Simulating spin flips in a quantum measurmenet scheme

[ramez]

I am trying to simulate a two-point quantum measurment on an ensemble of spin-1/2 nuclei. The purpose of this measurment is to mitigate the effects of quantum statistical noise. If we assume that the signal-to-noise ratio (SNR) looks P*SQRT(N) where P is the net polarization of spins in a magnetic field and N is the number of spins. Typical polarizations are on the order of 10^-5 therefore for N < 10^10 the SNR falls below 1. If instead we make a two-point measurement in which the fluctuations in the spin magnetization are measured at two times, the correlations in the fluctuations will produce a SNR that is approximately 1 all the way down to one spin.

I don't have very much experience in programming and would like to simulate this experiment for various numbers of spins. The spins are free to evolve for a time period t1 and are detected during a time period t2. I would like to assume that random spin flips may occur during both of these periods and presume that Monte Carlo methods may be best to use here. The only Monte Carlo simulations I've seen deal with Ising systems dealing with ferromagnetic or antiferromagnetic systems which I think are not applicable. I'm guessing the algorithm necessary to have random spin flips during a period of time is relatively straightforward, but I'm stuck. Any help would be appeciated. Thanks in advance!

 

[kleinwolf]

I don't understand : do you want to simulate an EPRB experiment ?

 

[ramez]

No, I want to simulate an NMR experiment in which the sample size is small enough for quantum mechanical spin noise to dominate all other noise sources.