Mixing light and matter waves: Principles and applications

The work of this dissertation is committed to theoretically explore rich physics involving quantum-mechanical mixing of light and matter waves, while specifically seeking applications in the fields of quantum interferometry, quantum information processing, and testing fundamental quantum mechanics. Towards this goal, the present research is guided by two lines. The first line is to study and manipulate collective behaviors of multi-atom systems at quantum-degenerate temperature, where the wave nature of atoms is maximized. Specifically, a variety of phase-coherent mixing processes of two macroscopic matter-waves, in the form of gaseous Bose-Einstein condensate (BEC), are investigated and engineered via (i) tuning atomic collisional interaction and/or inter-wave tunneling rate (ii) mixing with optical waves of phase-locked lasers. By these means, a series of novel applications are proposed for generating highly nonclassical states, Heisenberg-uncertainty phase measurements and ultra-fast quantum state mapping between light and matter waves. The second line is to coherently mix single atoms with light beams in free space. It is well known that the free-space atom-photon interactions are weak, usually dominated by incoherent dissipation via spontaneous emission. Usable couplings between atoms and photons are routinely realized by confining them in high-finesse optical cavities in the strong coupling regime. The goal of the present work is to use ultrahigh-sensitivity quantum interferometry and the quantum Zeno effect to overcome the weak free-space atom-photon coupling, thus leading to implementations of quantum information processing in free space.Along the first line of this dissertation, chapter II describes a dynamical approach to create many-particle Schrodinger cat states, created in a Bose-Einstein condensate trapped in a double-well potential, via the technique of Feshbach resonance. A detection scheme for cat states is proposed via revivial of the initial state. Also particularly studied is the environmental decoherence due to laser-induced interaction between BEC atoms and the electromagnetic vacuum. Chapter III then presents an optimized Mach-Zender interferometry scheme with gaussian number-difference squeezed input states for sub-shot-noise phase resolution over a large phase-interval, also implemented in the double-well BEC system. We find utilizing adaptive measurement schemes allows any phase to be measured at Heisenberg-scaling precision within only a few measurements. The scheme can be readily implemented in a double-well BEC system. Chapter IV focuses on searching for the optimal operational strategy in a matter-wave amplification process, in order to facilitate potential applications in the fields of matter-wave interferometry and quantum information processing. In particular, the laser propagation effect inside two spatially overlapping spinor condensates is studied via the semiclassical multi-mode theory.Along the second line, chapter V proposes to generate entanglement between single-atom qubits via a common photonic channel within the framework of quantum interferometry at ultrahigh phase sensitivities. Via this new approach, a scalable circuit element for quantum information processing is demonstrated at close-to-unity success probability and fidelity. Chapter VI employs environmental dissipation to implement on-demand interaction- and measurement-free quantum logic gates for hybrid quantum bits (qubits) of single atoms and single photons. By forcing qubits to stay in a decoherence-free subspace via the quantum Zeno effect, the problem of qubit decoherence, otherwise constituting a major challenge in implementing quantum computation and teleportation, is overcome counter-intuitively with the help of fast environmental dissipation.