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arXiv:1506.01433 · The Journal of Physical Chemistry Letters

Understanding the Fundamental Connection Between Electronic Correlation and Decoherence

Arnab Kar, Liping Chen, Ignacio Franco

Published Apr 14, 2016• 11 citations
arXivHTMLPDF

Abstract

We introduce a theory that exposes the fundamental and previously overlooked connection between the correlation among electrons and the degree of quantum coherence of electronic states in matter. For arbitrary states, the effects only decouple when the electronic dynamics induced by the nuclear bath is pure-dephasing in nature such that [H(S),H(SB)] = 0, where H(S) is the electronic Hamiltonian and H(SB) is the electron-nuclear coupling. We quantitatively illustrate this connection via exact simulations of a Hubbard-Holstein molecule using the Hierarchical Equations of Motion that show that increasing the degree of electronic interactions can enhance or suppress the rate of electronic coherence loss.

DOI
10.1021/acs.jpclett.6b00467

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We introduce a theory that exposes the fundamental and previously overlooked connection between the correlation among electrons and the degree of quantum coherence of electronic states in matter. For arbitrary states, the effects only decouple when the electronic dynamics induced by the nuclear bath is pure-dephasing in nature such that [H(S),H(SB)] = 0, where H(S) is the electronic Hamiltonian and H(SB) is the electron-nuclear coupling. We quantitatively illustrate this connection via exact simulations of a Hubbard-Holstein molecule using the Hierarchical Equations of Motion that show that increasing the degree of electronic interactions can enhance or suppress the rate of electronic coherence loss.
We introduce a theory that exposes the fundamental connection between the correlation among electrons and the degree of quantum coherence of electronic states in molecules and materials. Specifically, we show that the electronic interactions VSV^{S}VS that lead to correlation strongly modulate the electronic decoherence and that, conversely, the electron-nuclear interactions HSBH^{SB}HSB that lead to decoherence influence the correlation energy. The effects only decouple when [VS,HSB]=[HS,HSB]=0[V^{S},H^{SB}]=[H^{S},H^{SB}]=0[VS,HSB]=[HS,HSB]=0, where HSH^{S}HS is the electronic Hamiltonian. We quantitatively illustrate this connection via numerically exact simulations of a Hubbard-Holstein molecule.
Electronic decoherence processes in molecules and materials are usually thought and modeled via schemes for the system-bath evolution in which the bath is treated either implicitly or approximately. Here we present computations of the electronic decoherence dynamics of a model many-body molecular system described by the Su-Schrieffer-Heeger Hamiltonian with Hubbard electron-electron interactions using an exact method in which both electronic and nuclear degrees of freedom are taken into account explicitly and fully quantum mechanically. To represent the electron-nuclear Hamiltonian in matrix form and propagate the dynamics, the computations employ the Jordan-Wigner transformation for the fermionic creation/annihilation operators and the discrete variable representation for the nuclear operators. The simulations offer a standard for electronic decoherence that can be used to test approximations. They also provide a useful platform to answer fundamental questions about electronic decoherence that cannot be addressed through approximate or implicit schemes. Specifically, through simulations, we isolate basic mechanisms for electronic coherence loss and demonstrate that electronic decoherence is possible even for one-dimensional nuclear bath. Furthermore, we show that (i) decreasing the mass of the bath generally leads to faster electronic decoherence; (ii) electron-electron interactions strongly affect the electronic decoherence when the electron-nuclear dynamics is not pure-dephasing; (iii) classical bath models with initial conditions sampled from the Wigner distribution accurately capture the short-time electronic decoherence dynamics; (iv) model separable initial superpositions often used to understand decoherence after photoexcitation are only relevant in experiments that employ delta-like laser pulses to initiate the dynamics. These insights can be employed to interpret and properly model coherence phenomena in molecules.
The relationship between electronic interactions and electronic decoherence is a fundamental problem in chemistry. Here we show that varying the electron-electron interactions does not affect the electronic decoherence in the pure-dephasing limit. In this limit, the effect of varying the electronic interactions is to rigidly shift in energy the diabatic potential energy surfaces without changing their shape, thus keeping the nuclear dynamics in these surfaces that leads to the electronic decoherence intact. This analysis offers a simple and intuitive understanding of previous theoretical and computational efforts to characterize the influence of electronic interactions on the decoherence and opens opportunities to study exact electronic decoherence with approximate electronic structure theories.
We introduce a general theory of electronic decoherence for molecules in the condensed phase that captures contributions coming from pure dephasing effects, electronic transitions among diabatic states, and their interference. The theory is constructed by taking advantage of a recently developed [ J. Phys. Chem. Lett. 2017 , 8 , 4289 - 4294 ] general expression for decoherence times that is based on an early time expansion of the purity dynamics and extends early electronic decoherence models based on pure dephasing ideas. Using this theory, we construct the decoherence time for the displaced harmonic oscillator model amended with constant and linear diabatic couplings, which is a widely used model of the photoexcited dynamics of molecules. The validity of the short-time expansion is demonstrated by the quantitative agreement of the theory with exact numerical computations of the decoherence dynamics obtained using the hierarchical equation of motion method. These developments offer a rigorous understanding of early time electronic decoherence processes that accompany basic molecular events and demonstrate that electronic transitions among diabatic states play a major role in the decoherence dynamics.
Molecular spins offer promise in emerging quantum technologies such as quantum sensing and computing. At low temperatures, nuclear spin-spin interactions affect electron spin coherence lifetimes through pure dephasing. Nuclear-spin noise can originate from spin pairs within a molecule itself, pairs in a surrounding environment system, or pairs in which one spin is on the molecule and the other in the environment. Improving coherence times requires detailed knowledge of the dominant sources of dephasing. Here, we analyze the decoherence behavior of two molecular qubit candidates with various ligands and in different nuclear-spin containing solvents. We apply an electronic-structure enhanced, non-Markovian perturbative theoretical method to connect experimentally comparable dephasing times to individual spin pairs. This analysis allows the development of a computational workflow to strategically improve coherence lifetimes in spin systems where decoherence is dominated by spin-spin dephasing.
Molecular spins are promising candidates for quantum information science, leveraging coherent electronic spin states for quantum sensing and computation. However, the practical application of these systems is hindered by electronic spin decoherence, driven by interactions with nuclear spins in the molecule and the surrounding environment at low temperatures. Predicting dephasing dynamics remains a formidable challenge due to the complexity of the spin bath. In this work, we develop a non-Markovian time-convolutionless master equation to treat an electronic spin coupled to a nuclear-spin bath. By relating ab initio electronic structure parameters directly to the decoherence dynamics, we provide a framework that accounts for pure dephasing in the low-temperature limit. We apply this method to a series of molecular qubit candidates and demonstrate good agreement with experimental relaxation trends. This approach offers a computationally efficient path for the prediction of low-temperature decoherence trends in molecular spin systems.