Exciton-phonon Systems Research Articles

Unified Definition of Exciton Coherence Length for Exciton–Phonon Coupled Molecular Aggregates

Exciton coherence length (ECL) characterizes the spatial extent of coherently delocalized excited states of molecular aggregates. Constructive/destructive superpositions of coherent molecular dipoles lead to superradiance/subradiance, where the radiative rate is enhanced/suppressed compared to that of a single molecule. Longer ECLs correspond to faster/slower radiative rates for superradiant/subradiant aggregates. However, previous ECL definitions fail to produce monotonic relationships when exciton–phonon coupling is considered, even for simple 1D exciton–phonon systems. This problem is exacerbated for 2D aggregates with both constructive and destructive superpositions. In this Letter, we propose a novel ECL definition by virtue of sum rule for oscillator strengths, ensuring a bijective and monotonic relationship between ECL and radiative rate for both 1D/2D superradiant and subradiant aggregates. Using numerically accurate time-dependent matrix product states, we study large-scale, exciton–phonon coupled 2D aggregates and predict the existence of maximum superradiance at finite temperature, in contrast to the previously believed 1/T law. Our results provide new insights into the design and optimization of efficient light emitting materials.

Quantum decoherence in finite size exciton–phonon systems

Based on the operatorial formulation of the perturbation theory, the properties of a confined exciton coupled with phonons in thermal equilibrium is revisited. Within this method, the dynamics is governed by an effective Hamiltonian which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud whereas the phonons are clothed by virtual excitonic transitions. Special attention is thus paid for describing the time evolution of the excitonic coherences at finite temperature. As in an infinite lattice, temperature-enhanced quantum decoherence takes place. However, it is shown that the confinement softens the decoherence. The coherences are very sensitive to the excitonic states so that the closer to the band center the state is located, the slower the coherence decays. In particular, for odd lattice sizes, the coherence between the vacuum state and the one-exciton state exactly located at the band center survives over an extremely long time scale. A superimposition involving the vacuum and this specific one-exciton state behaves as an ideal qubit insensitive to its environment.

Parametric resonance-induced time-convolutionless master equation breakdown in finitesize exciton–phonon systems

A detailed analysis is performed to show that the second order time-convolutionless masterequation fails to describe the exciton–phonon dynamics in a finite size lattice. To proceed,special attention is paid to characterizing the coherences of the exciton reduced densitymatrix. These specific elements measure the ability of the exciton to developsuperimpositions involving the vacuum and the one-exciton states. It is shown that thecoherences behave as wavefunctions whose dynamics is governed by a time-dependenteffective Hamiltonian defined in terms of the so-called time-dependent relaxationoperator. Due to the confinement, quantum recurrences provide to the relaxationoperator an almost periodic nature, so the master equation reduces to a linearsystem of differential equations with almost periodic coefficients. We show that, inaccordance with the Floquet theory, unstable solutions emerge due to parametricresonances involving specific frequencies of the relaxation operator and specificexcitonic eigenfrequencies. These resonances give rise to an unphysical exponentialgrowth of the coherences, indicating the breakdown of the second order masterequation.

Phonon anharmonicity-induced decoherence slowing down in exciton–phononsystems

Based on a generalized Fröhlich model, a time-convolutionless master equation is establishedfor studying the dynamics of an exciton coupled with anharmonic phonons. Specialattention is paid to describing the influence of the phonon anharmonicity on specificelements of the exciton reduced density matrix. These elements, called coherences,characterize the ability of the exciton to develop quantum states that are superimpositionsinvolving the vacuum and the local one-exciton states. Whether the phonons are harmonicor not, it is shown that dephasing limited-coherent motion takes place. The coherencesirreversibly decrease with time, the decay rate being the so-called dephasing rate,so that they experience a localization phenomenon and propagate over a finitelength scale. However, it is shown that the phonon anharmonicity softens theinfluence of the phonon bath and reduces the dephasing rate. A slowdown inthe decoherence process appears so that the coherences are able to explore alarger region along the lattice. Moreover, the phonon anharmonicity modifies theway the dephasing rate depends on both the adiabaticity and the temperature.In particular, the dephasing rate increases linearly with the temperature in theweak anharmonicity limit whereas it becomes almost temperature-independentin the strong anharmonicity limit. Note that the present formalism is appliedto describe amide-I excitons (vibrons) in a lattice of H-bonded peptide units.

Phonon mediated electromagnetically induced transparency and ultraslow light in strongly coupled exciton-phonon systems

Phonon mediated electromagnetically induced transparency(EIT)and ultraslow light in strongly coupled exciton-phonon systems are investigated theoretically without making any approximation for excitons. It is shown that electromagnetically induced transparency mediated by phonons and the ultraslow light can occur in such systems as the signal field detuning from the exciton frequency is exactly equal to the phonon frequency. It is further shown that the phonon mediated EIT and ultraslow light calculated by using the exact exciton model is essentially the same as the numerical results obtained using the Bose approximation or the Dyson-Maleev approximation.

