Questions tagged [quantum-optics]
A research field within general optical physics concerned with light and its material interaction: where light is modelled by full quantum mechanical description.
1,090
questions
0
votes
1
answer
38
views
Ansatz of two-photon state
I am confused regarding the ansatz of the two-photon state. Generally, the two-photon state in the frequency domain is：
$$
|\psi\rangle=\int\int d\omega_1d\omega_2 f(\omega_1,\omega_2) a^+(\omega_1)a^+...
- 1
0
votes
0
answers
27
views
Coherent photon scattering on a 2-level system: How can the commutator of the Electric field and the dipole operator be nonzero?
Girish Argawal writes in his book Quantum statistical theories of spontaneous emission and their relation to other approaches (1974) at the end of chapter 7:
It may appear from (7.13) that the equal-...
- 6,477
1
vote
0
answers
26
views
Coupled quantum harmonic oscillators in vacuum state
I'm having some problems in understanding something conceptually. I believe that I have some unphysical results (so I did something wrong in the calculations) or maybe the results that I have are not ...
- 1,472
2
votes
1
answer
69
views
+50
Does the AC Stark Effect in Multilevel Systems depend on whether a state is populated or not?
For the sake of simplicity, assume a 3 level system, subject to a Hamiltonian $H_0$. The Hilbert space is then completely spanned by 3 states with energies $E_1$, $E_2$ and $E_3$.
I'd like to ...
- 6,477
0
votes
0
answers
25
views
Is there a way to find the superposition of two Wigner functions without finding their density operators?
Say I have two Wigner functions $W_1(x,p)$ and $W_2(x,p)$ representing pure states on optical phase space, and I want to know what the Wigner function of their superposition $W_{1+2}(x,p)$ looks like (...
-2
votes
0
answers
19
views
Relativistic image doubling effect and quantum foam possible correlation? [closed]
I came across these two interesting articles about the Relativistic Image Doubling RID effect or else called Relativistic Image Pair Creation and was wondering if this phenomenon could be correlated ...
- 3,404
1
vote
1
answer
41
views
What is the Weyl transform of narrow Gaussians and/or the Dirac delta?
Consider the family of Gaussians in $q$, $p$ with decreasing widths $σ$
$$Φ_σ(q,p) = \frac{2}{π σ^2} e^{-\frac{2}{σ^2}(q^2+p^2)}$$
or in complex plane coordinates
$$\tilde Φ_σ(α) = \frac{1}{π σ^2} e^{-...
- 1,297
0
votes
1
answer
47
views
Expectation value of Number operator in eigenstates of Hamiltonian involving creation and anihilation operators [duplicate]
I wish to estimate the expectation value of the number operator : $$\langle \hat{N} \rangle =\langle \hat{a}^{\dagger} \hat{a} \rangle$$
I know the Hamiltonian operator of my system, and thus want the ...
- 55
5
votes
1
answer
70
views
What are the eigenstates of the Displacement operator?
I know that the displacement operator:
$$ \hat{D}(\alpha)=e^{\alpha \hat{a}^{\dagger}-\alpha^*\hat{a}} $$
acts on the vacuum as: $$ \hat{D}(\alpha) \vert 0\rangle =\vert \alpha\rangle $$
But what are ...
- 55
0
votes
1
answer
50
views
Time switched quantum detection
Two thought experiments -
Modulated double slit
A double slit experiment in which one slit is repeatedly opened and closed. We expect a non-interference pattern when closed and interference pattern ...
0
votes
1
answer
27
views
Is there any physical explanation for negative extinction coefficient, $k(E)$, over a spectral range of energies?
Measured data for $n(E)$ of air were fitted to equations for $n(E)$ and $k(E)$. The measured data for n(E) spanned 0.734 to 6.702 eV. To obtain fits to the equations for n(E) and k(E) in the absence ...
- 1
2
votes
2
answers
75
views
Microscopic origin of phase matching in second harmonic generation
In second harmonic generation (SHG), the second-order nonlinearity of a medium is used to double the frequency of a driving field. In Boyd's book "Nonlinear Optics", he derives the solution ...
- 569
25
votes
9
answers
5k
views
Why does light travel in a straight line if the uncertainty principle is true?
I've asked this on different websites and never gotten an answer that a layperson can understand. Most people just say that light does not have a trajectory and then they do some hand waving. If light ...
- 361
0
votes
0
answers
15
views
Wigner function of a composite system consisting of two coherent states (Qutip weird result)
I have observed that when computing the Wigner function of a composite system consisting of two-coherent-state states using Qutip, the output is a negative Wigner function, which is unexpected as the ...
- 461
0
votes
0
answers
40
views
Homodyne Detection of Photon Number States
I'm currently trying to understand why you can detect the signal of single photons with homodyne detection. I found that the difference current $i_{34}$ is given by
$$i_{34}\sim -2 ⟨\Psi|_1⟨\alpha|_2\...
- 23
2
votes
2
answers
75
views
Local symplectic transformations on Gaussian states
According to Eqn. $(18)$ of this paper, given a two mode Gaussian state with the $4 \times 4$ covariance matrix $\sigma$, it is possible to find a symplectic matrix $S = S_1 \oplus S_2$, where $S_{1, ...
