloud: � � � � n peak ( t ) e − x 2 / 2 σ 2 x e − y 2 / 2 σ 2 y e − z 2 / 2 σ 2 n ( r , t ) d r = d r = N ( t ) (1) z N ( t ) ⇒ n peak ( t ) = . (2) (2 π ) 3 / 2 σ x σ y σ z 15

Cloud Density Assuming a thermal cloud: � � � � n peak ( t ) e − x 2 / 2 σ 2 x e − y 2 / 2 σ 2 y e − z 2 / 2 σ 2 n ( r , t ) d r = d r = N ( t ) (1) z N ( t ) ⇒ n peak ( t ) = . (2) (2 π ) 3 / 2 σ x σ y σ z 1 2 k B T = 1 2 m ω 2 i σ 2 (3) i � σ i = 1 k B T (4) ω i m 15

Reaction Rate Model n peak ( t ) = N ( t ) ω x ω y ω z m 3 / 2 (5) (2 π k B T ) 3 / 2 16

Reaction Rate Model n peak ( t ) = N ( t ) ω x ω y ω z m 3 / 2 (5) (2 π k B T ) 3 / 2 We can use the peak density to model the loss rate: n = − α n ( t ) − β n 2 ( t ) − γ n 3 ( t ) ˙ (6) 16

Reaction Rate Model n peak ( t ) = N ( t ) ω x ω y ω z m 3 / 2 (5) (2 π k B T ) 3 / 2 We can use the peak density to model the loss rate: n = − α n ( t ) − β n 2 ( t ) − γ n 3 ( t ) ˙ (6) which reduces to (two-body losses) n 0 n ( t ) = (7) 1 + β n 0 t 16

Results

State-dependence of Reaction Rate Accessible states Lifetimes comparison + v' = 20 c( 3 Σ g ) v = 0, N = 0 ν P v = 9, N = 0 6 v = 9, N = 2 ν S 6 n DB,max (10 11 / cm 3 ) FM v = 9 v = 8 4 4 v = 5 0 2 + a( 3 Σ u ) 2 X( 1 Σ g ) + 0 0 10 20 30 40 t (ms) 1 0 x 9 0 n m z ( C y O D T ) 6 Li 2 v = 0 Ti:Sapphire (STIRAP) Dichroic Mirror 17