# Tag Info

### What is QED about "Cavity QED"?

The terminology "cavity QED" is used to signal that one is treating the electromagnetic field as itself quantised and there is a cavity with mirrors in the problem. The alternative would be to treat ...
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### What does it mean to Fourier transform a ladder operator (in the input-output formalism)?

I will try to give some intuitive explanations, so long answer incoming... Physical picture, Hamiltonian and operators Let us first have a look at the bath model considered by Gardiner and Collett ...
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### What is QED about "Cavity QED"?

What would I be missing in Cavity QED if I had never learnt about quantum electrodynamcis? Excellent question, especially the way it is posed! The bottom line is that what the OP calls "standard ...
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### Lindblad and Input-Output Formalism in Quantum Optics

There is already a nice answer but I feel that some important aspects deserve additional attention. My answer is simply a list of observations: Master equations involve approximations: It is ...
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### Casimir force extraction

The precise interpretation of the Casimir effect is somewhat controversial. Casimir's original derivation was via van der Waals forces, not vacuum energies. See "The Casimir effect and the ...
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The minimal quantum model for spontaneous emission is given by the interaction Hamiltonian $$H = \int d\omega [g(\omega)a(\omega)\sigma^+ + g^*(\omega)a^\dagger(\omega)\sigma^-]$$ where $a(\omega), a^... • 11.5k 5 votes Accepted ### Is there a limit to photon density? The only fundamental limit is that eventually the energy density gets high enough that you form a black hole. In principle, you could achieve an unbounded number density by decreasing the energy of ... • 17.2k 5 votes ### What is QED about "Cavity QED"? Well if you are representing light as a quantum field and not as a classical field, then I suppose cavity QED is QED. The only difference is that cQED is usually done with nonrelativistic particles,... • 7,753 4 votes Accepted ### Quantum input-output theory : Why do we multiply by density of mode to have a number of photon **per unit of time** Some remarks: From the question (emphasis mine) Before moving further, it is important to underline that$b^†(ω)b(ω)$is not the number of photon of frequency$ω$because it has the dimension of ... • 11.5k 4 votes Accepted ### Coherent drive Hamiltonian The coherent drive represents an electromagnetic field interacting with the light/atom in the cavity. Say you have a drive (electromagnetic field): $$E\propto \epsilon b +\epsilon^*b^\dagger$$ and ... 4 votes Accepted ### Common subsystem-bath interaction operators? For the particular case specified in the OP (a cavity mode coupling to an external bath), the most standard form is probably the Gardiner-Collett Hamiltonian [see C. W. Gardiner and M. J. Collett Phys.... • 11.5k 4 votes Accepted ### Quantum theory for cavity trapping light For most of the physics of Fabry-Pérot cavities, classical optics is sufficient. You can calculate transmission and reflection coefficients (using Parratt's formalism or Abele's transfer matrix method)... • 11.5k 4 votes ### Rabi Hamiltonian with three instead of two Pauli matrices I probably should have searched more extensively before posting here, I did eventually find this Hamiltonian in Exceptional and regular spectra of a generalized Rabi model by Michael Tomka, Omar El ... 4 votes ### Rotating wave approximation and conservation of energy You are being misled by thinking that the terms$a^{\dagger}_j a_i$do conserve energy. What if the two systems$i$and$j$had different energy spacings? In the case of two oscillators, they can have ... • 4,810 3 votes ### Lindblad and Input-Output Formalism in Quantum Optics 'I'm confused as to what the analogue of the term$r_{in}$is in the Master equation' The analogue of$r_{in}(t)$in the Master equation is the set of bath modes which, in the master equation, you ... • 533 3 votes ### Why does Jaynes Cummings not describe an atom in free space? I just recently learned about the Jaynes-Cummings model and will attempt to answer this question, despite that it was asked three years ago. I imagine that the questioner probably already have an ... • 163 3 votes ### Cavity quantum electrodynamics: difference between Rabi oscillations and vacuum Rabi oscillations? The OP pointed out some similarities in the Hamiltonian of the two cases. There is, however, a clear physical distinction between the two cases. Vacuum Rabi oscillations are induced by strong ... • 11.5k 3 votes ### Can we change the frequency of a photon in a resonator by changing the refractive index? The exact answer depends on the actual implementation of this refractive index change - i.e., on the Hamiltonian that describes it. However, it is worth making some remarks: what is changed here is ... • 58.2k 2 votes Accepted ### Actual classical time evolution in a closed Cavity It's a perfect electrical conductor (PEC) at the endpoints. Assuming$u(x)$represents a component of the electric field perpendicular to the$x$-axis, the boundary conditions are$u(0)=u(L)=0$, which ... • 1,036 2 votes ### Does the Casimir effect allow to change the lifetime of a radiating atom? I was initially going to comment on Lagerbaer's excellent answer, but it got a bit too long. So to supplement his answer, here is some additional background: The effect was first predicted by Purcell ... • 11.5k 2 votes ### Hamiltonian for single-mode field in cavity Hints: The notation is confusing. In the first line$\int dV$is an integral over the space inside a volume$V$. It would be much nicer to write$\int_V d^3r$. Or, since the example seems to be one-... • 11.5k 2 votes ### Obtaining equations of motion for a three-level atom and plasmon system Some general remarks: The equations of motion for the expectation values$\langle \hat{a} \rangle$,$\langle \hat{\sigma}_{12} \rangle$,$\langle \hat{\sigma}_{23} \rangle$only have closed form at ... • 11.5k 2 votes ### Why does Jaynes Cummings not describe an atom in free space? You need a cavity so that the modes are well separated in frequency.In free space there are arbitrarily close-in-frequency modes, and so it is impossible to let the atom interact with only one of ... • 52.6k 2 votes Accepted ### What is a mode? Regarding electromagnetic waves in a closed cavity The different modes of electromagnetic waves in a cavity correspond to different eigenfunctions of the solutions of the electromagnetic wave equation given the boundary conditions of the walls of the ... • 15.8k 2 votes Accepted ### Mathematical formalism to show that an atom casts a small shadow in the photon field that illuminate it Upon reading the question carefully, I believe that the problems of the OP have nothing to do with the quantum nature of the interaction, but simply with the understanding of how modes work. To see ... • 11.5k 2 votes ### Quantum input-output theory : Why do we multiply by density of mode to have a number of photon **per unit of time** Disclaimer: I struggle with this question myself a bit. I think I have something to add that may be helpful to you but it isn't going to be a superpolished answer and it might be a little unclear at ... • 13.9k 2 votes ### What are some good resources for understanding Gauge transformation in QED? There are multiple layers to this: gauge transformations in electrodynamics in general and then in cavity QED specifically. For the general part, you will find useful information in almost any ... 2 votes Accepted ### Physical meaning of Cavity Finesse that finesse is the measure of the cavity losses and is independent of resonator separation I guess I would agree with that definition, but would add the word relative before "measure". The ... • 24.5k 2 votes ### Decay into continuum with complex energies Some notes: The central equation in the question $$\dot c(t) =-\left[\int_0^tdt'\int dk\,e^{-i(\omega_k-\omega_0)(t-t')}|g_k|^2\right]c(t') \,,$$ can be solved using Laplace transformations (... • 11.5k 2 votes Accepted ### Is one photon the quanta of excitation between modes or Energy eigenstates? higher energy means greater frequency means more photons No. The energy in the mode is the product of the frequency of the mode and the number of photons in that mode,$\$ E_k = \hbar \omega_k (n_k+\...
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