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The Journal of Chemical Physics

Quantum dynamical model of laser-stimulated isotope separation of adsorbed species: Role of anharmonicity, coupling strength, and energy feedback from the heated substrate

Jui‐Teng Lin, Thomas F. George

Published Apr 15, 1983• 5 citations
Publisher

Abstract

A quantum model of a heterogeneous system consisting of a mixture of isotopes adsorbed on a solid surface and subjected to laser radiation is presented. The model system is described by a total Hamiltonian including direct and indirect (surface-phonon-mediated) couplings. The equations of motion are derived in the Heisenberg–Markovian picture in which the many-body effects of the surface phonon modes and the adspecies are reduced to an overall broadening (damping factor) given by the sum of the energy (T1) and phase (T 2) relaxations. The effects of the dephasing and anharmonicity on the average excitation are investigated. The ‘‘bistability’’ feature with a red-shifted optimal detuning is discussed in terms of the solution of a cubic equation. A diagonalization procedure is presented in a new basis which reveals the effects of the coupling strength, the frequency difference, and the level width of the isotopes on the total steady-state excitation, which in turn reflects the surface spectrum of the model system. Finally, the isotope selectivity given by the numerical results of the time-integrated excitation is discussed. It is shown that the optimal detuning for a weak coupling strength is further red-shifted for a strong isotopic coupling strength. Finally, energy feedback effects of the bath modes on the excitations of the active modes are investigated by combining a quantum excitation equation and a classical heat diffusion equation.

