Resonant Enhancement and Dissipation in Nonequilibrium van der Waals Forces

1. Resonant Enhancement and Dissipation in Nonequilibrium van der Waals Forces Adam E. Cohen (Stanford) Shaul Mukamel (UC Irvine)

2. 3 + 3 = 6 Gauss: if and f is insensible between macroscopic objects, then van der Waals: a ~ index of refraction (empirically) McLachlan: T = 0: J = coupling ‘ a =polarizability T > 0: Intermolecular forces and optical response

3. coordinate operator classical source Liouville superoperator Liou. Space interaction picture Commutator Time-ordering superoperator Expectation value Anticommutator Start with perturbations to the individual molecules: Relating Nonlinear Optical Response to Intermolecular Forces Response given by Volterra series: Can calculate or measure R(1), R(2), … for any initial state. To calculate R(n):

4. Do the nonlinear response functions completely describe a molecule? In a quantum system or a classical ensemble, fluctuations have a life of their own Calculate response of fluctuations to a perturbation: (Compare with ) Call R+...+-...-Generalized Response Functions (GRFs) R++ and R+- are related by the Fluctuation-Dissipation Theorem (FDT) Causality  Generalized K-K relations Thermal equilibrium  Generalized FDT

5. Liouville superoperator Two coupled molecules Coupled molecules: Want to evaluate: Again Joint response function: Using superoperator algebra, we can factor the joint response function: The joint response of the coupled molecules depends on all GRFs of the individual molecules.

6. Example: Coupled Harmonic Oscillators 1st order response to coupling J(t)papb: Time domain: Frequency domain: Steady state coupling: Reproduces McLachlan formula for Ta = Tb bb/ ba c(1)(0) wb/ wa Phys. Rev. Lett.91, 233202 (2003)

7. Dissipation between coupled SHOs For time-varying J, need: Force Dissipation bb/ ba bb/ ba Re[c(1)] Im[c(1)] w w Possibility of negative friction

8. Do not fret for it leads only to evil. --Psalm 37 orientational factor donor emission spectrum lifetime of donor Example: FRET force Fluorescence Resonance Energy Transfer (FRET) is mediated by the same dipole-dipole interaction that mediates the vdW force. Forster rate of FRET: Interaction energy from FRET: Kramers-Kronig relation between kFRETand UFRET UFRET can also be thought of as optical trapping of acceptor in near-field of excited donor. J. Phys. Chem. A107 (19) 3633 (2003)

9. Sample calculation Chlorophyll b in diethyl ether FRET force FRET FRET force may be either attractive or repulsive FRET force may be much stronger than vdW force

10. Possibilities for experimental verification • NLO effects in critical systems (gasses, binary mixtures, polymers) • Conformational changes in tethered bichromophores • Concentration quenching • Solid state measurements (Casimir-type)

11. Conclusions • Quantum ensemble described by Generalized Response Functions (GRFs) • Response functions of two coupled systems may be expressed in terms of the GRFs of the constituents • vdW forces between objects at different temperatures or in relative motion show resonant enhancement and (possibly negative) dissipation • A mechanical force accompanies FRET

12. Acknowledgments Professor Shaul Mukamel (UCI) $$ Hertz Foundation $$