Quantum Coherence in Electrical Circuits

This thesis studies quantum coherence in macroscopic and mesoscopic dissipative electrical circuits, including LC circuits, microwave resonators, and Josephson junctions. For the LC resonator and the terminated transmission line microwave resonator, second quantization is carried out for the lossless system and dissipation in modeled as the coupling to a bath of harmonic oscillators. Stationary states of the linear and nonlinear resonator circuits as well as the associated energy levels are found, and the time evolution of uncertainty relations for the observables such as flux, charge, current, and voltage are obtained. Coherent states of both the lossless and weakly dissipative circuits are studied within a quantum optical approach based on a Fokker-Plank equation for the P-representation of the density matrix which has been utilized to obtain time-variations of the averages and uncertainties of circuit observables. Macroscopic quantum tunneling is addressed for a driven dissipative Josephson resonator from its metastable current state to the continuum of stable voltage states. The Caldeira-Leggett method and the instanton path integral technique have been used to find the tunneling rate of a driven Josephson junction from a zero-voltage state to the continuum of the voltage states in the presence of dissipation. Upper and lower bounds are obtained for the tunneling rate at the intermediate loss and approximate closed form expressions are derived for the overdamped and underdamped limits

Interband Cascade Lasers, from Fabry-Pérot Waveguides to Subwavelength Cavities

This research in centered around engineering approaches to improve the electro-optical performance of interband cascade lasers. The enhancement strategies are ranging from empirical design optimizations and fabrication and packaging techniques to design and application of optical coating. These improvements resulted in room temperature (RT) CW optical powers of 40 mW, as well as, internal loss and threshold current densities as low as 4.9 cm^-1 and 365 A/cm^2 respectively. Moreover, additional improvements resulted in devices with threshold current density as low as 320 A/cm^2 and wall plug efficiency reaching up to 5.9% for a 1 mm device producing 20.3 mW CW RT output power. Application of Antireflection (AR) coatings to interband cascade lasers not only led to identification of several promising material combinations for AR coatings in Mid-Infrared (Mid-IR) region of the spectrum, but was also used to study the fundamental laser parameters such as internal efficiency and leakage current. AR coatings ranging from 0.15 to 7E-4 were designed and fabricated on ICL waveguide facets. By monitoring the laser performance before and after coating a direct relation between carrier concentration and leakage currents was observed and an optimal reflectivity value of 9.6E-3 was experimentally extracted in order to achieve the maximum slope efficiency for a 1 mm device. As the next step toward utilization of the Mid-IR ICLs a systematic approach to design of sub-wavelength cavities was developed with universal applications in active plasmonic cavities. Key parameters such as quality factor, confinement factor, and threshold gain have been calculated and their dependence of cavity parameters are demonstrated which enables a flexible design for various applications. In particular a coaxial cavity with energy confinement factor of 84% and mode volume of 0.14 λ/2n^3 and quality factor of Q=515 was designed at 3.55 λm. The dependence of the emission wavelength to the surrounding refractive index was also demonstrated with potential sensing applications

Quantum Key Distribution over Probabilistic Quantum Repeaters

A feasible route towards implementing long-distance quantum key distribution (QKD) systems relies on probabilistic schemes for entanglement distribution and swapping as proposed in the work of Duan, Lukin, Cirac, and Zoller (DLCZ) [Nature 414, 413 (2001)]. Here, we calculate the conditional throughput and fidelity of entanglement for DLCZ quantum repeaters, by accounting for the DLCZ self-purification property, in the presence of multiple excitations in the ensemble memories as well as loss and other sources of inefficiency in the channel and measurement modules. We then use our results to find the generation rate of secure key bits for QKD systems that rely on DLCZ quantum repeaters. We compare the key generation rate per logical memory employed in the two cases of with and without a repeater node. We find the cross-over distance beyond which the repeater system outperforms the non-repeater one. That provides us with the optimum inter-node distancing in quantum repeater systems. We also find the optimal excitation probability at which the QKD rate peaks. Such an optimum probability, in most regimes of interest, is insensitive to the total distance.Comment: 12 pages, 6 figures; Fig. 5(a) is replace