Spin boson models for quantum decoherence of electronic excitations of biomolecules and quantum dots in a solvent

Gilmore, Joel; McKenzie, Ross H.

doi:10.1088/0953-8984/17/10/028

Cited by 75 publications

(112 citation statements)

References 56 publications

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“…Most importantly, the Rabi model is the single-mode version of a dissipative (infinite-mode) spin-boson model [21], signifying that light-matter interaction is a simplified manifestation of a more fundamental interaction between a two-state system and a dissipative environment. Previous dissipative [22][23][24][25] generalizations have neither extended the symmetry nor preserved this correspondence. Motivated by these properties, this Letter presents a symmetry-preserving N -state extension of the Rabi model.…”

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confidence: 87%

Quantum Rabi Model forN-State Atoms

Albert

2012

Phys. Rev. Lett.

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A tractable N -state Rabi Hamiltonian is introduced by extending the parity symmetry of the two-state model. The single-mode case provides a few-parameter description of a novel class of periodic systems, predicting that the ground state of certain four-state atom-cavity systems will undergo parity change at strong coupling. A group-theoretical treatment provides physical insight into dynamics and a modified rotating wave approximation obtains accurate analytical energies. The dissipative case can be applied to study excitation energy transfer in molecular rings or chains. Interactions between spin systems and harmonic oscillators (boson modes) have been studied for over 70 years [1][2][3]. One of the most well-known, the quantum Rabi model [1], is a phenomenological Hamiltonian describing interactions between a two-level system and a cavity mode. The model has also formed a basis of understanding for exciton-phonon interactions [4] and, along with its multi-mode extension, has numerous established applications in chemistry and physics (see [5][6][7] and refs. therein). The Jaynes-Cummings (J-C) [3] model is obtained by taking the Rabi model in the rotating wave approximation (RWA), where the "counter-rotating" terms are ignored (see e.g. [8]). While the J-C model is sufficient to study small atom-field coupling, the RWA breaks down at large coupling [9,10] Many-site spin-boson interaction, e.g. multi-state atom-cavity interaction [14] or excitation energy transfer in multi-chromophoric systems [15], continues to be a subject of significant interest, dictating a need for extensions of the two-state model. Extensions of the J-C model have been studied extensively [16][17][18][19], but are no longer applicable in the strong-coupling regime. Exciton-phonon generalizations which extend the parity/reflection symmetry of the Rabi system [20] are neither tractable nor applicable to atom-cavity systems. Most importantly, the Rabi model is the single-mode version of a dissipative (infinite-mode) spin-boson model [21], signifying that light-matter interaction is a simplified manifestation of a more fundamental interaction between a two-state system and a dissipative environment. Previous dissipative [22][23][24][25] generalizations have neither extended the symmetry nor preserved this correspondence. Motivated by these properties, this Letter presents a symmetry-preserving N -state extension of the Rabi model. The extension includes counter-rotating terms in a rigorous, intuitive, and mathematically manageable way, using a minimal number of parameters and paving the way for applications to multi-level atom-cavity experiments at both weak and strong coupling. A grouptheoretical approach [2] provides numerical advantages and physical insight into dynamics of the single-mode case. The symmetric generalized RWA [7] is applied to obtain accurate analytical energies/eigenstates valid for strong coupling. The above procedures are significantly simplified via the generalized spin matrices [26], providing a new tool for the treat...

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confidence: 87%

Quantum Rabi Model forN-State Atoms

Albert

2012

Phys. Rev. Lett.

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“…Here, an excitation in one chromophore may be transferred to a nearby chromophore by the Coulomb interaction, typically dipole-dipole interactions. A coupled system of molecules such as this may be mapped to the spin-boson model [6], where the two quantum states refer to the location of the excitation, ǫ is the difference in the two chromophore's excited energy levels, and J(ω) describes the coupling of the excitation to the environments surrounding each molecule. We have previously shown [6] that the appropriate spectral density is simply the sum of the spectral density of each individual chromophore-protein complex.…”

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confidence: 99%

Quantum Dynamics of Electronic Excitations in Biomolecular Chromophores: Role of the Protein Environment and Solvent

