Separation of molecules by chirality using circularly polarized light

Transcription

1 Separation of molecules by chirality using circularly polarized light Anton Andreev Boris Spivak Department of Physics University of Washington Phys. Rev. Lett. 102, (2009) Quantum Coherent Properties of Spins III, 12/20/2010

2 Chiral Molecules Many molecules exist as right- and left- handed isomers (enantiomers) Proline molecule: C 5 H 9 NO 2 Molecular Weight: R Characteristic time of conversion (by tunneling or thermal activation) may be extremely long Enantiomers distinct stable molecules L Often one needs to extract specific enantiomers from a racemic (50/50) mixture 1) Conversion L R 2) Spatial separation

3 Chiral separation with light Chiral current density: Inversion: Time reversal: In an ac electric field: by symmetry: - time average Circularly polarized light has handedness (photon spin) and can produce chiral current What are the mechanisms and magnitude of the effect?

4 Chiral separation due to torque Circularly polarized light exerts torque on a particle For chiral objects torque induces rotation and drift Hydrodynamic regime (chiral particles in a liquid) Baranova, Zel dovich Chem. Phys. Lett. 78 Drift velocity: angular momentum per photon is small: propeller effect Is chiral separation possible in the absence of torque?

5 Chiral separation in gases Molecules: mass -, size - Light: frequency -, wavelength - molecule momentum: Rotational motion is classical angular momentum: Neglect transfer of linear and angular momentum from light to molecules

6 Simplified model: uniaxial rotation excited state Resonant absorption at molecule angular velocity ground state Doppler shift: L- and R- molecules absorb light equally (dipole approximation) Light absorption changes collision cross-section L-R collision

7 Mechanism comparison Let s assume: Momentum transfer from L to R upon collision From cross-section change From photon torque Ratio:

8 Similarity to optical piston effect Resonantly absorbing atoms in a buffer gas Doppler shift: No momentum transfer from light to atoms Gel mukhanov, Shalagin JETP 1980 Experimental observation: Werij, Heverkort, Woerdman, Phys. Rev. A, 33, 3270 (1986) Drift velocities:

9 Boltzmann equation Spatially homogeneous case - collision integral Equilibrium distribution Photo-excitation (independent of chirality) absorption probability light intensity

10 Symmetry considerations Inversion: Optical excitations are independent of: Stationary Boltzmann equation: if collision cross-section were chirality-independent we would have Then chiral current would vanish For chirality-dependent collisions arises due to chirality-dependence of collision cross-section

11 Solution outline To find chiral current: 1. Determine absorption rate 2. Solve kinetic equation Absorption probability is obtained by transforming electric field to reference frame co-rotating with the molecule Model: Dipole approximation Monochromatic light: Absorption cross-section,, for stationary molecule is assumed known

12 Light absoption probability Circular polarization along Angular momentum along Euler angles Assume symmetric top molecule: In body frame has several frequencies

13 Absorption probability Need absorption asymmetric in Photo-excitation rate: Absorption probability (non-symmetric in )

14 Collision integral For simplicity: dilute recemic mixture in a buffer gas Collisions mostly with buffer gas. Buffer gas in equilibrium. - scattering rate from state to Collision integral: 100% de-excitation upon collision

15 Boltzmann equation Chiral drift velocity: Order of magnitude estimate

16 Summary Novel mechanism of separation of enantiomers by circularly polarized light No transfer of linear or angular momentum from light to molecules Similar to the (experimentally observed) optical piston effect Analogous mechanism should exist in liquids Need for experiments