Nonlinear optical responses due to exciton-phonon interactions in strongly coupled exciton-phonon systems

The excitonic nonlinear optical responses due to exciton-phonon interactions in strongly coupled exciton-phonon systems are investigated theoretically. It is shown that the influence of exciton-phonon interactions on the nonlinear optical absorptions and Kerr nonlinear coefficients is significant as the signal field frequency detuning from the exciton frequency approaches to the optical phonon frequency. How to manipulate the nonlinear optical responses by using the control fields is also presented.

Electromagnetically induced transparency mediated by phonons in strongly coupled exciton-phonon systems

It is shown theoretically that electromagnetically induced transparency (EIT) due to strong exciton–phonon coupling can occur in strongly coupled exciton–phonon systems such as polymers and organic semiconductors and lead to ultra-slow light effects. The results indicate that the strong coupling of excitons and phonons is important, but the exciton– exciton interaction plays a small role in the generation of the EIT. Numerical results for polydiacetylene–toluene sulfonate are also presented. This EIT in a solid-state medium might be utilized for efficient multiwave mixing and quantum nondemolition measurements, as well as for novel acousto-optical devices.

Transfer dynamics of the two-site prototype polaron model

Abstract In earlier work on the temporal evolution of exciton-phonon systems usually a semiclassical approximation was employed, i.e., the phonon system was treated classically. However, it has been shown that this approach may lead to solutions which contradict the exact solution in relevant parameter ranges, even qualitatively. On the other hand, a fully quantum mechanical treatment is practically impossible, especially in extended exciton-phonon systems. One possibility for overcoming the huge computational difficulties is to subject the coupled system to a tractable unitary transformation which approximately diagonalizes the Hamiltonian. Then the temporal evolution can be calculated in the transformed space. This method is demonstrated for the example of the two-site model (1 exciton, 1 oscillator, 2 sites). A comparison of the temporal evolution obtained in this way with the exact numerical solution shows that the unitary transformation method yields semiquantitatively correct results even in paramet...

Coherent and diffusive features of polaron transport in exciton–phonon systems: A Mori approach

Employing Mori-formalism we calculate the polaron transport of an exciton–phonon system with linear site-occupational coupling. The main feature of our approach is a consistent treatment of the memory function, which is of 2nd order in an effective “smallness parameter” appearing after a Lang–Firsov transformation has been made. The memory function is divided into a quasicoherent part, which can be interpreted as a band type motion, decreasing with increasing temperature, an incoherent part describing usual hopping dynamics and two crossterms. In contrast to previous similar approaches our results do not display any divergence problem. It is found that the two cross terms yield a small transport contribution of coherent nature, at least within the accuracy of the present approximation. Due to this term, although higher order effects may result in a damping, the transport will display coherent features for a long time.

Coherence tendencies in the transport of translationally invariant exciton-phonon systems.

The motion of an exciton in a translationally invariant exciton-phonon system is considered within the frame of the generalized Fulton-Gouterman (FG) transformation, which diagonalizes the coupled exciton-phonon Hamiltonian in the excitonic subspace and yields a set of exact equations for the purely oscillatory FG wave functions. An exact expression for the second moment of the local excitonic occupation numbers is presented in terms of the FG wave functions, for which two different sets of displaced phonon states are discussed. A numerical computation of the second moment characterizes the exciton motion as a coherent process. This result is also found in an improved calculation which is based on the application of the Goldberger-Adams relation. \textcopyright{} 1996 The American Physical Society.

Calculations of the ground-state energy for strong- and intermediate-coupling exciton-phonon systems.

A concise approach for the calculations of the ground-state energy in strongly bound exciton-phonon systems is presented in this paper. The coherent state with two-phonon correlation is introduced to represent the phonon wave function, which is related to the wave function of the relative motion \ensuremath{\varphi}(r). A nonlinear integro-differential equation satisfied by \ensuremath{\varphi}(r) is derived. Numerical calculations are carried out for several strongly and intermediate-bound polar materials and the ground-state energy of the corresponding excitons is found to be close to the experimental one. \textcopyright{} 1996 The American Physical Society.

Squeezed oscillatory states in extended exciton-phonon systems.

In earlier work it was found that for prototype exciton-phonon systems (dimer, trimer) the spatial extension of the oscillatory wave functions strongly depends on the intrinsic material constants. In the present paper we demonstrate that this holds true also for extended systems with translational invariance. Our Hamiltonian is subjected to the Fulton-Gouterman (FG) transformation which exactly eliminates the excitonic degrees of freedom. The evolving FG equations elucidate most clearly the two counteracting tendencies of the model: self-trapping and anti-self-trapping. It is shown both analytically and variationally that, if these two tendencies are approximately equally strong, the phonon wave functions are spatially narrowed or broadened depending on the energetic region. This behavior can be adequately described by unitary squeezing transformations. \textcopyright{} 1996 The American Physical Society.

Squeezed excited states in exciton-phonon systems.