2008

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We consider continuum dielectric models as minimal models to understand the effect of a surrounding globular protein and solvent on the quantum dynamics of electronic excitations in a biological chromophore. For these models we derive expressions for the frequency dependent spectral density which describes the coupling of the electronic levels in the chromophore to its environment. The magnitude and frequency dependence of the spectral density determines whether or not the quantum dynamics is coherent or incoherent, and thus whether on not one can observe quantum interference effects such as Rabi oscillations. We find the contributions to the spectral density from each component of the chromophore environment: the bulk solvent, protein, and water bound to the protein. The relative importance of each component to the quantum dynamics of the chromophore is determined by the time scale on which one is considering the dynamics. Our results provide a natural explanation and model for the different time scales observed in the spectral density extracted from the solvation dynamics probed by ultra-fast laser spectroscopy techniques such as the dynamic Stokes shift and three pulse photon echo spectroscopy. Our results are used to define under what conditions the dynamics of the excited chromophore is dominated by the surrounding protein and when it is dominated by dielectric fluctuations in the solvent. We show that even when the chromophore is shielded from the solvent by the protein ultra-fast solvation can be dominated by the solvent. Hence, we suggest that the ultra-fast solvation recently seen in some biological chromophores should not necessarily be assigned to ultra-fast protein dynamics. The magnitudes of the spectral density that we estimate from our continuum models and extracted from experiment suggest that most quantum dynamics of electronic excitations is incoherent. A possible exception is transfer of excitons between neigbouring chromophores in photosynthetic systems.

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“…In the following, we discuss the strong-coupling limit J 0 /ω c > 1, where an appreciable modification of the electronic spectrum occurs. Recent estimates [22] of the latter parameter using the classical Onsager model for molecule-solvent interactions suggest that this regime can be realized in a water environment. In Fig.…”

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Quantum Transport through a DNA Wire in a Dissipative Environment

2005

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Electronic transport through DNA wires in the presence of a strong dissipative environment is investigated. We show that new bath-induced electronic states are formed within the bandgap. These states show up in the linear conductance spectrum as a temperature dependent background and lead to a crossover from tunneling to thermal activated behavior with increasing temperature. Depending on the strength of the electron-bath coupling, the conductance at the Fermi level can show a weak exponential or even an algebraic length dependence. Our results suggest a new environmentalinduced transport mechanism. This might be relevant for the understanding of molecular conduction experiments in liquid solution, like those recently performed on poly(GC) oligomers in a water buffer (B. Xu et al., Nano Lett. 4, 1105 (2004)).In the emerging field of molecular electronics, DNA oligomers have drawn in the last decade the attention of both experimentalists and theoreticians [1]. This has been mainly motivated by DNA exciting potential applications which include its use as a template in molecular devices or by exploiting its self-assembling and selfrecognition properties [2]. Alternatively, DNA strands might act as molecular wires either in periodic conformations as in poly(GC), or by doping with metal cations as is the case of M-DNA [3]. As a consequence, the identification of the relevant charge transport channels in DNA systems becomes a crucial issue. Transport experiments in DNA derivatives are however quite controversial [4,5]. DNA has been characterized as insulating [6], semiconducting [7] or metallic [8,9]. It becomes then apparent that sample preparation and experimental conditions are more critical than in transport experiments on other nanoscale systems. Meanwhile, a variety of factors that appreciably control charge propagation along the double helix have been theoretically identified: static [10] and dynamical [11] disorder related to random base pair sequences and structural fluctuations, respectively, as well as environmental effects associated with correlated fluctuations of counterions [12] or with the formation of localised states within the bandgap [4,13].Recently, Xu et al. [9] have carried out transport experiments on poly(GC) oligomers in aqueous solution. These experiments are remarkable for different reasons: (i) it was shown that transport characteristics of single molecules were probed, (ii) the molecules displayed ohmic-like behavior in the low-bias I-V characteristics and (iii) the linear conductance showed an algebraic dependence g ∼ N −1 on the number N of base pairs. This latter result suggests the dominance of incoherent charge transport processes. Complex band structure calculations [14] for dry poly(GC) oligomers predict, on the contrary, a rather strong exponential dependence of the conductance on the wire length, a typical result for coherent tunneling through band gaps. Hence,

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Spin boson models for quantum decoherence of electronic excitations of biomolecules and quantum dots in a solvent

Cited by 75 publications

References 56 publications

Quantum Rabi Model forN-State Atoms

Quantum Rabi Model forN-State Atoms

Quantum Dynamics of Electronic Excitations in Biomolecular Chromophores: Role of the Protein Environment and Solvent

Quantum Transport through a DNA Wire in a Dissipative Environment

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