Quantum State-to-State Rates for Multistate Processes from Coherences

Dani, Reshmi; Makri, Nancy

doi:10.1021/acs.jpclett.2c02286

Cited by 14 publications

(25 citation statements)

References 40 publications

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“…This has recently been successfully applied to investigations of multistate problems. 23 However, here we are not interested in a rate perspective. We rather want to understand the full time dynamics with additional information about the channel-dependent contributions.…”

Section: Methodsmentioning

confidence: 99%

Impact of solvent on state-to-state population transport in multistate systems using coherences

Bose¹,

Walters²

2023

Preprint

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We present an approach of analyzing the transport of a quantum particle in a non-trivially connected extended system interacting with a dissipative medium. There are broadly two different aspects of the problem that affect the route taken by the transport process. First is obviously the couplings between the various sites, which translates into the intrinsic "strength" of a channel. Apart from the inter-site couplings, the solvents affecting the energies of the sites, and their relative coupling strengths and time-scales form the second factor. This impact of the such dissipative media is significantly more difficult to analyze. The Channel-Dependent Population Transfer (CDPT) method of analyzing the transport allows us to account for both the effects in a rigorous manner. We demonstrate the richness hidden behind the transport even for relatively simple systems -the effect of the local dissipative media is highly non-trivial and can mask the simplicity of the effect of the relative magnitude of the inter-site couplings. This opens up possibilities in terms of detailed study of the impact of factors on the nature of dynamics, especially possibilities of design of novel systems with an eye towards quantum control.

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Section: Methodsmentioning

confidence: 99%

Impact of solvent on state-to-state population transport in multistate systems using coherences

Bose¹,

Walters²

2023

Preprint

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“…In recent work we showed that the rate of population change is related to the imaginary parts of the coherences through the expression normald normald t ρ̃ k k ( t ) = 2 normalℏ ∑ j = 1 n H j k normalI normalm ρ̃ j k ( t ) where H j k are the matrix elements of the bare system Hamiltonian, eq . Equation is exact, regardless of the form of the bath Hamiltonian, as long as the system-bath coupling is diagonal in the system basis.…”

Section: General Features Of Coherence Mapsmentioning

confidence: 99%

“…Imaginary Components of Coherences. In recent work 18 we showed that the rate of population change is related to the imaginary parts of the coherences through the expression…”

Section: General Features Of Coherence Mapsmentioning

confidence: 99%

Time-Evolving Quantum Superpositions in Open Systems and the Rich Content of Coherence Maps

Dani

Makri

2022

J. Phys. Chem. B

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We discuss the general features of the time-evolving reduced density matrix (RDM) of multistate systems coupled to dissipative environments and show that many important aspects of the dynamics are visualized effectively and transparently through coherence maps, defined as snapshots of the real and imaginary components of the RDM on the square grid of system sites. In particular, the spread, signs, and shapes of the coherence maps collectively characterize the state of the system and the nature of the dynamics, as well as the equilibrium state. The topology of the system is readily reflected in its coherence map. Rows and columns show the composition of quantum superpositions, and their filling indicates the extent of the surviving coherence. Linear combinations of imaginary RDM elements specify instantaneous population derivatives. The main diagonal comprises the incoherent component of the dynamics, while the upper/lower triangular areas give rise to coherent contributions that increase the purity of the RDM. In open systems, the coherence map evolves to a band surrounding the principal diagonal whose width decreases with increasing temperature and dissipation strength. We illustrate these behaviors with examples of 10-site model molecular aggregates with Frenkel exciton couplings, where the electronic states of each monomer are coupled to harmonic vibrational baths.

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“…The usual practice is to focus the numerical studies on the evolution of the population in the excited states of each of the chromophores. Here, we additionally use the recently developed coherencebased analytic techniques [43][44][45][46] to unravel the pathways that the excitation takes and the impact of the vibrational modes. Baker and Habershon [47] have explored these pathways in FMO using the Lindblad master equation.…”

mentioning

confidence: 99%

“…Wu et al [43] have built flux networks to analyze the flows along different pathways. More recently, Dani and Makri have shown that the time-derivative of the on-site populations is related to linear combinations of the off-diagonal terms of the reduced density matrix [44], and visualized the coherences in forms of maps that encode information about the dynamics of the system [45]. We extended these ideas to partition the time-dependent population change on a site in terms of transport along different state-to-state channels, which is useful for understanding the instantaneous population transfer in these systems with complex interconnects [46].…”

mentioning

confidence: 99%

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex

Bose¹,

Walters²

2023

Preprint

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The dynamics of the excitation energy transfer (EET) in photosynthetic complexes is an interesting question both from the perspective of fundamental understanding and the research in artificial photosynthesis. Challenges persist in numerically simulating these systems both in parameterizing them and following their dynamics over long periods of time. Over the past decade, very accurate spectral densities have been developed to capture spatial inhomogeneties in the Fenna-Matthews-Olson (FMO) complex. We investigate the dynamics of FMO with an exact treatment of various theoretical spectral densities. Because FMO has Hamiltonian elements that connect most of the bacteriochlorophyll sites together, it becomes difficult to rigorously identify the energy transport pathways in the complex. We use the recently introduced ideas of relating coherence to population derivatives to analyze the transport process and reveal some of the pathways.

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Quantum State-to-State Rates for Multistate Processes from Coherences

Cited by 14 publications

References 40 publications

Impact of solvent on state-to-state population transport in multistate systems using coherences

Impact of solvent on state-to-state population transport in multistate systems using coherences

Time-Evolving Quantum Superpositions in Open Systems and the Rich Content of Coherence Maps

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex

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