In earlier work unusual excited exciton-phonon states have been found for prototype exciton-phonon Hamiltonians (dimer, trimer). These states have been calculated numerically by diagonalizing the respective Fulton-Gouterman equations. Their physical character is such that the motion of the effective exciton becomes free whereas in the vibrational subspace the dynamics is governed by an effective stiffening of the nearest-neighbor interaction. In the present work it is shown analytically by means of a Fr\"ohlich-type transformation, how the stiffening in the phonon dynamics is generated, such that the phononic part for these nonconventional exciton-phonon states is well described by squeezed oscillatory functional forms.

External optical feedback for exciton-phonon systems in optical cavities

Effects of external optical feedback on the behavior of input-cavity-field relations are investigated for an electron–phonon system inside an optical cavity exposed to an incident laser field. The external feedback by conventional mirrors and by phase-conjugate mirrors is considered separately. Steady-state results are obtained numerically for a typical phonon–exciton material of polydiacetylene. In the case of conventional external feedback, the threshold, the contrast, and the switching behavior of optical bistability can be changed by adjustment of the feedback parameters without causing any instability, whereas in the case of phase-conjugate feedback the cavity field intensity shows five states corresponding to a single input field intensity as long as the feedback is strong enough. However, all these states are unstable because of the amplified phase-conjugate reflection, which limits the application of phase-conjugate mirrors in optical multistabilities.

On a class of squeezed excited states in exciton-phonon and Jahn-Teller systems (“exotic states”)

Employing the Fulton-Gouterman transformation (FGT), a non-conventional type of excited states (“exotic”) in exciton-phonon systems has been found recently. These states are characterized by a stiffening of the phononic subsystem. It is shown that the phononic part for these non-conventionalexciton-phonon states is well described by squeezed oscillatory functional forms. This can be understood analytically by subjecting the FG Hamiltonian to a Fröchlich-type of unitary transformation.

Mori approach to exciton memories in initially unrelaxed excitonphonon systems: direct and reorganized perturbation expansions

Starting from the Mori formalism, memory functions of excitons coupled to harmonic phonons in periodic crystals with linear exciton-phonon coupling are calculated in two limiting cases: that of the narrow unrenormalized exciton band with only site local coupling and that of the weak exciton-phonon coupling. Mutual correspondence as well as that with results of analogous works is discussed. By a mathematical trick, perturbational series for memory kernel of initially unrelaxed excitons interacting locally with harmonic phonons is then reorganized. Using that, full agreement is achieved with previous results obtained by Generalized Master Equations for initially relaxed excitons in case of narrow exciton band width. For the weak exciton-phonon coupling case, appreciable reduction of damping of the quasicoherent channel may be achieved on account of polaron effects. Crucial role of the exciton bandwidth beyond the lowest order is found in both cases for the low-temperature exciton diffusivity. Some predictions on the temperature dependence of the phonon-scattering limited exciton diffusion constant are given

Self-trapping in quasi-one-dimensional electron- and exciton-phonon systems

We study self-trapping of electrons (excitons) in one-dimensional systems with three realistic types of coupling with phonons, applying a variational procedure valid for the whole range of system parameters. Various types of self-trapped states are identified and mapped in the parameter space. Our results are compared to the results of previous studies. The particular case of biological systems is studied and it is shown that the Davydov-soliton concept can be used for the description of electron transport in biological systems, but not for the energy transfer in terms of amide-I vibrations (CO stretching vibration mode).

Quantum coherence in a coupled system of two boson fields.

On the basis of an exactly soluble model of exciton-phonon coupling systems, we have calculated the quantum coherence of the exciton and phonon field operators. It is shown that the correlation effect is always very large and cannot be neglected at all.

Transient nonlinear optical phenomena in exciton-phonon systems.

Propagation of a light pulse in the bulk and hole bleaching in the absorption spectrum from a film of polydiacetylene-toluene sulfonate are investigated in the transient regime. This polymer is treated as an example of an exciton-phonon coupling system with only two phonon modes dominating the coupling. For the propagation, we use the Maxwell wave equation to express the field in terms of the polarization density, which is found microscopically from a set of optical Bloch-like equations in the semiclassical approximation. Phonon-mediated phenomena predicted in this work include the photon echo in a solid and bistable behavior of both the absorption coefficient and refraction index. The absorption spectrum is calculated for a thin film of an exciton-phonon system under a strong pump field and a weak probe field from the optical Bloch-like equations only. Phonon-mediated bleaching of holes is obtained in good agreement with experiments.

Solitonic Bloch functions and others in the Fulton–Gouterman frame of exciton-phonon systems

A one-dimensional model for Frenkel excitons interacting with acoustical phonons is considered. The generalized Fulton–Gouterman (FG) transcription reduces the problem to a pure vibrational one and simultaneously guarantees the Bloch nature of any exciton-phonon eigenfunction. A general variational ansatz is established with regard to the specific topological structure of the FG equations. Simplified versions of this ansatz are shown to yield lower ground-state energies than any previously used dressed exciton or localized solitonic (‘‘non-Blochian’’) trial functions for all coupling-transfer regimes. This evinces the practicability of the FG conception also in extremal coupling-transfer situations. Since the calculation is easily extended to excited states, the FG approach seems to be an adequate means to investigate energy transport in exciton-phonon systems. In particular, the solitonic problem in these systems may be analyzed on a discrete footing.