- 336
0
votes
1
answer
69
views
Which operator can implement a fermionic Bogoliubov Transformation?
In bosonic systems (for example in Quantum Optics), two-mode Bogoliubov transformations are implemented via squeezing operators as $$\hat{S}_2(\xi)=\exp(\xi^{*}\hat{a}\hat{b}-\xi\hat{a}^\dagger\hat{b}^...
- 310
3
votes
1
answer
108
views
Squeezed vacuum through a beam splitter in the Fock basis
Let's say we have a beam splitter like the one shown in the image below, where we have two inputs: a field (generally the field we want to study) in the signal mode $\hat{a}_0$, and a local oscillator ...
1
vote
0
answers
31
views
Theoretical criterion for single photon sources
I am having a question regarding the theoretical classifications of a single photon source. Normally, this is accounted by finding values in the second order correlation function $g^{(2)}(0)$ as low ...
0
votes
1
answer
53
views
What even IS scattering both in the context of QM and with waves more generally?
Like, when I think "scattering" I imagine little balls hitting each other and being repelled backwards, but obviously that's not really what happens with, e.g., Compton scattering, because ...
2
votes
1
answer
80
views
The action of $50:50$ quantum beam splitter
I have a question regarding the action of the $50:50$ beam splitter. According to Peter Knight's book, the action is
$$B=\frac{1}{\sqrt{2}}\begin{pmatrix}1 & i\\
i & 1
\end{pmatrix}.$$
However,...
- 21
3
votes
0
answers
46
views
How to describe an imperfect beam splitter?
A polarization beam-splitter (PBS) transmits horizontal polarization and reflects vertical polarization, i.e. $PBS|\Psi\rangle =PBS(\alpha |x h \rangle + \beta |y v \rangle) = \alpha |x h \rangle$. ...
- 246
2
votes
2
answers
110
views
What exactly is the difference between a quasiparticle and composite particle in QFT/particle physics?
I'm specifically thinking about quasiphotons as the superposition of photons and other interacting particles when light is traveling through a medium. I've been told there's a fundamental difference ...
2
votes
0
answers
47
views
Why does the Eigen-Energy-Shift for the AC-Stark-Shift, calculated in the "rotating frame", actually matter?
As is neatly described in this answer, the AC-Stark Shift is the observation that the energy-eigenvalues of stationary states in the "rotating frame" of a two-level-system behave as (Adam ...
- 6,477
3
votes
1
answer
66
views
Displacement operator similarity transformation using the squeezed operator
I have been trying to get the analytical expression for the Wigner function of squeezed vacuum states. Using the characteristic function representation, the WF can be written as
$$W(\alpha)=\frac{1}{\...
1
vote
1
answer
65
views
Why does the Lindblad master equation in Heisenberg picture not preserve commutation relations?
From the book of Breuer and Petruccione [1], the Lindblad master equation for open quantum systems reads $\mathrm{d} \rho (t) / \mathrm{d}t = \mathcal{L} \rho(t)$, where $\mathcal{L}$ is the Lindblad ...
- 403
0
votes
0
answers
23
views
How can there be absorption and reemission of photons when there is a coherent part of the resonance fluorescence radiation?
When we expose a 2-level system to monochromatic light and we are in the stationary state of resonance-fluorescence, the atom radiates into all space.
A part of the light that is emitted from the 2-...
- 6,477
0
votes
1
answer
67
views
Recoil of an atom absorbing a photon
I am reading the article named Manipulating Atoms with Photons by Claude Cohen-Tannoudji and Jean Dalibard. On page no. 16, the following is said.
Consider the atom in its ground state $g$ and its ...
- 2,883
0
votes
0
answers
77
views
Deriving the Purcell effect from the Jaynes-Cummings model
I'm trying to understand the approximations which lead from the Jaynes-Cummings model to the Fermi's-Golden-Rule-like Purcell effect. There should actually be a simple way to derive the cavity ...
- 2,839
1
vote
0
answers
40
views
Calculating the spectral correlation tensor in quantum optics
Given an electromagnetic field bath, by the Hamiltonian
$$
H_B = \sum\limits_{\mathbf{k}}\sum\limits_{\lambda\in\{1,2\}}
\hbar \omega_{\mathbf{k}} b^\dagger_{\lambda}(\mathbf{k})b^{\phantom{\...
- 275
0
votes
2
answers
45
views
In the adiabatic theorem, how do we know which eigenstate we start on? (STIRAP)
I am aware of the question here, but it doesn't have an answer and also doesn't answer my question. I'm wondering about a specific case in STIRAP, where the 3 eigenstates are $$|\Psi_\pm\rangle = \...
- 654
14
votes
4
answers
2k
views
What will happen to an entangled pair of photons if one of them is absorbed and remitted by an atom?
Imagine if I have an entangled photon pair in linear polarisation, let them be named photon A and photon B, and if photon A is absorbed by an atom and then re-emitted what would be the state of photon ...
1
vote
1
answer
82
views
Beam splitter that splits two incoming beams differently
ב"ה
Is there any way to build a beam splitter that will split two incoming beams differently?
