טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentAssaf Ohad
SubjectQuantum Noise in Length Measurements Using a Michelson
Interferometer
DepartmentDepartment of Physics
Supervisor Professor Jacob Ben-Aryeh


Abstract

This thesis deals with the quantum limitations on detecting a change, in the length difference between a Michelson interferometer’s two arms, that are due to the quantum nature of light. These limitations become significant when one is trying to measure extremely small length changes, such as the expected effect of a gravitational wave. We treat the two most fundamental causes of quantum noise in the Michelsom interferometer: a) the Photon-Counting (PC) noise, which is the uncertainty in obtaining the exact number of outgoing photons and b) the Radiation Pressure (RP) noise, which is the uncertainty in obtaining the momenta transferred to the two interferometer’s mirrors by the photons. The limit these noise causes place on the measurements is analyzed using two different models. The first is a basic model, which deals with the two kinds of noise seperately and thus it does not allow any correlation between them. We calculate the quantum noise in a squeezed-state interferometer (in which a squeezed vacuum enters the “unused” input port), using the basic model, for various fourth-order output operators (in the light’s boson operators) and find that the optimal signal-to-noise ratio is not improved relative to the original-treated second-order operators. Furthermore, we find that the so-called Standard Quantum Limit (SQL) is valid under the assumptions of the basic model. The second model we use allows the possibility of a correlation between the two kinds of noise, and therefore we call it the unified model. In the framework of the unified model we analyze first the coherent-state interferometer (in which the vacuum enters the “unused” input port). Calculating the exact expression for the signal enables us to recognize two interesting effects related to RP: first, the interference pattern can be destroyed and second, there is a possible large shift in the interference phase. Next we analyze the squeezed-state interferometer using the unified model. We find the dependence of the quantum noise on the relative phase of the incoming light’s modes, showing the possibility to reduce the noise below the SQL. In particular, we find the general condition for the optimal relative phase, in which the noise reduction is maximal. It is noted that the reduction of the quantum noise below the SQL, is achieved only for a very narrow region around the optimal value of the incoming modes’ relative phase.