| dc.description.abstract | This thesis is divided into three parts, with each part concerned with one of the three
pillars of Theoretical Quantum Optics: ‘Microscopic models of Light-Matter Interaction’,
‘Quantum Measurements’ and finally, ‘Driven Non-Markovian systems’. In the first part,
I discuss in detail a widespread assumption, yet still unproven, in the description of
Superconducting Circuit QED that: ‘electromagnetic modes above the superconducting
gap have short lifetimes and contribute weakly to the qubit dynamics’. It is well known
that superconducting waveguides strongly attenuate the propagation of electromagnetic
waves with frequencies beyond the superconducting gap. The interaction between Transmon
qubits and superconducting resonators invariably involves the Transmon coupling
to a large set of resonator modes. So far, strong dispersion effects near and beyond the
superconducting-gap have been ignored in quantization models. Rather, it is assumed
that the superconducting resonator behaves ideally across the large frequency intervals.
In this thesis I present a quantization approach which includes the superconducting
frequency-dependent surface impedance and demonstrate that superconducting dispersion
plays a role in determining the effective light-matter interaction cut-off.
Going ahead, in the next part I present a new formulation for the emergence of classical dynamics
in a quantum world by considering a path integral approach that also incorporates
continuous measurements. This program is conceptually different from the decoherence
program as well as the quantum-to-classical transition framework with coarse-grained measurements. The path-integral formulation provides the joint statistics of a sequence
of measurements with each Feynman path picking up an additional random phase due to
measurements. The magnitude of this phase is proportional to the measurement strength,
and we give conditions under which the dominant contribution to the probability amplitude
comes from the trajectories in the vicinity of the classical paths. The proliferation
of this information across the environment, an essential feature of quantum Darwinism,
takes place via scattering of plane-wave probes by the system. Extending to repeated
measurements, I show that in the continuous limit, each system trajectory picks up an
additional phase due to the momentum kicks from the probes - origin of the back-action
force. We provide conditions for which the measurement provides sufficient “which-path”
information and keeps the wave packet sufficiently localized. This allows for description
of quantum-to-classical transition at the level of individual trajectories in contrast to
the statistical ensemble interpretation provided by density matrices in the decoherence
program. Finally, I show the connection of continuous quantum measurements to purely
classical quantities, namely, the Hamilton-Jacobi equations and the Poisson Bracket.
The final part concerns itself with a novel experimental regime that has been made
possible due to the rapid progress in fabrication methods and microwave electronics,
ushering in an entirely new regime of Quantum Optics. The multi-mode regime of Circuit
Quantum Electro/Acoustodynamics involves the simultaneous coupling of a Qubit to
a large set of discrete bosonic modes. The structured environment, as opposed to an
infinite heat bath, in the multimode regime offers a versatile platform for investigating
non-Markovian dynamics as well as the possibility of tailoring interactions between
the modes for technological applications. In this work, I study a monochromatically
driven Qubit interacting with a multi-mode, engineered cavity using coherent state path
integrals. I calculate the contributions of the various multi-photon virtual processes
to the self-energy corrections and demonstrate that resonance conditions between the
Rabi frequency and the mode frequencies leads to strong qubit-mode and qubit mediated
mode-mode interactions. Finally, this work proceeds towards explaining some of the
key features observed in experiments (PRX 5, 021035 (2015)). Further, I also discuss
the driven non-Markovian dynamics in such discrete environments by formulating an
integro-differential equation for the Rabi-flopping amplitude and demonstrate that the
dynamics are modified due to higher order environmental correlators, previously not
considered in other works. | en_US |
