i) The quantum mechanics of higher order parametric amplifiers is studied. It is shown that these devices produce meaningful quantum states; numerical calculations are performed that demonstrate the convergence of matrix elements associated with these states. Further, the correspondence between the classical and quantum evolution for these devices is studied and the differences explained by a kind of \"quantum diffusion.\" Finally, the possibility of producing ordinary squeezed light with these devices is noted.
\r\n\r\nii) The generation of squeezed light always involves some scheme that amounts to pumping electromagnetic modes at near twice their natural frequency. When the pump is itself treated quantum mechanically, extra noise is introduced that ultimately limits the amount of squeezing achievable. Detailed calculations are carried out in this regard for the parametric amplifier. It is found that the pump's initial phase noise is responsible for this limit.
\r\n\r\niii) Quantum-mechanical measurements are usually described by applying the standard quantum rules to a measurement model. They can also be described by a formalism that uses mathematical objects called Effects and Operations. These two descriptions should be equivalent. D'Espagnat has raised a question about the usage of this formalism of Effects and Operations for repeated measurements. This question is cleared up, and the source of the discrepancy is given a simple interpretation.
\r\n\r\niv) Usually, an inequality that is chained becomes a weaker inequality. Chaining the Bell inequality, however, leads to stronger violations by quantum mechanics. Further, a new kind of Bell inequality, based on the information obtained in a measurement, is derived. This information Bell inequality can be used to formulate tests of local realism in very general circumstances, e.g., higher spin versions of the EPR experiment. These new inequalities yield an interpretation for the size of their violation and lead to the formulation of a hierarchy of Bell inequalities for which two-particle Bell inequalities play a special role.
\r\n", "doi": "10.7907/9K1B-7X39", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:4376", "collection": "thesis", "collection_id": "4376", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-11022007-131309", "type": "thesis", "title": "A Theoretical Study of the Generation of Squeezed-State Light via Degenerate Parametric Amplification", "author": [ { "family_name": "Crouch", "given_name": "David Dale", "clpid": "Crouch-David-Dale" } ], "thesis_advisor": [ { "family_name": "Caves", "given_name": "Carlton M.", "orcid": "0000-0001-8876-1186", "clpid": "Caves-C-M" }, { "family_name": "Bellan", "given_name": "Paul Murray", "orcid": "0000-0002-0886-8782", "clpid": "Bellan-P-M" } ], "thesis_committee": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" }, { "family_name": "Caves", "given_name": "Carlton M.", "orcid": "0000-0001-8876-1186", "clpid": "Caves-C-M" }, { "family_name": "Gould", "given_name": "Roy Walter", "clpid": "Gould-R-W" }, { "family_name": "Vahala", "given_name": "Kerry J.", "orcid": "0000-0003-1783-1380", "clpid": "Vahala-K-J" }, { "family_name": "Corngold", "given_name": "Noel Robert", "clpid": "Corngold-N-R" }, { "family_name": "Bellan", "given_name": "Paul Murray", "orcid": "0000-0002-0886-8782", "clpid": "Bellan-P-M" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light.
\r\n\r\ni) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations \u2014 spatial Langevin equations \u2014 that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed.
\r\n\r\nii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large \u03c7(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy.
\r\n\r\niii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier.
\r\n\r\niv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold \u2014 and possibly unrealizable \u2014 assumption, that the in-phase and quadrature Langevin sources which are responsible for the \"noisiness\" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.
\r\n", "doi": "10.7907/55jn-f921", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:10414", "collection": "thesis", "collection_id": "10414", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09062017-132307035", "type": "thesis", "title": "Theoretical Investigations in Nonlinear Quantum Optics, Theory of Measurement, and Pulsations of General Relativistic Models of Neutron Stars", "author": [ { "family_name": "Schumaker", "given_name": "Bonny Laura", "clpid": "Schumaker-Bonny-Laura" } ], "thesis_advisor": [ { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "thesis_committee": [ { "family_name": "Phillips", "given_name": "Thomas G.", "clpid": "Phillips-T-G" }, { "family_name": "Whitcomb", "given_name": "Stanley E.", "clpid": "Whitcomb-S-E" }, { "family_name": "Caves", "given_name": "Carlton M.", "orcid": "0000-0001-8876-1186", "clpid": "Caves-C-M" }, { "family_name": "Thorne", "given_name": "Kip S.", "orcid": "0000-0002-9475-4318", "clpid": "Thorne-K-S" } ], "local_group": [ { "literal": "TAPIR" }, { "literal": "Astronomy Department" }, { "literal": "div_pma" } ], "abstract": "This thesis is a collection of six papers. The first four constitute the heart of the thesis; they are concerned with quantum mechanical properties of certain harmonic-oscillator states. The first paper is a discourse on single-mode and two-mode Gaussian pure states (GPS), states produced when harmonic oscillators in their ground states are exposed to potentials that are linear or quadratic in oscillator position and moment um variables (creation and annihilation operators). The second and third papers develop a formalism for analyzing two-photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the ouput modes arise from two-photon transitions, i.e., are created or destroyed two at a time. The states produced by such devices are single-mode and two-mode \"squeezed states\", special kinds of GPS whose low-noise properties make them attractive for applications in such fields as optical communications and gravitational wave detection. The fourth paper is an analysis of the noise in homodyne detection, a phase-sensitive detection scheme in which the special properties of (single-mode) squeezed states are revealed as an improved signal-to-noise ratio relative to that obtained with coherent states (the states produced, e.g., by a laser).
\r\n\r\nThe fifth and sixth papers deal with problems of a different nature from that of the previous papers. The fifth paper considers the validity of the \"standard quantum limit\" (SQL) for measurements which monitor the posi\u00adtion of a free mass. It shows specifically that when the pre-measurement wave functions of the free mass and the measuring apparatus(es) are Gaus\u00adsian (in the general sense, which includes so-called \"contractive states\"), measurements described by linear couplings to the position or to both the position and momentum are limited by the SQL. The sixth paper develops the mathematical theory of torsional (toroidal) oscillations in fully general relativistic, nonrotating, spherical stellar models, and of the gravitational waves they emit.
", "doi": "10.7907/fwvz-7t26", "publication_date": "1985", "thesis_type": "phd", "thesis_year": "1985" } ]