Quantum Control of Thermodynamic Processes in Semiconductors - Murphy, Conor (Trinity College Dublin. School of Physics. Discipline of Physics, 2022)
In this thesis, we explore theoretically the thermodynamics of heat exchange in laser driven solid state systems. In particular, we focus on the heat exchanged between phonons and a semiconductor quantum dot exciton, driven by both shaped laser pulses and continuous wave lasers, examining how the formation of strong-field dressed states allows a solid state emitter to absorb or emit acoustic phonons in a controlled way. We discuss these effects from the perspective of quantum thermodynamics and outline the possibility of using them to implement controlled thermodynamic processes and for optical cooling of solids to low temperatures, proposing a laser cooling protocol that makes active use of strong coherent driving. We derive a secularised Bloch-Redfield master equation to calculate the dynamics of an exciton in a GaAs/InGaAs quantum dot, driven by a linearly chirped Gaussian laser pulse. Using full counting statistics, we compute the statistics of the heat transfer between the exciton and the phonon bath, along with the statistics of the work done on the exciton by the driving laser. We construct a thermodynamic cycle, where the laser driving of the exciton forms the hot stroke. Analysing the efficiency of this engine, we identify parameter regimes of the driving laser which lead to quasi reversible heat absorption from the phonons by the quantum dot exciton. We find that certain classes of linearly chirped pulses result in isothermal heat transfers, with heat being absorbed by the exciton when it has a temperature close to that of the phonon bath. We extend the model of a heat engine composed of a laser driven exciton coupled to phonons to include a driving laser which has a more complex time dependent driving frequency, beyond that of simple linear chirping. Using numerical optimisation methods, we maximise the efficiency with respect to the temporal profile of the frequency of the driving laser. We find that it is always possible to achieve higher efficiencies compared to a linearly chirped pulse, with most improvement found for short Gaussian pulses. Moreover, we find that the frequency profiles of the laser which maximise the efficiency of the heat engine, also lead to increased heat absorption, when compared to their linearly chirped counterparts. These optimised shapes all result in a longer duration for isothermal heat transfer, leading to increased efficiencies. To analyse the heat absorption that arises from steady state driving, we derive secularised Bloch-Redfield master equation, which includes the dissipation due to the spontaneous emission of photons by the quantum dot. We analytically solve for the steady state of the system, and write an analytical expression for the power of the heat absorption from the phonons. The dependence of the heat absorption is explicitly seen in the analytical expression, where the role of the effective temperature of the photon scattering processes is evident. We identify the region in the space of parameters of the driving laser where heat absorption from the phonons is achieved. Finally, we calculate the full probability distribution for the number of excitations exchanged between the exciton and each bath, which appears to have a Gaussian structure at late times, with a mean which shifts linearly in time. We extend the quantum dot heat pumping model to treat heat pumping of phonons using steady state laser driving of Silicon vacancy centres in diamond. We find that the heat absorption from the phonons is strong enough to counteract the background heating of the material due to the driving laser. With this net heat absorption, we propose a laser cooling protocol based on this driven silicon vacancy platform. In this instance, we use a non-secular Bloch-Redfield master equation along with full counting statistics to calculate the cooling spectrum. The cooling spectra exhibit significant changes with increasing driving strength, where the cooling power is significantly increased and cooling is sustained over a much larger range of driving frequencies. Finally, we compare the cooling spectra from a secular, non-secular and phenomenological Lindblad model, and identify regimes where each theory is appropriate. We find that the secular theory is inappropriate at weak driving, where the secular approximation is invalid due to degeneracies in the Hamiltonian. At strong driving, where the secular approximation is valid, the secular and non-secular theories agree, and at weak driving the non-secular theory and the phenomenological Lindblad theory agree.
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Keywords: Thermodynamics; Open Quantum System; Quantum Dot; Quantum Control; Quantum Thermodynamics