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physica status solidi (b)

Non‐Resonant Energy Transfer between Donor and Acceptor Systems in Presence of Relaxation

Belkacem Boulil, Marcel Giry, Olivier Henri‐Rousseau

Published Apr 1, 1990• 5 citations
Publisher

Abstract

Abstract The non‐resonant energy transfer at zero temperature between two interacting two‐level quantum systems in the presence of relaxation is studied by aid of the density matrix formalism in the framework of the Markoff approximation. This gives the time evolution of the four probabilities to find the system in each of the four levels owing to the fact that at the initial time, the energy is in the excited state of the donor. The results obtained lead to the Davydov and Serikov solutions for resonant transfer of energy, and to the special one for the indirect coupling between a single level and a continuous medium.

DOI
10.1002/pssb.2221580224

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Effects of Donor-Acceptor Quantum Coherence and Non-Markovian Bath on the Distance Dependence of Resonance Energy Transfer

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Accurate information on the distance dependence of resonance energy transfer (RET) is crucial for its utilization as a spectroscopic ruler \re{of} nanometer scale distances. In this regard, understanding the effects of donor-acceptor quantum coherence and non-Markovian bath, which become significant at short distances, has significant implications. The present work investigates this issue theoretically by comparing results from a theory of coherent RET (CRET) with a nonequilibrium version of Förster's RET (FRET) theory, both accounting for non-Markovian bath effects. Even for a model where the donor-acceptor electronic coupling is of transition dipole interaction form, it is shown that the RET rate in general deviates from the inverse sixth power distance dependence as opposed to the prediction of the original FRET. It is shown that the donor-acceptor quantum coherence makes the \re{distance} dependence steeper than the sixth power although detailed manner of enhancement is sensitive to specific values of parameters. On the other hand, the non-Markovian bath effects make the \re{distance} dependence more moderate than the sixth power for both CRET and nonueqilibrium FRET because finite time scale of the bath causes the rate to be smaller than the prediction of original FRET. While these effects are \re{demonstrated clearly} in the population dynamics at sub-picosecond time scales, their contributions to the conventional RET efficiency are relatively minor. This indicates that the actual detection of such effects through conventional RET efficiency measurement requires either high precision or utilization of a donor with fast spontaneous decay rate of excitation.

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Nonlinear Resonance Effects in Multilevel Quantum Systems Weakly Coupled to a Thermal Reservoir

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Calculations are made to determine the response (power absorbed, magnetization, etc.) of a multilevel quantum system under the influence of any number of classically described driving fields (well defined in amplitude and phase). A nonperturbative theory is developed to account for those fields that are in resonance with the system. The nonresonant effects, such as virtual energy shifts, are included in the theory. We limit ourselves to a discussion of quantum systems that are in weak contact with a thermal reservoir. The procedure is the following A projection-operator formalism is developed which separates the density matrix of a system into two parts. One part is related to those portions of the driving fields that interact quite strongly with the system. The other part is the nonresonant or weakly interacting portion. An exact equation of motion, which includes the effects of the nonresonant part, is derived for the strongly interacting part of the density matrix. It is then shown that when relaxation can be represented by phenomenological decay constants, a unitary transformation can be found which reduces the equation of motion for the strongly interacting part of the density matrix so that an exact solution is possible. This solution is shown to give the major effects of the driving fields and can be used as the zeroth-order solution in a perturbation treatment of the whole density matrix. Frequency shifts such as the Bloch-Siegert shift and shifts due to couplings between the levels of interest (resonance levels) and other levels (nonresonance levels) all arise in the same natural way in our treatment. Our results in many instances are the extensions of the well-known results for a two-level quantum-mechanical systemm to an $N$-level one, and include resonant multiple quantum effects. As an example, a straightforward application of the method is carried out in order to compute the shifts in the resonance frequencies of a four-level system, driven by two oscillating fields connecting three of the levels, due to the counter-rotating components of the driving fields and the presence of the fourth level, which is not coupled to the other levels by the driving fields.

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Saturation Effects in Resonant Two-Photon Processes

B. R. Mollow

Resonant two-photon absorption is discussed for the case in which the exciting field may be intense enough and near enough to resonance to cause appreciable saturation. A single pair of levels in an otherwise quite general atom is assumed to satisfy the appropriate resonance condition, and equations are derived governing the time evolution of the associated 2 \ifmmode\times\else\texttimes\fi{} 2 submatrix of the full atomic density matrix. Atomic relaxation is treated explicitly. The analysis, which treats both inversion-symmetric and inversion-nonsymmetric cases within the same general formalism, is developed systematically, the necessary approximations receiving careful discussion. The results are analogous to those for the corresponding one-photon process, but with a shift in the resonance frequency proportional to the intensity of the exciting field. This frequency shift is not identical to the one calculated by time-independent (second-order) perturbation theory, and becomes large when the energy of an intermediate state of the atom approaches the mean of the energies of the active states.

