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
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.
Easton Johnson
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.
Jason Martin
>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]
Grayson Myers
>[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
Gabriel Bell
I know, but I'm retarded, how is the last equality true?
Juan Lewis
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?
Brody Clark
One bump before bed
Jace Richardson
I took physics in 10th grade and all i can fucking remember are kinematics
