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Entropy

Enhanced von Neumann Entropy in Dense Two-Level Ensembles

Аурелиан Исар, Tatiana Mihaescu, Mihai Macovei

Published Oct 18, 2026• 0 citations
Publisher

Abstract

We investigate the equilibrium properties of the von Neumann entropy in a dense, dipole-dipole coupled ensemble of two-level emitters confined in a fully symmetric Dicke subspace, which additionally interact through a common thermal bath. The static dipole-dipole interactions are assumed to be strong, though remaining smaller than the transition frequency. Consequently, the resulting thermal equilibrium entropy of the ensemble is characterized as a function of these coupling strengths. As a consequence, we have demonstrated that the von Neumann entropy enhances when stronger dipole-dipole couplings among the two-level emitters are being involved. Furthermore, the entropy can even be reduced for an opposite sign of the dipole-dipole coupling strength compared to the former case.

DOI
10.3390/e28101146

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We investigate the equilibrium properties of the von Neumann entropy in a dense, dipole-dipole coupled ensemble of two-level emitters confined in a fully symmetric Dicke subspace, which additionally interact through a common thermal bath. The static dipole-dipole interactions are assumed to be strong, though remaining smaller than the transition frequency. Consequently, the resulting thermal equilibrium entropy of the ensemble is characterized as a function of these coupling strengths. As a consequence, we have demonstrated that the von Neumann entropy enhances when stronger dipole-dipole couplings among the two-level emitters are being involved. Furthermore, the entropy can even be reduced for an opposite sign of the dipole-dipole coupling strength compared to the former case.
The quantum dynamics of a dense and dipole-dipole-coupled ensemble of two-level emitters interacting via their environmental thermostat is investigated. The static dipole-dipole interaction strengths are being considered strong enough but smaller than the transition frequency. Therefore, the established thermal equilibrium of ensemble's quantum dynamics is described with respect to the dipole-dipole-coupling strengths. We have demonstrated the quantum nature of the spontaneously scattered light field in this process for weaker thermal baths as well as non-negligible dipole-dipole couplings compared to the emitter's transition frequency. Furthermore, the collectively emitted photon intensity suppresses or enhances depending on the environmental thermal baths' intensities. Published by the American Physical Society 2024
We investigate the resonance fluorescence features of a small ensemble of closely packed and moderately laser-pumped two-level emitters at resonance. The mean distance between any two-level radiators is smaller than the corresponding emission wavelength, such that the dipole-dipole interactions are not negligible. We have found that under the secular approximation, the collective resonance fluorescence spectrum consists of 2 N + 1 spectral lines, where N is the number of emitters from the sample. The 2 N spectral sidebands, symmetrically located around the generalized Rabi frequency with respect to the central line at the laser frequency, are distinguishable if the dipole-dipole coupling strength is larger than the collective spontaneous decay rate. This way, one can estimate the radiators number within the ensemble via measuring of the spontaneously scattered collective resonance fluorescence spectrum. Contrarily, if the dipole-dipole coupling is of the order of or smaller than the cooperative spontaneous decay rate, but still non-negligible, the spectrum turns into a Mollow-like fluorescence spectrum, where the two sidebands' spectral lines broaden proportional to the dipole-dipole coupling strength. Published by the American Physical Society 2024
We introduce a generalized Dicke-like model to describe two-level systems coupled with a single bosonic mode. In addition, the two-level systems mutually interact via direct dipole–dipole interaction. We apply the model to an ensemble of dye molecules coupled to a plasmonic excitation in a metallic nanoparticle and study how the dipole–dipole interaction and configurational randomness introduced to the system affect the energy spectra. Comparing the system eigenenergies obtained by our model with the light spectra from a multiple-scattering simulation, we suggest a way to identify dark modes in our model. Finally, we perform a parameter sweep in order to determine the scaling properties of the system and to classify the regions of the parameter space where the dipole–dipole interactions can have significant effects.
The steady-state quantum dynamics of three dipole-dipole coupled two-level emitters, fixed at the vertices of an equilateral triangle, and interacting via the environmental thermostat is investigated. We have analytically obtained the populations of the involved three-atom cooperative states as well as of the second- and third-order spatial photon correlation functions of the light scattered by the few-qubit sample. As a consequence, we have demonstrated that this incoherently excited system spontaneously generates streams of single photons possessing sub-Poissonian photon statistics. In analogy to the dipole-dipole blockade, one may expect that at smaller inter particle distances, compared to the photon emission wavelength, the reported phenomenon has the same origin. However, we have shown that the quantum photon features are due to the interaction's nature of the few symmetrically arranged two-level emitters with the surrounding thermal reservoir. Respectively, at larger atomic intervals the effect occurs because of high-order spatial interference phenomena. Sub-wavelength interference fringes can be observed too, via measurements of spatial higher-order photon correlation functions.
Let ${|{\ensuremath{\psi}}_{1}〉,\dots{},|{\ensuremath{\psi}}_{n}〉{;p}_{1},\dots{}{,p}_{n}}$ be an ensemble of pure quantum states. We show that it is possible to increase all of the pairwise overlaps $|〈{\ensuremath{\psi}}_{i}|{\ensuremath{\psi}}_{j}〉|,$ i.e., make each constituent pair of the states more parallel (while keeping the prior probabilities the same), in such a way that the von Neumann entropy S is increased, and dually, make all pairs more orthogonal while decreasing S. We show that this phenomenon cannot occur for ensembles in two dimensions but that it is a feature of almost all ensembles of three states in three dimensions. It is known that the von Neumann entropy characterizes the classical and quantum information capacities of the ensemble and we argue that information capacity, in turn, is a manifestation of the distinguishability of the signal states. Hence, our result shows that the notion of distinguishability within an ensemble is a global property that cannot be reduced to considering distinguishability of each constituent pair of states.
Two qubits strongly coupled to a common bosonic reservoir can become entangled with each other, despite having no direct interaction. In equilibrium, such coupling-induced coherences can be described by the mean-force Gibbs state. Here we derive approximate, analytic expressions for the two-qubit mean-force Gibbs state, and use these to characterize equilibrium qubit-qubit entanglement mediated by a thermal reservoir. Entanglement, which is highest at lowest temperatures, is a non-monotonic function of the system-reservoir coupling strength. Moreover, we find that broadening the reservoir spectral density beyond a single mode, as is realistic for typical baths, can enhance the qubit entanglement. Our results provide a comprehensive understanding of reservoir-mediated two-qubit entanglement in thermal equilibrium and provide a benchmark to compare with numerical methods, as well as demonstrating the utility of strong system-reservoir coupling as a resource.