The concept of polaron, emerged from condense matter physics, describes the dynamical interaction of moving particle with its surrounding bosonic modes. This concept has been developed into a useful method to treat open quantum systems with a complete range of system-bath coupling strength. Especially, the polaron transformation approach shows its validity in the intermediate coupling regime, in which the Redfield equation or Fermi’s golden rule will fail. In the polaron frame, the equilibrium distribution carried out by perturbative expansion presents a deviation from the canonical distribution, which is beyond the usual weak coupling assumption in thermodynamics. A polaron transformed Redfield equation (PTRE) not only reproduces the dissipative quantum dynamics but also provides an accurate and efficient way to calculate the non-equilibrium steady states. Applications of the PTRE approach to problems such as exciton diffusion, heat transport and light-harvesting energy transfer are presented.

Quantum coherence has been demonstrated in various systems including organic solar cells and solid state devices. In this article, we report the lower and upper bounds for the performance of quantum heat engines determined by the efficiency at maximum power. Our prediction based on the canonical three-level Scovil and Schulz-Dubois maser model strongly depends on the ratio of system-bath couplings for the hot and cold baths and recovers the theoretical bounds established previously for the Carnot engine. Further, introducing a fourth level to the maser model can enhance the maximal power and its efficiency, thus demonstrating the importance of quantum coherence in the thermodynamics and operation of the heat engines beyond the classical limit.

The constraint relation for efficiency and power is crucial for the design of optimal heat engines operating within finite time. We find a universal constraint between efficiency and output power for heat engines operating in the low-dissipation regime. Such a constraint is validated with an example of a Carnot-like engine. Its microscopic dynamics is governed by the master equation. Based on the master equation, we connect the microscopic coupling strengths to the generic parameters in the phenomenological model. We find the usual assumption of low-dissipation is achieved when the coupling to thermal environments is stronger than the driving speed. Additionally, such a connection allows the design of a practical cycle to optimize the engine performance.

Light absorption and energy transfer were studied in a bionic system with donors and an acceptor. In the optimal case of uniform couplings, this seemingly complicated system was reduced to a three-level Λ-type system. With this observation, we showed that the efficiency of energy transfer through a dark-state channel, which is free of the spontaneous decay of the donors, was dramatically improved. After the overall average transfer time was evaluated, it was revealed that the time required for transfer through this channel was not optimal. To find the optimal parameters for the present system, we defined a new quantity, output power, which characterizes the average mean output of the whole transfer process. We estimated the optimal parameters of the system to achieve the maximum output power. The splitting behaviour of the maximum power may be used to explain the phenomenon of photosynthetic systems primarily absorbing two colours of light.

Efficiency at maximum power has been investigated extensively, yet the practical control scheme to achieve it remains elusive. We fill this gap with a stepwise Carnot-like cycle, which consists of the discrete isothermal process (DIP) and adiabatic process. With DIP, we validate the widely adopted assumption of the $\mathcal{C}/t$ relation of the irreversible entropy generation $S^{\left(\mathrm{ir}\right)}$ and show the explicit dependence of the coefficient $\mathcal{C}$ on the fluctuation of the speed of tuning energy levels as well as the microscopic coupling constants to the heat baths. Such a dependence allows us to control the irreversible entropy generation by choosing specific control schemes. We further demonstrate the achievable efficiency at maximum power and the corresponding control scheme with the simple two-level system. Our current work opens new avenues for an experimental test, which was not feasible due to the lack the of the practical control scheme in the previous low-dissipation model or its equivalents.