Physical Review A•Oct 1, 1971•26 citations
Abstract The non‐resonant energy transfer at zero temperature between two interacting two‐level quantum systems in the presence of relaxation is studied by aid of the density matrix formalism in the framework of the Markoff approximation. This gives the time evolution of the four probabilities to find the system in each of the four levels owing to the fact that at the initial time, the energy is in the excited state of the donor. The results obtained lead to the Davydov and Serikov solutions for resonant transfer of energy, and to the special one for the indirect coupling between a single level and a continuous medium.
Abstract In this study, the steepest-entropy-ascent quantum thermodynamics (SEAQT) framework is used to investigate the excitation transfer (ET) dynamics of two-level nanosystems (TLSs), focusing on non-resonant processes that involve a dynamic local phonon system. In contrast to other methods based on Markovian or non-Markovian quantum master equations, SEAQT analysis always guarantees the positivity of the density operators, thus enabling the discussion of both transient and long-term dynamics of nanosystems. The findings of this study demonstrate that the relaxation time of coherent phonons, relative to the Rabi oscillation period in two TLSs, significantly affects the relaxation process of non-resonant ETs. Moreover, the degree of mutual synchronization between ET dynamics of TLSs and local (coherent) phonons can either prolong or shorten the decoherence time, presenting a way to control the coherence in nanosystems and stimulate quantum device applications.
Accurate information on the distance dependence of resonance energy transfer (RET) is crucial for its utilization as a spectroscopic ruler \re{of} nanometer scale distances. In this regard, understanding the effects of donor-acceptor quantum coherence and non-Markovian bath, which become significant at short distances, has significant implications. The present work investigates this issue theoretically by comparing results from a theory of coherent RET (CRET) with a nonequilibrium version of Förster's RET (FRET) theory, both accounting for non-Markovian bath effects. Even for a model where the donor-acceptor electronic coupling is of transition dipole interaction form, it is shown that the RET rate in general deviates from the inverse sixth power distance dependence as opposed to the prediction of the original FRET. It is shown that the donor-acceptor quantum coherence makes the \re{distance} dependence steeper than the sixth power although detailed manner of enhancement is sensitive to specific values of parameters. On the other hand, the non-Markovian bath effects make the \re{distance} dependence more moderate than the sixth power for both CRET and nonueqilibrium FRET because finite time scale of the bath causes the rate to be smaller than the prediction of original FRET. While these effects are \re{demonstrated clearly} in the population dynamics at sub-picosecond time scales, their contributions to the conventional RET efficiency are relatively minor. This indicates that the actual detection of such effects through conventional RET efficiency measurement requires either high precision or utilization of a donor with fast spontaneous decay rate of excitation.
Calculations are made to determine the response (power absorbed, magnetization, etc.) of a multilevel quantum system under the influence of any number of classically described driving fields (well defined in amplitude and phase). A nonperturbative theory is developed to account for those fields that are in resonance with the system. The nonresonant effects, such as virtual energy shifts, are included in the theory. We limit ourselves to a discussion of quantum systems that are in weak contact with a thermal reservoir. The procedure is the following A projection-operator formalism is developed which separates the density matrix of a system into two parts. One part is related to those portions of the driving fields that interact quite strongly with the system. The other part is the nonresonant or weakly interacting portion. An exact equation of motion, which includes the effects of the nonresonant part, is derived for the strongly interacting part of the density matrix. It is then shown that when relaxation can be represented by phenomenological decay constants, a unitary transformation can be found which reduces the equation of motion for the strongly interacting part of the density matrix so that an exact solution is possible. This solution is shown to give the major effects of the driving fields and can be used as the zeroth-order solution in a perturbation treatment of the whole density matrix. Frequency shifts such as the Bloch-Siegert shift and shifts due to couplings between the levels of interest (resonance levels) and other levels (nonresonance levels) all arise in the same natural way in our treatment. Our results in many instances are the extensions of the well-known results for a two-level quantum-mechanical systemm to an NNN-level one, and include resonant multiple quantum effects. As an example, a straightforward application of the method is carried out in order to compute the shifts in the resonance frequencies of a four-level system, driven by two oscillating fields connecting three of the levels, due to the counter-rotating components of the driving fields and the presence of the fourth level, which is not coupled to the other levels by the driving fields.
Resonant two-photon absorption is discussed for the case in which the exciting field may be intense enough and near enough to resonance to cause appreciable saturation. A single pair of levels in an otherwise quite general atom is assumed to satisfy the appropriate resonance condition, and equations are derived governing the time evolution of the associated 2 \ifmmode\times\else\texttimes\fi{} 2 submatrix of the full atomic density matrix. Atomic relaxation is treated explicitly. The analysis, which treats both inversion-symmetric and inversion-nonsymmetric cases within the same general formalism, is developed systematically, the necessary approximations receiving careful discussion. The results are analogous to those for the corresponding one-photon process, but with a shift in the resonance frequency proportional to the intensity of the exciting field. This frequency shift is not identical to the one calculated by time-independent (second-order) perturbation theory, and becomes large when the energy of an intermediate state of the atom approaches the mean of the energies of the active states.