Recent content by jamie.j1989

  1. J

    A Why is the quantum Fisher information useful in quantum metrology?

    I'm getting interested in quantum-enhanced metrology and have come across the quantum Fisher information (QFI) as a measure of how much a quantum state ##|\Psi(\theta)\rangle## changes with respect to some variable, for example, the phase accumulated during an interferometer, ##\theta##. This is...
  2. J

    I Atoms in a harmonic oscillator and number states

    The number operators can also be used to count atoms, see here https://en.wikipedia.org/wiki/Fock_state, I've done a bit more reading and it does seem one needs to look at the context, for example in this paper https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.110.163604 they represent...
  3. J

    I Atoms in a harmonic oscillator and number states

    I am confused about the relation between the number state ##|n\rangle## with the annhilation and creation operators ##a^\dagger## and ##a## respectively, and the number of atoms in the harmonic oscillator. I'll try to express my current understanding, I thought the number states represent the...
  4. J

    Machine Learning or Deep Learning for a Lab Experiment

    Yes, current loops are static, varying the currents in the loops control the location of the magnetic field zero. I can see how I should vary the currents to accomplish what I need, It would just be a nice project to see how I could set up some sort of machine learning process that could...
  5. J

    Machine Learning or Deep Learning for a Lab Experiment

    Hi, I want to try out a bit of machine learning or deep learning with an optimisation problem in the lab. However, I'm confused at what the best option would even be or whether my optimisation problem is even applicable to either. Firstly, the lab set up hasn't been built yet, I am computing...
  6. J

    Velocity of a particle at time t in a rotating frame

    I was under the impression that the matrix ##R## I suggested I should use was a quaternion? However, on closer inspection, it says for a constant rotation axis. Does this need a numerical approach? It doesn't seem obvious how to define ##\theta## (the amount rotated about the axis of rotation)...
  7. J

    Velocity of a particle at time t in a rotating frame

    I think this explains a lot of my confusion, so in my example, I know the rotation of the rotating frame about the inertial which I have labelled ##\boldsymbol{\Omega}## which I need to apply ##\hat{D}## to, to get ##\boldsymbol{\Omega}'=\hat{D}\boldsymbol{\Omega}##. So would this also be...
  8. J

    Velocity of a particle at time t in a rotating frame

    If I understand correctly what you have shown, and if I can write it down in a way I find easier to read, I have \begin{equation} \begin{pmatrix} v_x \\ v_y \\ v_z \end{pmatrix} = \begin{pmatrix} v_x' \\ v_y' \\ v_z' \end{pmatrix} + \begin{pmatrix} 0&-\Omega_z&\Omega_y\\ \Omega_z&0&-\Omega_x \\...
  9. J

    Velocity of a particle at time t in a rotating frame

    Ok, so I've convinced myself that the result is fine. However, I am now confused about coordinate transformations. If I write ##\dot{\boldsymbol{r}}=\boldsymbol{v}## as \begin{equation} \boldsymbol{v}=v_{x'}\boldsymbol{\hat{i}'}+v_{y'}\boldsymbol{\hat{j}'}+v_{z'}\boldsymbol{\hat{k}'}...
  10. J

    Velocity of a particle at time t in a rotating frame

    Yes, I am concerned that it is wrong when having a time-dependent rotation, this is because the result I get Eq.(3), doesn't seem to make sense when I consider particular examples of rotation with a time dependence. Admittedly this could just be a mistake in my workings or reasoning about the...
  11. J

    Velocity of a particle at time t in a rotating frame

    Would the correct equation to use for time-dependent ##\boldsymbol{\Omega}## be \begin{equation} \boldsymbol{a} = \boldsymbol{a}'+2\boldsymbol{\Omega}\times\boldsymbol{v}' + \boldsymbol{\Omega}\times(\boldsymbol{\Omega}\times\boldsymbol{r}') +...
  12. J

    Velocity of a particle at time t in a rotating frame

    Specifically I am trying to look at the difference of the absolute velocities squared of two particles, one going clockwise (-) around a circuit in the rotating-frame and the other anticlockwise (+). When plugging in for ##\boldsymbol{r}_{\pm}'=r(\cos(\phi(t)),\pm\sin(\phi(t)),0)## into Eq.(1)...
  13. J

    Velocity of a particle at time t in a rotating frame

    Imagine two frames one inertial (x,y,z) and the other rotating (x',y',z'), their origins are always coincident. The rotating frame is rotating as seen from the inertial frame with a time-dependent angular velocity ##\boldsymbol{\Omega}(t)=(\Omega_x(t),\Omega_y(t),\Omega_z(t))##. In the rotating...
  14. J

    I Composite traps with two-level atoms

    Let's say we have a system of spatially separated traps and two-level atoms where the levels are denoted as ##|a_i\rangle## and as ##|b_i\rangle##, and the subscript ##i## labels the trap number. The traps are initially loaded with ##N_i## atoms in the state ##|a\rangle##. If the two levels are...
  15. J

    I Feynman's Thesis, 3 Principles

    Hi, I've just started studying Feynman's thesis and am in need of some discussion regarding the three principles he put forward on the development of his 'Principle of least action in quantum mechanics'. The three principles are 1) The acceleration of a point charge is due to the sum of its...
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