Say, beam coming from the left (x axes) will transfer 70% and reflect 30% while beam coming from ...
- 11
1
vote
1
answer
83
views
How to derive the dipole interaction term in coulomb gauge QED from minimal coupling?
In quantum optics, one usually "quantizes" in the coulomb gauge, with amounts to the assumption that there are no charges present $\rho = 0$. I will introduce my question by roughly ...
- 6,477
0
votes
0
answers
43
views
What is difference between Electromagnetically induced transparency (EIT) and Coherent population trapping (CPT)?
EIT: Electromagnetically induced transparency
CPT: Coherent population trapping
When two resonant light fields (probe field and strong coupling field) are incident on an opaque material whose atoms ...
- 23
0
votes
0
answers
19
views
How is the spectral degree of coherence phase related to the Stokes parameter?
How is the Correlation coefficient phase related to the Stokes parameter? How to affect stokes parameter
- 31
0
votes
0
answers
33
views
Calculating the first moment of the probability distribution function in the coherent state
I want to calculate the first momentum, the mean value, of the phase distribution function in the coherent state $|\alpha\rangle = |re^{i\theta}\rangle$, in my attempt so far I have hit a hurdle I ...
1
vote
1
answer
36
views
How can beamsplitters and measurements be used to make a quantum cNOT gate?
It's possible to create a two-photon gate using detectors and linear optics, which can be used as the basis for a quantum computer.
I am struggling to get a basic understanding of how this works. I'm ...
- 2,037
0
votes
1
answer
38
views
How do you get the distribution of a linear combination of the quadratures using the Wigner function?
I know you can get the distribution of a quadrature, x or p, by integrating the Wigner function over all the rest of variables (2N-1 variables for an N mode state). But how do you get the ...
1
vote
1
answer
89
views
What is the most general wave function of a minimum uncertainty (Gaussian) state in quantum mechanics?
For some state $|\psi\rangle$ it is possible to recover the uncertainty principle using the fact that $$\left|(\hat{\sigma_{Q}}-i\lambda\hat{\sigma_{P}})|\psi\rangle\right|^{2}\geq0,$$where$$\hat{\...
- 729
0
votes
0
answers
7
views
I have a covariance matrix using Heisenberg-lengvin without noise. How can i get one with noise terms included
I have a paper i which they have represented the interaction between a coplanar waveguide and a capacitor using Heisenberg-lengvin equations. Which is further used for covariance matrix. But they ...
0
votes
0
answers
30
views
When local field effects should be included at dielectric function calculations with DFT?
There exist macroscopic and microscopic dielectric function. When local field effects are not important ( ex:for metals) there is no significant difference between microscopic and macroscopic ...
1
vote
2
answers
157
views
Question about Glauber-Sudarshan $P$ representation
I'm reading Scully's 'Quantum Optics'. I've got some question about the Glauber-Sudarshan $P$ representation.
It's straight forward that
$$
P(\alpha) = \frac{e^{\vert \alpha \vert ^2}}{\pi^2} \int \...
- 13
0
votes
0
answers
111
views
What is difference between Quantum optics and photonics in general?
Might be a vague Question, But I'm hard to understand it.
My Interest is Quantum optics, which studies Atom optics, Optical coherence, and experimentally proven foundations of Quantum Mechanics.
...
- 11
3
votes
0
answers
36
views
What is a stochastic electromagnetic wave?
In statistical optics we always talking about stochastic electromagnetic wave but I am not able to understand how this wave is different from electromagnetic wave
- 31
1
vote
1
answer
59
views
What is the state of the light emitted by an esemble of independent single photon emitters?
Upon proper excitation, single molecules (e.g. fluorescent dyes, quantum dots, etc.) spontaneously emit single photons, namely Fock states $|1\rangle$. These states have no statistical uncertainity ...
- 895
2
votes
0
answers
127
views
Cavity Input-Output Formalism: Physical significance and intuitive understanding
I have spent a lot of time trying to understand the input-output formalism for cavities. I sort of understand the idea
Fields inside an optical cavity(our system) will have losses because the mirrors ...
- 63
2
votes
1
answer
64
views
Photon though a single-slit and uncertainty in the $z$- (longitudinal) direction
Heisenberg's uncertainty principle is sometimes invoked in explaining the width of the diffraction pattern as light passes a single slit. In the case of single photons, when a photon is directed ...
- 6,437
0
votes
0
answers
31
views
Two-level system with natural frequency $\omega_{21}$ exposed to an EM radiation of frequency $\omega$
Consider a two-level system with energies $E_1$ and $E_2(\gt E_1)$, and an energy gap $$E_2-E_1=\hbar\omega_{21}.$$ If this system is excited by an EM radiation of frequency $\omega(\lll\omega_{21})$, ...
- 10.4k
0
votes
0
answers
43
views
Husimi $Q$-function of Infinite Square well
Eigen-Wavefunction of infinite square well is
$$\psi(x)=\sqrt{2/l}\sin(n\pi x/l).$$ I want to write Husimi $Q$ function for infinite square well. General expression of Q function is $$Q=(1/2)\pi \...
- 741