Undergrad Coherence time for repeated spin measurements

[aa2ll2]

TL;DR

"What is the half life of the correlation between repeated spin measurements on the same electron?

Consider repeated spin measurements, along the same axis, on the same electron, at t=0 and at t=t. For small t, the results are identical, so the correlation function, C(t,0)=1, but for large t, C(t,0) -> 0.

Define C(t,0) = P(same) - P(different) = N(same) - N(different) / N(same) + N(different), where N(same) is the number of trials where the measurements at t=0 and at t=t return the same result etc.

How does this correlation function depend on t?

 

[PeroK]

TL;DR Summary: "What is the half life of the correlation between repeated spin measurements on the same electron?

Consider repeated spin measurements, along the same axis, on the same electron, at t=0 and at t=t. For small t, the results are identical, so the correlation function, C(t,0)=1, but for large t, C(t,0) -> 0.

Define C(t,0) = P(same) - P(different) = N(same) - N(different) / N(same) + N(different), where N(same) is the number of trials where the measurements at t=0 and at t=t return the same result etc.

How does this correlation function depend on t?

It depends on the Hamiltonian for the system. For a free electron, the spin state does not evolve. The spin state would evolve in a magnetic field.

 

[aa2ll2]

It's a noise question. So, the free particle spin evolving in noise, does not remain forever the same, with prob. 1, right? I actually have in mind an NV centre, which I think is free for the purpose to hand.

 

[PeroK]

It's a noise question. So, the free particle spin evolving in noise, does not remain forever the same, with prob. 1, right? I actually have in mind an NV centre, which I think is free for the purpose to hand.

You'll need to specify a Hamiltonian for your "noise".

 

[aa2ll2]

The standard, coupling to bath, model. A bit of context may help. The single qubit coherence time is T_coh. I'm anticipating the time dependence should involve T_coh, something like C(t,0) = e^[-t/T_coh]. Or, are you saying coherence time is not pertinent?

 

[PeroK]

The standard, coupling to bath, model. A bit of context may help. The single qubit coherence time is T_coh. I'm anticipating the time dependence should involve T_coh, something like C(t,0) = e^[-t/T_coh]. Or, are you saying coherence time is not pertinent?

Is this to do with quantum computing?

 

[aa2ll2]

It is actually something that came up with loophole free Bell tests, but quite similar to computing.

 

[aa2ll2]

Hi Perok,

Looking at some papers, the question of what hamiltonian to use seems a bit of a red herring. The starting point is the density matrix, where off diagonal terms decay as exp[-t/T_coh] In the model used for predicting the Bell violation in noise. My question should then be quite simple . How does the C(t,0) defined above depend on time?

 

[PeroK]

Hi Perok,

Looking at some papers, the question of what hamiltonian to use seems a bit of a red herring. The starting point is the density matrix, where off diagonal terms decay as exp[-t/T_coh] In the model used for predicting the Bell violation in noise. My question should then be quite simple . How does the C(t,0) defined above depend on time?

There's not enough context in this thread for me to comment. Perhaps someone else who is more familiar with the specific subject matter may be able to help. But, in such specific cases, you ought to provide the full background to the question.

 

[aa2ll2]

Thanks for your attention to this matter.