A Master Equation Approach to Spin Noise

Datta, Amlan (2021) A Master Equation Approach to Spin Noise. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Amlan Datta (16MS156)) 16MS156_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

We started with a quantum dynamical ensemble. We designed a toy model and implemented the modified quantum master equation to that model for deeper understanding of spin noise. I have already stated in the beginning that researchers have tried to come up with a proper theory to explain spin noise [1–3]. Similarly we have also tried to understand from different point of view. We have used Redfield type quantum master equation and after solving the QME for our model, we have seen that our master equation approach can give an insight what is happeing inside [4, 5]. We have finally given insight to theoretical development of Spin Noise using QME. Numerical simulations are performed and shown in the thesis. In Chapter 1, we discussed about two doubts. Regarding the first doubt, σx2 is not zero which is evident from the set equation obtained in equation (3.22). The numerical solution and experimental result justified our claim. Now for the second doubt, in our calculation we have shown that due to imperfection in density matrix which in turn produce dynamical fluctuations even after spatio-temporal averaging in coarse-grained time scale in addition to equilibrium fluctuation. And this partially give an answer to the doubt and atleast confirms that more than √N number of spins are actually participating in the process. And this makes the experiments bit practical and one can see signal in short time rather than waiting for 1000 years as per Bloch’s argument in his original paper [6, 7]. But still a few questions remain unanswered which are summarized in the list below and can be part of future plans:

Actions (login required)

View Item