Effective quantum field theories with dissipation are used to describe nonlinear crystals or fibers. Using phase-space representations, one can obtain tractable equations that accurately describe the quantum noise and coherence produced with laser inputs.
Playing a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and classical electrodynamics is assumed, but no prior knowledge of nonlinear optics is required.
The normalized phase-amplitude representation and the Darboux figure are first defined. Then as an example, we establish the quantum optics description for the field in photonic crystal fibers in the defined representation. The field is evolved from one Darboux state to another state in the Darboux figure. By the continuous inputting (pump) of light, the waves induced by nonlinear effects become stronger (the wave frequency number remains constant at the same distance, and their intensities accumulate). The blueshifted waves induced by the third-order resonant susceptibility are not strong enough to cover other nonlinear effect and turn weak along the length (pump turns weak).
Generation of light with nonclassical properties, such as squeezed light, has gathered a lot of attention because of possible uses in such areas as quantum state engineering, quantum imaging, continuous variable quantum computing, and detection of gravitational waves. Squeezed light is generally produced by transporting light through a nonlinear medium. One such media is Kerr-nonlinear optical fibres. We aim to find the parameters for a fibre polarization squeezing setup by studying the dependencies of quantum noise suppression on the duration of the pulse and the input power. This is performed by modeling the light field propagation using the split-step Fourier method to numerically solve the stochastic nonlinear Schrödinger equation obtained by using the Wigner representation. This equation includes such physical effects as damping, quantum loss noise, dispersion, Kerr and Raman nonlinearities, and stochastic Raman noise.
Recent developments in the field of optical clocks and quantum information have fueled the necessity for both fiber phase noise cancellation and laser stabilisation. The Quantum Information group at Lund University is conducting research on quantum computation experiments based on rare earth ion doped crystals and also application of slow light effects induced by spectral hole burning in these rare earth ion doped crystals. Slow light effects can significantly improve laser stabilisation by increasing effective cavity length without inducing mechanical noise. In this thesis a fiber phase noise cancellation setup was designed and built. The fiber stabilisation will be used in a setup where a laser is stabilised using a slow light crystal cavity as frequency reference and a setup was designed for this application. By partially reflecting back light through a fiber and by performing a phase measurement and through feedback control, the fiber phase noise can be effectively cancelled. A method for first creating a slow light crystal cavity and then locking the laser to one of the resonance peaks of the cavity was planned and designed incorporating two fiber locking setups for phase noise cancellation. Suitable components for building the system was investigated and put together. Fiber locking experiment was then carried out.