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Physical Review Letters

Absorption Spectra of Quantum Aggregates Interacting via Long-Range Forces

Alexander Eisfeld, J S Briggs

Published Mar 22, 2006• 45 citations
Publisher

Abstract

We present a simple formula by which the shape of the absorption spectrum of an aggregate of quantum "monomers" (cold atoms, molecules, quantum dots, nanoparticles, etc.) interacting via dipole-dipole forces can be calculated from the averaged spectrum of the quantum monomer itself. Spectral broadening, due to a wide variety of causes, is included explicitly so that the formula is applicable not only to the idealization of a discrete spectrum but also to the practical situation of a continuously broadened spectrum. In simple cases, analytic results are obtained showing the strong dependence of the aggregate spectrum on the precise nature of the broadening of the quantum monomer spectrum. The formula is compared with results of exact diagonalization of model aggregate Hamiltonians and with experiment.

DOI
10.1103/physrevlett.96.113003

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We present a simple formula by which the shape of the absorption spectrum of an aggregate of quantum "monomers" (cold atoms, molecules, quantum dots, nanoparticles, etc.) interacting via dipole-dipole forces can be calculated from the averaged spectrum of the quantum monomer itself. Spectral broadening, due to a wide variety of causes, is included explicitly so that the formula is applicable not only to the idealization of a discrete spectrum but also to the practical situation of a continuously broadened spectrum. In simple cases, analytic results are obtained showing the strong dependence of the aggregate spectrum on the precise nature of the broadening of the quantum monomer spectrum. The formula is compared with results of exact diagonalization of model aggregate Hamiltonians and with experiment.
Linear optical spectra of molecular aggregates are often approximated by classical optics methods such as the discrete-dipole approximation (DDA), coherent exciton scattering (CES), and coherent potential approximation (CPA), where the only quantum-mechanical input to the calculation is the linear susceptibility of the monomers. However, the limits of validity of these classical optics methods remain opaque. Here, starting from a quantum mechanical Hamiltonian for the aggregate, we identify a limit where DDA/CPA/CES is exact: all-to-all coupled permutationally symmetric aggregates of N→∞N \to \inftyN→∞ monomers. The permutational symmetry of this molecular version of the Lipkin-Meshkov-Glick model, which is closely related to that of the molecular polariton problem of many identical molecules coupled to a single-cavity mode, allows us to borrow recent techniques developed for the latter. In particular, we identify a 1/N1/N1/N expansion that corrects the classical optics limit with finite NNN corrections to the linear response of the aggregate. These corrections feature as Raman-like transitions of a single monomer. We illustrate these findings with calculations on the very physically-relevant setup of a homodimer. Our findings clarify how quantum optical features that go beyond classical optics can already be present in simple arrays of quantum emitters such as molecular aggregates.
We consider three distinct methods of calculating the vibronic levels and absorption spectra of molecular dimers coupled by dipole-dipole interactions. The first method is direct diagonalization of the vibronic Hamiltonian in a basis of monomer eigenstates. The second method is to use creation and annihilation operators leading in harmonic approximation to the Jaynes-Cummings Hamiltonian. The adiabatic approximation to this problem provides insight into spectral behavior in the weak and strong coupling limits. The third method, which serves as a check on the accuracy of the previous methods, is a numerically exact solution of the time-dependent Schrodinger equation. Using these methods, dimer spectra are calculated for three separate dye molecules and show good agreement with measured spectra.
We present a new approach for investigating the Markovian to non-Markovian transition in quantum aggregates strongly coupled to a vibrational bath through the analysis of linear absorption spectra. Utilizing hierarchical algebraic equations in the frequency domain, we elucidate how these spectra can effectively reveal transitions between Markovian and non-Markovian regimes, driven by the complex interplay of dissipation, aggregate–bath coupling, and intra-aggregate dipole–dipole interactions. Our results demonstrate that reduced dissipation induces spectral peak splitting, signaling the emergence of bath-induced non-Markovian effects. The spectral peak splitting can also be driven by enhanced dipole–dipole interactions, although the underlying mechanism differs from that of dissipation-induced splitting. In addition, with an increase in aggregate–bath coupling strength, initially symmetric or asymmetric peaks with varying spectral amplitudes may merge under weak dipole–dipole interactions, whereas strong dipole–dipole interactions are more likely to cause peak splitting. Moreover, we find that spectral features serve as highly sensitive indicators for distinguishing the geometric structures of aggregates while also unveiling the critical role that geometry plays in shaping non-Markovian behavior. This study not only deepens our understanding of the Markovian to non-Markovian transition but also provides a robust framework for optimizing and controlling quantum systems.
Electromagnetically induced transparency (EIT), which is known as an efficient control method of optical absorption property, is investigated using the polarizability spectra and population dynamics obtained by solving the quantum Liouville equation. In order to clarify the intermolecular interaction effect on EIT, we examine several molecular aggregate models composed of three-state monomers with the dipole-dipole coupling. On the basis of the present results, we discuss the applicability of EIT in molecular aggregate systems to a new type of optical switch.
In this article, we present a simulation study of the linear and nonlinear spectroscopy of dense atomic vapors. Motivated by recent experiments, we focus on double quantum spectroscopy, which directly probes dipole-dipole interactions. By explicitly including thermal velocity, we show that temperature has an important impact on the self-broadening mechanisms of the linear and nonlinear spectra. We also provide analytical expressions for the response functions in the short time limit using the two-body approximation, which shows that double quantum spectroscopy for atomic vapors directly probes the transition amplitude of the electronic excitation between two atoms. We also propose an expression for the double quantum spectrum that includes the effect of Doppler broadening, and we discuss the effect of density on the spectrum. We show that when Doppler broadening is negligible compared to self-broadening, the double quantum spectrum scales with the atomic density, while when Doppler broadening dominates, it scales as the square of the density.
In quantum theory, the description of radiation by a system of charged particles in stationary and nonstationary cases requires different approaches. While radiative processes in stationary systems are covered in textbooks, the emission of radiation by nonstationary systems driven by an external time-dependent force has not received due attention. In this paper, we develop a quantum theory describing the spectrum of photons emitted by a generic nonstationary atomic system and show how to implement it in practical calculations. We also discuss the approximation in which the exact quantum formula for the spectrum reduces to the well-known classical formula with the classical dipole moment replaced by the expectation value of the dipole moment calculated quantum mechanically. This approximation underlies the classical ansatz commonly used in the theory of high-order harmonic generation (HHG). To illustrate the theory, we apply it to calculating HHG spectrum for a one-dimensional zero-range-potential model. The spectra obtained from the quantum formula and from the ansatz are different and the difference grows as the probability of ionization grows. This difference is an observable effect predicted by the present theory.