Resonant Enhancement and Dissipation in Nonequilibrium van der Waals Forces

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Resonant Enhancement and Dissipation in
Nonequilibrium van der Waals Forces

• Adam E. Cohen (Stanford)
• Shaul Mukamel (UC Irvine)

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Intermolecular forces and optical response

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Relating Nonlinear Optical Response to
Intermolecular Forces
Start with perturbations to the individual
molecules

Response given by Volterra series
Can calculate or measure R(1), R(2), for any
initial state.
To calculate R(n)

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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-Dissipa
tion Theorem (FDT)
Causality ? Generalized K-K relations Thermal
equilibrium ? Generalized FDT
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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.
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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)
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Dissipation between coupled SHOs
For time-varying J, need
Force
Dissipation
bb/ ba
bb/ ba
Rec(1)
Imc(1)
w
w
Possibility of negative friction
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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 kFRET and UFRET
UFRET can also be thought of as optical
trapping of acceptor in near-field of excited
donor.
J. Phys. Chem. A 107 (19) 3633 (2003)
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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
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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)

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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

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Acknowledgments
Professor Shaul Mukamel (UCI)
Hertz Foundation