טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentBarak Ronen
SubjectQuantum Optics Tomography -
Interferometry and Photon Statistics
DepartmentDepartment of Physics
Supervisor Professor Jacob Ben-Aryeh
Full Thesis textFull thesis text - English Version


Abstract

The quantum measurement process is examined in three different linear quantum optical systems. The first includes the analysis of the quantum phase distribution using a POVM distribution. The second system includes a linear quantum optic apparatus for the calculation of a quantum fast Fourier transformation. And finally, photon statistics effects are analyzed for linear Mach-Zehnder and Michelson interferometers in special configurations which show improved measurement sensitivity.


In the first system, POVM phase distributions are analyzed for one-mode and two-mode electromagnetic (em) waves. The use of these methods is demonstrated by analyzing the phase distribution for the em field output from a Mach-Zehnder interferometer. For a one-mode em field the POVM phase distribution is given indirectly by the one-mode density matrix which is obtained by measurements of the quadrature probability distribution and integration based on sampling pattern functions. This is demonstrated for a coherent state input. A compensation for non-unitary detection efficiency is also demonstrated by explicit calculations. For a two-mode em field the POVM relative phase distribution is related to an angular momentum basis.  This is demonstrated for a Fock state input. The analysis is compared with measurements made by other authors.


In the second system, linear quantum optics is used for the implementation of the quantum fast Fourier transform. An experimental implementation based on the Cooley-Tukey algorithm is shown, by the use of beam splitters and phase shifters in a linear quantum optical system. Configurations implementing 1, 2 and 3 qubits discrete Fourier transform (DFT) are described explicitly and a general method for implementing the n-qubit DFT is analyzed. These transformations are used for various systems by which phase estimation and order finding can be computed.


In the third system, the photon statistics is analyzed for linear Mach-Zehnder and Michelson interferometers in which a strong coherent state is inserted into one input port and a squeezed vacuum state is inserted into the other input port. The effects related to the entanglement between the two output ports are studied using two theoretical methods: a) The Zassenhaus perturbation theory as a function of the squeezing parameter, b) The Lie group disentangling method. For the case in which the coherent state exits through one port and the squeezed vacuum through the other, under special conditions, the signal in the ``dark'' port caused by a phase shift can be amplified by orders of magnitude and at the same time the quantum noise is reduced.