Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism

Celardo, G. L.; Kaplan, L.

doi:10.1103/physrevb.79.155108

Cited by 102 publications

(162 citation statements)

References 49 publications

(42 reference statements)

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“…Therefore, we restrict our considerations to the 7 × 7 matrix i|ρ|j , 1 ≤ i, j ≤ 7, which however does not have constant trace. In order to compute the evolution of the reduced density matrix, we introduce an effective non-Hermitian Hamiltonian [9,16,23] which in general can be written as,…”

Section: The Model For Superradiance Transitionmentioning

confidence: 99%

Superradiance Transition in Photosynthetic Light-Harvesting Complexes

et al. 2012

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We investigate the role of long-lasting quantum coherence in the efficiency of energy transport at room temperature in Fenna-Matthews-Olson photosynthetic complexes. The excitation energy transfer due to the coupling of the light harvesting complex to the reaction center ("sink") is analyzed using an effective non-Hermitian Hamiltonian. We show that, as the coupling to the reaction center is varied, maximal efficiency in energy transport is achieved in the vicinity of the superradiance transition, characterized by a segregation of the imaginary parts of the eigenvalues of the effective non-Hermitian Hamiltonian. Our results demonstrate that the presence of the sink (which provides a quasi-continuum in the energy spectrum) is the dominant effect in the energy transfer which takes place even in absence of a thermal bath. This approach allows one to study the effects of finite temperature and the effects of any coupling scheme to the reaction center. Moreover, taking into account a realistic electric dipole interaction, we show that the optimal distance from the reaction center to the Fenna-Matthews-Olson system occurs at the superradiance transition, and we show that this is consistent with available experimental data.

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Section: The Model For Superradiance Transitionmentioning

confidence: 99%

Superradiance Transition in Photosynthetic Light-Harvesting Complexes

et al. 2012

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“…The details are worked out in [1], [2] and [9]. This method provides a general framework applicable to a broad range of systems from loosely bound nuclei [9] to electron transport in nanosystems [10]. The approach taken here is to make the most minimal adjustment to the GOE that would mimic openness and see how the RMT results are affected.…”

Section: Opening the System Energies And Entropymentioning

confidence: 99%

Open quantum systems and random matrix theory

Mulhall

2014

AIP Conference Proceedings

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A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper the effect of opening the system on the level statistics is seen. In particular the ∆ 3 (L) statistic, the width distribution and the level spacing are examined as a function of the strength of this coupling. The emergence of a superradiant transition is observed. The level spacing and ∆ 3 (L) statistic exhibit the signatures of missed levels or intruder levels as the super-radiant state is formed. * Electronic address: mulhalld2@scranton.edu

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“…Technically speaking, one uses actually an effective Hamiltonian obtained by formal elimination of the degree of freedom of the leads, however, as the price to be paid, the result is a non-Hermitian Hamiltonian with complex eigenvalues. The method of non-Hermitian Hamiltonian has been used for the calculation of transport properties of the quantum dots in the Landauer-Büttiker formalism (see for instance [6]), but also in the localization-delocalization problem in the 1D non-Hermitian Anderson model [7][8][9]. In these two different problems, the non-hermicity arises from different sources, however we do not enter here such peculiar aspects.…”

Section: Introductionmentioning

confidence: 99%

Phosphorene confined systems in magnetic field, quantum transport, and superradiance in the quasiflat band

Ostahie

Aldea

2016

Phys. Rev. B

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Spectral and transport properties of electrons in confined phosphorene systems are investigated in a five hopping parameter tight-binding model, using analytical and numerical techniques. The main emphasis is on the properties of the topological edge states accommodated by the quasi-flat band that characterizes the phosphorene energy spectrum.We show, in the particular case of phosphorene, how the breaking of the bipartite lattice structure gives rise to the electron-hole asymmetry of the energy spectrum. The properties of the topological edge states in the zig-zag nanoribbons are analyzed under different aspects: degeneracy, localization, extension in the Brillouin zone, dispersion of the quasi-flat band in magnetic field.The finite-size phosphorene plaquette exhibits a Hofstadter-type spectrum made up of two unequal butterflies separated by a gap, where a quasi-flat band composed of zig-zag edge states is located.The transport properties are investigated by simulating a four-lead Hall device (importantly, all leads are attached on the same zig-zag side), and using the Landauer-Büttiker formalism. We find out that the chiral edge states due to the magnetic field yield quantum Hall plateaus, but the topological edge states in the gap do not support the quantum Hall effect and prove a dissipative behavior. By calculating the complex eigenenergies of the non-Hermitian effective Hamiltonian that describes the open system (plaquette+leads), we prove the superradiance effect in the energy range of the quasi-flat band, with consequences for the density of states and electron transmission properties.

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Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism

Cited by 102 publications

References 49 publications

Superradiance Transition in Photosynthetic Light-Harvesting Complexes

Superradiance Transition in Photosynthetic Light-Harvesting Complexes

Open quantum systems and random matrix theory

Phosphorene confined systems in magnetic field, quantum transport, and superradiance in the quasiflat band

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