Title:

Aspects of work in quantum thermodynamics

Landauer's principle states that it costs at least k_{B}T ln 2 of work to reset one bit in the presence of a heat bath at temperature T. The bound of k_{B}T ln 2 is achieved in the unphysical infinitetime limit. Here we consider two different finitetime protocols  one with discretised time and the second in the continuous limit. We prove analytically that the discrete time protocol enables one to reset a bit with a work cost close to k_{B}T ln 2 in a finite time. We construct an explicit protocol that achieves this, which involves thermalising and changing the system's Hamiltonian so as to avoid quantum coherences. Using concepts and techniques pertaining to singleshot statistical mechanics, we furthermore prove that the heat dissipated is exponentially close to the minimal amount possible not just on average, but guaranteed with high confidence in every run. Moreover we exploit the protocol to design a quantum heat engine that works near the Carnot efficiency in finite time. We further contrast this to a continuous time version of the protocol which is substantially less energy sufficient. We also consider the fluctuations in the work cost, and calculate how their magnitude is suppressed by a factor depending on the length of the protocol. We demonstrate with an experiment how molecules are a natural testbed for probing fundamental quantum thermodynamics. Singlemolecule spectroscopy has undergone transformative change in the past decade with the advent of techniques permitting individual molecules to be distinguished and probed. By considering the timeresolved emission spectrum of organic molecules as arising from quantum jumps between states, we demonstrate that the quantum Jarzynski equality is satisfied in this setup. This relates the heat dissipated into the environment to the free energy difference between the initial and final state. We demonstrate also how utilizing the quantum Jarzynski equality allows for the detection of energy shifts within a molecule, beyond the relative shift.
