Time-Reversal Based Hybrid Quantum State Transfer and the Interference of Two Interference Effects

Abstract

Much of quantum science is about developing and employing methods for controlling quantum systems to perform tasks that are either classically hard, interesting (e.g., novel or useful), or ideally both. In this dissertation, we analyze the essential role of controlling the modes photons occupy (e.g., their shape, polarization, and path taken) in performing quantum-information-processing tasks. This dissertation includes two disjoint but complementary research directions. The first and primary direction concerns the deterministic transfer of quantum information or entanglement between heterogeneous quantum systems using itinerant photons. We present a unitary transformation that time reverses, frequency translates, and stretches the photon wave packet emitted by one system to match the spectral properties of the receiving system. We show how the underlying input-output formalism is modified due to such manipulations, leading to a new interpretation, wherein the receiving system is effectively driven by a fictitious version of the emitter that evolves backwards in time at a new decay rate and frequency. The probability of interfacing successfully is determined by the temporal-spectral overlap of the actual photonic wave packet and an ideal shape. This allows us to analytically and numerically analyze how the probability of success is impacted by realistic errors and show the utility of our scheme in consonance with known error correction methods. In the second direction, we analyze a linear-optical setup in which two kinds of standard interference effects---namely, Mach--Zehnder interference and Hong--Ou--Mandel interference---interfere with one another, partially canceling each other out. This new perspective, along with the overall pedagogical exposition of this work, illustrates how quantum effects can combine nontrivially, the importance of photon indistinguishability for interference, and, moreover, that quantum interference happens at measurement. This work can serve as a pedagogical bridge to more advanced quantum mechanical concepts, including photonic quantum computing, complementarity, and tests of quantum mechanics (e.g., Hardy’s Paradox). This dissertation contains previously published as well as unpublished co-authored materials