Interplay of Quantum Coherence and Nonequilibrium Quantum Transport: An Exact Density Matrix Formulation in the Heisenberg Framework

TL;DR

This paper develops an exact Heisenberg framework to analyze quantum coherence and nonequilibrium transport in a double-dot system, revealing steady-state coherence and its relation to transport properties under various coupling regimes.

Contribution

It introduces a precise density matrix formulation in the Heisenberg picture for quantum transport, capturing strong coupling and non-Markovian effects in a double-dot system.

Findings

Quantum coherence reaches a non-zero steady state.

Transport current is connected to quantum coherence.

Finite reservoir spectral width influences transient and steady-state behaviors.

Abstract

We aim to bridge the gap between quantum coherence, quantum correlations, and nonequilibrium quantum transport in a quantum double-dot (QDD) system interacting with fermionic reservoirs. The system-reservoir coupling is modeled using a Fano-Anderson-type Hamiltonian. The density operator elements of the QDD system are expressed in terms of expectation values involving various combinations of the fermionic creation and annihilation operators associated with the system. By utilizing the quantum Langevin equation and the Heisenberg equation of motion, we derive the precise temporal behavior of these operator averages in terms of nonequilibrium Green's functions and subsequently obtain the time evolution of the density operator elements. Our approach is valid in both the strong coupling and non-Markovian regimes. Additionally, we examine the time evolution of quantum coherence in the QDD system, quantifying it using standard measures such as the l1-norm and the relative entropy of coherence. As observed, coherence reaches a non-zero steady-state value, highlighting its significant potential for applications in quantum information processing and quantum technologies. Furthermore, we establish a connection between quantum coherence and transport current in a QDD system serially coupled to fermionic reservoirs. We then investigate the effects of coupling strength and reservoir memory by tuning the finite spectral width of the reservoir, examining their impact on both transient and steady-state properties, such as quantum coherence and particle current, which could play a crucial role in ultrafast nanodevice applications.