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The Journal of Chemical Physics

Interplay between classical and quantum dissipation in light–matter dynamics

Facundo Tarasi, Tchavdar N. Todorov, Carlos M. Bustamante, Esteban D. Gadea, Lorenzo Stella, Tzveta Apostolova, Damián A. Scherlis

Published Dec 3, 2024• 2 citations
Publisher

Abstract

A quantum-electrodynamics approach is presented to describe the dynamics of electrons that exchange energy with both photon and phonon baths. Our ansatz is a dissipative quantum Liouville equation, cast in the Redfield form, with two driving terms associated with radiative and vibrational relaxation mechanisms, respectively. Remarkably, within the radiative contribution, there is a term that exactly replicates the expression derived from a semiclassical treatment where the power dissipated by the electronic density is treated as the emission from a classical dipole [Bustamante et al., Phys. Rev. Lett. 126, 087401 (2021)]. Analysis of the distinct contributions to the total radiation shows that the semiclassical emission depends on the coherences, with the remainder of the quantum-electrodynamics driving term determined by the excited populations, thus accounting for the relaxation of eigenstates or incoherent mixed states. This approach is used to investigate the response of the Su-Schrieffer-Heeger model for trans-polyacetylene to both pulsed and continuous laser irradiation. Upon excitation with a short pulse and in the absence of the vibrational mechanism, the conducting band population exhibits a stepwise relaxation, characterized by cycles of exponential decay followed by a transient subradiant state. The latter arises from the collective coupling between Bloch states featuring a quasi-continuum energy spectrum in reciprocal space. The separate examination of the semiclassical dynamics reveals that it is this contribution that is responsible for the collective behavior. If vibrational dissipation is active, following the laser pulse, the excited electrons rapidly populate the minimum of the conduction band, and the emission spectrum shifts to lower frequencies with respect to absorption. Meanwhile, continuous irradiation drives the system to a stationary state with a broad emission spectrum.

DOI
10.1063/5.0240135

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A quantum-electrodynamics approach is presented to describe the dynamics of electrons that exchange energy with both photon and phonon baths. Our ansatz is a dissipative quantum Liouville equation, cast in the Redfield form, with two driving terms associated with radiative and vibrational relaxation mechanisms, respectively. Remarkably, within the radiative contribution, there is a term that exactly replicates the expression derived from a semiclassical treatment where the power dissipated by the electronic density is treated as the emission from a classical dipole [Bustamante et al., Phys. Rev. Lett. 126, 087401 (2021)]. Analysis of the distinct contributions to the total radiation shows that the semiclassical emission depends on the coherences, with the remainder of the quantum-electrodynamics driving term determined by the excited populations, thus accounting for the relaxation of eigenstates or incoherent mixed states. This approach is used to investigate the response of the Su-Schrieffer-Heeger model for trans-polyacetylene to both pulsed and continuous laser irradiation. Upon excitation with a short pulse and in the absence of the vibrational mechanism, the conducting band population exhibits a stepwise relaxation, characterized by cycles of exponential decay followed by a transient subradiant state. The latter arises from the collective coupling between Bloch states featuring a quasi-continuum energy spectrum in reciprocal space. The separate examination of the semiclassical dynamics reveals that it is this contribution that is responsible for the collective behavior. If vibrational dissipation is active, following the laser pulse, the excited electrons rapidly populate the minimum of the conduction band, and the emission spectrum shifts to lower frequencies with respect to absorption. Meanwhile, continuous irradiation drives the system to a stationary state with a broad emission spectrum.
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We have studied quantum-mechanical behavior of a driven Morse oscillator coupled to a bath of harmonic oscillators. The purpose is to compare the quantum behavior of such a system with the classical solutions of a driven damped Morse oscillator. We start with the quantum Liouville equation, in which the Hamiltonian of the Morse oscillator is expressed in terms of generators of an su(2) Lie algebra. This algebra and the Markovian approximation allow us to derive the generalized master equation (for the reduced density matrix of the Morse oscillator), which contains level-dependent energy and phase relaxation terms. We have numerically integrated the differential equations of the matrix elements to obtain the time evolution of the reduced density matrix and the energy of the Morse oscillator. We show that the energy of the Morse oscillator in general varies with time and eventually reaches an asymptotic oscillatory state. The mean energy value of the asymptotic oscillatory state is studied as a function of the relaxation rates and laser frequency and amplitude. Vibrational distributions have also been found as functions of laser frequency and amplitude. The shape of the distribution changes gradually as laser amplitude increases; it first peaks at the ground state at a small field amplitude, then it peaks at some excited state at a large field amplitude, and for an amplitude in between it can have two maxima. This bimodal vibrational distribution reflects the bistability observed in the classical and semiclassical models. Thus bistability exists in quantum results, not as a hysteresis loop, but as a bimodal distribution. Finally, we show that as laser intensity increases, the time series of the oscillator energy evolves from regular to quasiperiodic behavior, and eventually a chaotic-looking series appears.
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The dynamics of electrons and holes in semiconductors and semiconductor heterostructures have been extensively discussed in the literature, and are governed by their mutual Coulomb interaction, by their interaction with lattice vibrations (phonons) and by their radiative recombination (for an overview see e.g. Ref. [1]). A powerful technique to study the carrier dynamics in semiconductors utilizes short optical pulses to photoexcite electrons from the valence to the conduction band (i.e. to create electron-hole pairs) that subsequently relax until the photon energy stored in the medium is dissipated and the system has recovered the thermal equilibrium. The dynamics of the carriers photoexcited by the short optical pulse can be followed by monitoring two main optical observables: the interband population difference and the induced polarization. Both quantities decay with time after the photoexcitation due to the carrier dynamics. While the induced polarization (which is an ensemble average over many photoexcited dipole moments) is sensitive to scattering events that break the phase relationship among the individual dipoles and/or with the light field creating them (dephasing processes), the population difference is sensitive only to events that change the energy state of the carriers. Transient coherent optical spectroscopy addresses the time-evolution of the induced polarization in the time-regime during and immediately following the photoexcitation by a short laser pulse, in which the photoexcited dipoles have retained a defined phase relationship among each other and with the exciting coherent radiation.
We have developed a unified quantum optical master equation that includes the dissipative mechanisms of an impurity molecule in crystals. Our theory applies generally to polyatomic molecules where several vibrational modes give rise to intramolecular vibrational redistributions. The usual assumption on identical shapes of the nuclear potentials in ground and excited electronic states and the rotating wave approximation have been relaxed, i.e. the vibrational coordinates are different in the ground and excited states, with counter-rotating terms included for generality. Linear vibrational coupling to the lattice phonons accounts for dissipations via non-radiative transitions. The interaction of a molecule with photons includes Herzberg-Teller coupling as the first order non-Condon interaction where the transition dipole matrix elements depend linearly on vibrational coordinates. We obtain new cross terms as the result of mixing the terms from the zeroth-order (Condon) and first-order (non-Condon) approximations. The corresponding Lamb shifts for all Liouvilleans are derived explicitly including the contributions of counter-rotating terms. The computed absorption and emission spectra for carbon monoxide is in good agreement with experimental data. We use our unified model to obtain the spectra for nitrogen dioxide, demonstrating the capability of our theory to incorporate all typical dissipative relaxation and decoherence mechanisms for polyatomic molecules. The molecular quantum master equation is a promising theory for studying molecular quantum memory.
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