Alladi Ramakrishnan Hall

Quantum-dot heat engines, quantum clocks and a Landauer principle for time-keeping

Bhaskaran Muralidharan

IIT Bombay

In this talk, we present recent works on two distinct aspects related to quantum dots. In the first part, thermoelectric response of a dissipative quantum dot heat engine based on the Anderson-Holstein model is analyzed. We delve into two relevant operating limits, (i) when the dot phonon modes are out of equilibrium, and (ii) when the dot phonon modes are strongly coupled to a thermal environment. We discuss several nuances related to the heat engine operation under both limits. When relaxation via a heat bath is involved, we estimate the dot temperature by incorporating a thermometer bath, and it is shown that the dot temperature deviates from the bath temperature as electron-phonon interaction in the dot becomes stronger. Consequently, it is demonstrated that the dot temperature controls the direction of phonon heat currents, thereby influencing the thermoelectric performance.
In the second part, we bring in a Bayesian viewpoint to the analysis of clocks, specifically taking the Salecker Wigner clock formulation and explore a novel set up to estimate the tunneling time between electrons in a contact and a quantum dot weakly coupled to it. Using the exponential tunneling distribution as a priors for clocks, we analyze the case of a single precessing spin in a quantum dot. We find that, at least with a single qubit, quantum mechanics does not allow exact timekeeping. We find the optimal ratio of angular velocity of precession to rate of the exponential distribution that leads to maximum accuracy. Further, we find an energy versus accuracy tradeoff in a form reminiscent of the Szilard-Landauer principle --- the energy cost is at least k_BT times the improvement in accuracy as measured by the entropy reduction in going from the prior distribution to the posterior distribution.