Quantum coherence-control of thermal energy transport: the V model as a case study

Abstract

Whether genuine quantum effects, particularly quantum coherences, can offer an advantage to quantum devices is a topic of much interest. Here, we study a minimal model, the three-level V system coupled to two heat baths, and investigate the role of quantum coherences in heat transport in both the transient regime and in the nonequilibrium steady-state. In our model, energy is exchanged between the baths through two parallel pathways, which can be made distinct through the nondegeneracy of excited levels (energy splitting $\Delta$) and a control parameter $\alpha$, which adjusts the strength of one of the arms. Using a nonsecular quantum master equation of Redfield form, we succeed in deriving closed-form expressions for the quantum coherences and the heat current in the steady state limit for closely degenerate excited levels. By including three ingredients in our analysis: nonequilibrium baths, nondegeneracy of levels, and asymmetry of pathways, we show that quantum coherences are generated and sustained in the V model in the steady-state limit if three conditions, conjoining thermal and coherent effects are {\it simultaneously} met: (i) The two baths are held at different temperatures. (ii) Bath-induced pathways do not interfere destructively. (iii) Thermal rates do not mingle with the control parameter $\alpha$ to destroy interferences through an effective local equilibrium condition. Particularly, we find that coherences are maximized when the heat current is suppressed. Although we mainly focus on analytical results in the steady state limit, numerical simulations reveal that the transient behavior of coherences {\it contrasts} the steady-state limit: Large long-lived transient coherences vanish at steady state, while weak short-lived transient coherences survive, suggesting that different mechanisms are at play in these two regimes. Enhancing either the lifetime of transient coherences or their magnitude at steady state thus requires the control and optimization of different physical parameters.

Population Oscillations and Ubiquitous Coherences in Multilevel Quantum Systems Driven by Incoherent Radiation

“…In equilibrium, noise-induced coherences are important only in the transient response of the system because it will eventually reach an incoherent thermal steady state. However, when the system is coupled to multiple baths, the non-equilibrium steady state (NESS) may be coherent, with non-zero coherences that can alter the energy transfer rates and heat currents through the system. ,− Coherent NESSs, i.e., in which the density matrix contains non-zero off-diagonal density matrix elements in the energy eigenbasis, have been seen when the system (1) has some non-zero p alignment parameters and (2) is coupled to several baths at different temperatures . The arguments here address the first condition, indicating that systems capable of supporting coherent NESSs when coupled to suitable baths are ubiquitous.…”

Impact of Quantum Coherence on Inelastic Thermoelectric Devices: From Diode to Transistor

“…[9][10][11][12][13][14][15] Coherence offers a promising viewpoint for investigating non-equilibrium open quantum systems, providing valuable insights for both theoretical foundations and practical applications. [16][17][18][19][20][21] However, exploration of phononthermoelectric devices with quantum coherence, e.g., diodes and transistors, is still on demand.…”