WMD - Write my dissertation

Hello Anons,

I'm in my final 2 years of a physics PhD but I'm a dumb experimentalist that doesn't understand the theory well, so I want to discuss some of the issues I have with you guys.

I'll post irregularly (whenever I have time to write) about some probably fairly technical topic.

If you help me write at least 1/3rd of the theory section, I'll include Veeky Forums in the acknowledgements

>inb4 do your own homework, the questions I'd like to discuss are quite different than your typical homework problem and aim more at interpretation or technicalities.

So, for now, let's start with something simple.

We all know that quantum states can be written as a wavefunction, but those fail to correctly grasp the concept of mixed states in which case we need to introduce the density matrix formalism with a density matrix [math]\rho = \sum_{i,j} c_i c_j^* |\Psi_i\rangle\langle\Psi_j||[/math]
How exactly is this a better way of quantifying quantum states? I know that the off-diagonal elements are supposed to be coherences, but due to the hermicity of [math]\rho[/math] I thought you could always diagonize it getting rid of any off-diagonal elements by choosing the correct basis.
>pic related is a Bloch-sphere for a single qubit

Other urls found in this thread:

arxiv.org/pdf/1409.0535.pdf
twitter.com/SFWRedditGifs

dat formatting, off to a good start I see...

How exactly is this a better way of quantifying quantum states? I know that the off−diagonalel ements are supposed to be coherences, but due to the hermicity of [math]\rho[/math] I thought you could always diagonize it getting rid of any off-diagonal elements by choosing the correct basis.

Though ρ is a tad more general in the sense that there are infinite ways in which you can get the same density operator, it is way more useful in entangled systems. There, when you have the density matrix of the system you can always reduce it to the density matrix of one of its subsystems by taking the trace over the states that do not belong to the system you want to study. Thus, you get a "reduced density matrix" describing only a specific subsystem, which can't be done using the wavefunction alone.

>There, when you have the density matrix of the system you can always reduce it to the density matrix of one of its subsystems by taking the trace over the states that do not belong to the system you want to study. Thus, you get a "reduced density matrix" describing only a specific subsystem, which can't be done using the wavefunction alone.
This part is kinda clear to me already, although it seems we just construct a density matrix that only contains stuff we are interested in from the get go anyways.

>Though ρ is a tad more general in the sense that there are infinite ways in which you can get the same density operator, it is way more useful in entangled systems.
This part I actually don't understand. How is it helpful if there are infinitely many combinations of getting the exact same density matrix? Isn't that something we would not want because now we lack uniqueness?
One more technical problem I have is to show that the expectation value of an operator is the same in density matrix formalism and wavefunction formalism (I know, I should know this from QM, but it's been too long) Any help?

[math]\langle A \rangle = \sum_i p_i \langle \Psi_i | A | \Psi \rangle = \sum_i p_i |\Psi_i \rangle \langle \Psi_i | A =? Tr(\rho A)[/math]

>[math]\langle A \rangle = \sum_i p_i \langle \Psi_i | A | \Psi \rangle = \sum_i p_i |\Psi_i \rangle \langle \Psi_i | A =? Tr(\rho A)[/math]
It's literally just plugging it in and using the cyclic property of the trace
This has nothing to do with physics

I know, but I'm retarded, how is the last equality true?

Another thing I'm trying to get a better understanding of the photon-echo and non-echo signals that are generated in a transient four-wave mixing experiment.

How do you interpret the echo/non-echo signal and why is the echo so much stronger?
My current understanding is that a first pulse flips all spins in the Bloch sphere to the other pole, then they start to dephase, after some time a second pulse hits which has opposite phase-evolution, and makes them return their phase back to what it was initially.
However, in a typical experiment the first and second pulse seem to be indistinguishable to me (except for a different wavevector) so how do I get different signals?

One bump before bed

I took physics in 10th grade and all i can fucking remember are kinematics

v^2=u^2+2as?

fucking lmao

Underaged high school students are getting creative now I see. Fuck off and ask your teacher for help after school.

ctrl plus

no seriously though
arxiv.org/pdf/1409.0535.pdf

i found a lot of good shit in here

uh oh

Wow, thanks for that one. How do you easily find dissertations like that? Looking for quantum metrology would definitely not have been the first thing that comes to my mind and there's such a vast amount of garbage on the arxiv that it's hard to tell if it's even worth the time to read the abstract.
I see relations to the density matrix interpretation, but nothing about the photon echo.
Either way, this will be helpful, especially since I'm somewhat familiar with metrology (did that as an undergrad project).

If there's any NMR peeps, I'm sure I can learn a lot from you since you've been looking at photon echos for decades now.

Yea never followed through with physics that much, i still love it but aerospace restricted how much time i could put into it.I kept up as much as i could and that one had so much useful stuff i've printed out like half of it by now to take notes in.But yea unless i send 747s into black holes and shit tommorow i dont get into that much anymore.

Bumping for NMR

Also interested in semiconductor band-structures and especially the weird Brillouin zone point-labeling. All solid-state physics books say there's a labeling convention but never go in depth about their meaning. What are K-points, and why are there two? (probably trivial once I understand what is a K-point)

Bump
Come on theorists of Veeky Forums help a fellow that's trying to prove your theories out.

Cant believe that people still fall for quantum pseudo science nonsense. It's all convoluted BS designed to trap minds by having them chase their tails. Real science is supported by repeatable physical experimentation...not math and theory.

t. someone who has never studied the history and philosophy of science for even one second

Wtf are you trying to say?
Sounds pretty retarded to me desu.
Theory is there to und erstand your experiments since the fanciest Experiment is worth nothing if you cant explain it.

bump for interest

>If there's any NMR peeps, I'm sure I can learn a lot from you since you've been looking at photon echos for decades now.

Bumping for NMR or photon echo/nonecho explanations.

Will post a quick summary of my density matrix understanding later today for anyone that may be interested.

Forgot my tripfagging

So, here's the promised summary. If anything is wrong, please point it out.

The density matrix is a way to summarizes a /whole system/ while the wavefunction formalism only allows one state to be described at a time. Of course, one could make the wavefunction more complex and add in more and more details, but it will still only describe a single possible quantum state, while the density matrix allows one to look at all quantum states at once. This is expressed by the sum
[math] \sum_i p_{ij} | \Psi_i \rangle \langle \Psi_j | [/math]
Now for the diagonalization. An eigenbasis can always be chose, but may not be the most convenient basis to work with (at least for me as an experimentalist) so we choose an eigenbasis which we can handle well, namely the energy eigenstates of the atom/molecule/whateversystem we have. Then the diagonal elements of the density matrix can be interpreted as the number of electrons/excitations in that state.
The off-diagonal entries then are the coherence between the populations.
On this I'd still like some more input by you guys as to why this is the correct interpretation, my current understanding is that [math] | \Psi_i \rangle \langle \Psi_j | [/math] acts as a projection of state j onto state i, practically measuring how much of j is in the state i, which can only be non-zero if j and i are coherent.