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The requirement is that $\chi^{(2)}$ be non-centrosymmetric. That's a bit different than having a particular parity. The states involved must be neither odd nor even; the parity must be mixed. That way the dipole matrix element exists between all three intermediate states involved in calculation of the susceptibility.


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Here is probably the simplest argument that I have heard of. Detection of a photon from a thermal source gives a rise to a probability to detect several more in a short interval of time due to stimulated emission. Assume that you have some atoms in a medium that emits light, and they are in an excited state. If you know that one atom emitted a photon, this ...


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It seems I have figured out an answer for 2 terms in the original state. Suppose that the state is $$\rho = a |\alpha \rangle \langle \alpha | + (1-a) |\beta\rangle \langle \beta|$$ We need to write it in a basis, which is $$|+\rangle = \frac{|\alpha\rangle + |\beta\rangle}{\sqrt{2}}; \quad |-\rangle = \frac{|\alpha\rangle - |\beta\rangle}{\sqrt{2}}. $$ ...


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These two points of view are not so different in fact. To see that, let's work in the grand-canonical ensemble (which is the most natural to talk about the chemical potential in the Mott phase, since it is not well defined in the canonical ensemble). At a given (and small enough) $t/U$, there is a range of chemical potential $[\mu_-,\mu_+]$ where the ...


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How does the matter-radiation system, on its own, goes over to the Blackbody distribution? Evolution towards equilibrium (in macroscopic sense) happens when the system matter + radiation is isolated, for example if a piece of matter is inside a cavity that slows down leakage of energy out of the system. For example, a piece of coal in a well reflecting ...


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Just as a supplement to ACuriousMind's answer, it is worth noting that buried in the bottom of their paper they actually show what the "spin 1/2" eigenstates are in terms of the regular basis: $|j=1/2\rangle=\frac{1}{\sqrt{2}}(|1, -1 \rangle + |0,1\rangle$) $|j=-1/2\rangle=\frac{1}{\sqrt{2}}(|-1, 1 \rangle + |0,-1\rangle$) where $|l, \sigma\rangle$ is the ...


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The rotating-wave approximation requires a transformation to a rotating frame. In particular, use the transformation $U(t) = {\rm e}^{{\rm i} \omega_d t a^\dagger a}$, i.e. transform your states as $\lvert \psi(t)\rangle \to \lvert \tilde{\psi}(t)\rangle = U(t) \lvert \psi(t)\rangle $. Now, in the original frame, the evolution is given by the Schroedinger ...


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Nothing is happening. At least, nothing except that a new generalized quantity suggestively called "angular momentum" was defined and subsequently measured. But nothing we know about the usual angular momentum of photons is changed by this in any way. Standard total angular momentum is $J = L + S$, where $L$ is the orbital and $S$ the spin angular momentum. ...


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Your problem is more math related than physics. To find proper full-width at half maximum $\Delta t$ and $\Delta \omega$ you have to equate the functions to $x$, with some proportionality coefficient so that when $x=1$ you're at the maximum of the function. This way after solving for $t$ or $\omega$ you'll find the half-width half-maximum by plugging in ...


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The title of the paper is "Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States". Random guessing is an ambiguous discrimination procedure. It can return the wrong answer without telling you that it failed. More generally, unambiguous discrimination procedures are less likely to succeed because removing any chance of accidental ...


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Perhaps the question is, how do you measure an arbitrary number of photons without destroying the system? It's certainly the case that somehow measuring the number of photons in the cavity would collapse the state into a Fock state, but it's not obvious how to do that without actively destroying the system in some way; there has been some work done in ...


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The answer is no, and the details are clearly spelled out in Glauber's Les Houches lectures (circa 1964). Glauber introduces a "T-representation" which can represent any operator in the Fock space of harmonic oscillator states, a less general "R-representation" which can represent any density operator, and the still less general "P-representation" which can ...



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