DOI
10.1063/1.445390

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Topical Meeting on Microphysics of Surfaces, Beams, and Adsorbates•Jan 1, 1985•0 citations
A quantum model of a heterogeneous system consisting of a mixture of isotopes adsorbed on a solid surface and subjected to laser radiation is presented. The model system is described by a total Hamiltonian including direct and indirect (surface-phonon-mediated) couplings. The equations of motion are derived in the Heisenberg–Markovian picture in which the many-body effects of the surface phonon modes and the adspecies are reduced to an overall broadening (damping factor) given by the sum of the energy (T1) and phase (T 2) relaxations. The effects of the dephasing and anharmonicity on the average excitation are investigated. The ‘‘bistability’’ feature with a red-shifted optimal detuning is discussed in terms of the solution of a cubic equation. A diagonalization procedure is presented in a new basis which reveals the effects of the coupling strength, the frequency difference, and the level width of the isotopes on the total steady-state excitation, which in turn reflects the surface spectrum of the model system. Finally, the isotope selectivity given by the numerical results of the time-integrated excitation is discussed. It is shown that the optimal detuning for a weak coupling strength is further red-shifted for a strong isotopic coupling strength. Finally, energy feedback effects of the bath modes on the excitations of the active modes are investigated by combining a quantum excitation equation and a classical heat diffusion equation.
Adsorbed species on a solid-state surface interact with the large number of substrate modes, which gives rise to thermal relaxation. Commonly, the temporal evolution of the quantum state of the adsorbate is described by a master equation for the level populations (vibrational bond, internal modes, etc). It is pointed out that this approach does not necessarily give a correct account of the coupling to the solid when the effective level widths become comparable to the level separations, or larger. It is shown that the evolution of the populations does not decouple any more from the time evolution of the coherences (off-diagonal matrix elements), which implies that a random-phase approximation cannot be justified, and that the density matrix of the adsorbate is not determined only by the golden-rule transition constants. Especially, the line profiles turn out to be very sensitive to the coherence-coherence couplings. Although the coherences vanish in thermal equilibrium, their time-regression operator, and hence their mutual couplings and their couplings to the populations, which determine the absorption profile, do not. This information is lost in a master-equation treatment of relaxation.
The irradiation by infrared laser light of an atom adsorbed on the surface of a harmonic crystal is considered. The dynamic coupling between the atom (its motion) and the substrate degrees of freedom (phonon field) in the presence of a confining potential well (van der Waals bond between atom and crystal) gives rise to thermal relaxation of this adbond configuration. Both the atom and the substrate are assumed to be transparent, but the bond is allowed to have non-vanishing dipole-moment matrix elements, which couple the external field to the adsorbate. The equation of motion for the reduced adbond density operator is obtained with reservoir theory, and the relaxation constants are expressed in properties of the crystal. With a similar method, the spectral profile for absorption of weak radiation is derived. Subsequently, the illumination by a strong finite-linewidth laser field which is in close resonance with a single transition of the adbond is examined. The optical Bloch equations in operator form are derived and applied to study the process of laser heating of the crystal. It is pointed out how this mechanism can be understood as resulting from (multi)photon-phonon conversion reactions which are mediated by the adbond.
We investigate the effect of inter-mode coupling on the vibrational relaxation dynamics of molecules in weak dissipative environments. The simulations are performed within the reduced density matrix formalism in the Markovian regime, assuming a Lindblad form for the system-bath interaction. The prototypical two-dimensional model system representing two CO molecules approaching a Cu(100) surface is adapted from an ab initio potential, while the diatom-diatom vibrational coupling strength is systematically varied. In the weak system-bath coupling limit and at low temperatures, only first order non-adiabatic uni-modal coupling terms contribute to surface-mediated vibrational relaxation. Since dissipative dynamics is non-unitary, the choice of representation will affect the evolution of the reduced density matrix. Two alternative representations for computing the relaxation rates and the associated operators are thus compared: the fully coupled spectral basis, and a factorizable ansatz. The former is well-established and serves as a benchmark for the solution of Liouville-von Neumann equation. In the latter, a contracted grid basis of potential-optimized discrete variable representation is tailored to incorporate most of the inter-mode coupling, while the Lindblad operators are represented as tensor products of one-dimensional operators, for consistency. This procedure results in a marked reduction of the grid size and in a much more advantageous scaling of the computational cost with respect to the increase of the dimensionality of the system. The factorizable method is found to provide an accurate description of the dissipative quantum dynamics of the model system, specifically of the time evolution of the state populations and of the probability density distribution of the molecular wave packet. The influence of intra-molecular vibrational energy redistribution appears to be properly taken into account by the new model on the whole range of coupling strengths. It demontrates that most of the mode mixing during relaxation is due to the potential part of the Hamiltonian and not to the coupling among relaxation operators.
Adsorbed atoms on the surface of a harmonic lattice are immersed in a strong laser field. The optical Bloch equations are derived, which include the thermal relaxation and the coherent excitation of the adbond. This is accomplished by a transformation to dressed states, which diagonalizes the interaction with the laser. The single-phonon couplings are then understood as transitions between dressed states. The radiative contributions for arbitrarily strong fields are obtained in the master equation, and it is shown that the coherences with respect to the dressed states decay exponentially, due to the phonon relaxation. General properties of the competing phonon-induced redistribution and optical excitation of the level populations are presented, and exemplified by an explicit elaboration of a three-level system. The results are amenable to analytical evaluation once the interaction potential is prescribed, and extensions of the approach to include multiphonon processes are straightforward.
The influence of a solid surface on the electronic excitation of a group of two-level adatoms and the associated power spectrum is investigated by means of a nonlinear surface-dressed Bloch equation. In the presence of a surface at a distance from the adatom which is comparable to the optical wavelength, the energy transfer dynamics is inflenced by the following factors: (i) nonradiative energy relaxation of the excited adatom via electron-phonon coupling, (ii) radiative spontaneous decay and stimulated emission caused by both the applied field and the reflected field, (iii) the oscillatory behavior of the adatom lifetime due to the interference between the applied and reflected field, (iv) the reflectivity and refrection index of the surface, (v) dipole dephasing caused by the surface phonons and plasmons, and (vi) interaction among the adatoms.