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.
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Lindblad operator in an Input-Output formalism in superconducting quantum circuit
I would like to understand the relationship between the Quantum Langevin Equations, Input-Output formalism, and Master Equation.
I already read these questions:
Lindblad and Input-Output Formalism in ...
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How do the entangled photons from an SPDC source behave?
As I understand SPDC sources emit entangled photons, but always in the same polarisation. If this source always outputs this certain polarisation are the photons then still in superposition of each ...
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The coherence length is much longer than the manufacturer claims and has an oscillating visibility
The problem is that the coherence length of a laser I am experimentally measuring is much longer than the manufacturer claims and has an oscillating visibility. Let me explain the situation: I have an ...
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Anti-Hermitian Hamiltonians in Quantum Mechanics and Open Systems
The Schrodinger equation (SE) with a Hermitian operator $H$ generates unitary evolution, and it is well-known that plenty of quantum processes can be described by SE and appropriately chosen $H$. That ...
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Invariance of creation and annihilation operators under mode transformation
In exercise1.4 of "Introduction to Optical Quantum Information Processing",
the commutation relations for the mode operators is preserved under mode function transformation.Where,$\hat{b}_{\...
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Decomposing density matrix on non-orthogonal and incomplete set of states
I've recently come across the following conclusion in a quantum optics paper. The paper studies the dissipative dynamics of a two-qubit system and presents the following approximation for the steady-...
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The response of a linear quantum amplifier to broadband signals
I have been studying related knowledge of quantum linear amplifier noise limit recently, and the main reference material is Caves' literature. In this paper, the author uses equations (4.5, 4.40a, 4....
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Extending pairwise beam splitters operators to an overall transformation
Let $\bar x_s, \sigma_s$ be the vector of first moments and the covariance matrix of an $N$-mode Gaussian state $\rho_s$. If $\rho_s$ is paired with an empty environment of similar dimension, the ...
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How to Numerically Solve the Steady State of a Lindblad Equation with Parity Symmetry?
I am trying to reproduce some figures from this paper. like below:
The effective Hamiltonian of the system is
\begin{align}
H_{\text{eff}} = \frac{3g_x^2}{\omega} |e\rangle \langle e| + \frac{2g_x^...
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Squeezing degredation via photon loss
Consider a partially reflecting beamsplitter with two input modes $\hat{a}_{in}$ and $\hat{b}_{in}$. It has a transmission coefficient of $\eta$. If the photon in mode $\hat{b}_{in}$ is in the vacuum ...
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Beam Splitter acting as unitary time evolution
I have a problem understanding a really important fact about quantum mechanical beam splitters and how to evaluate their action on two incoming modes.
Suppose we have a beam splitter that transforms ...
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How can I find the unitaries for the Bloch-Messiah decomposition?
I'm currently trying to understand the Bloch-Messiah decomposition in quantum optics, which basically states that every second-order nonlinear quantum optical circuit can be decomposed into a ...
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How do light rays know what the surface of an object is shaped like?
In school we learn about optics and how rays of light reflect off of surfaces and travel through lenses. These trajectories depend 100% on the shape of the surface (convex, concave, angle of incidence,...
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Precise form of two-mode squeezed state
Starting with the two-mode squeezing operator
$
S_2(\xi) = \exp \left( \xi^* a_1 a_2 - \xi a_1^\dagger a_2^\dagger \right)$, we can factor it into [1]
$$
S_2(\xi) = \frac{1}{\cosh r} \exp\left( -a_1^\...
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Heterodyne measurement gives us complex measurement result?
Quantum mechanics tell us that the measurement result can possess real values. However, in quantum optics, there's a kind of measurement called heterodyne measurement which can be described ...
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Simulation of photon correlation measurements for entangled photons generated in SPDC
I am trying to simulate the measurement that one would have corresponding to type-I spontaneous parametric downconversion (SPDC), for the case when we have say a single-photon -sensitive time-stamping ...
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How to transform collapse operators in rotating frame?
I want to simulate the evolution of a transmon qubit driven by a classical voltage using qutip. The problem is that the qubit (and the drive) have a frequency of around 5GHz and I typically run ...
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Is dipole approximation valid for ground - Rydberg transition?
I was curious following the dynamic equations of atom-light interaction (e.g., Ch. 5 of Quantum Optics from Scully), that we assume dipole approximation where size of the atom, $r$, is very small ...
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In atomic ionization via laser, the process is more efficient using a wavelength only slightly bluer than the threshold rather farther detuned. Why?
I have seen this phenomena referenced in several instances; however, I have been unsuccesful in finding a clear explanation for where this enhancement comes from or the term to describe this process.
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Units of electric field in quantum optics
Similarly, the expectation value for number operator in mode 4 is the same for a 50/50 beam splitter. This simply implies that the average number of photons in either one of the output ports is $50\%$,...
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Are Gaussian states equivalently defined as "ground and thermal states of quadratic Hamiltonians?"
There are several definitions of a (bosonic) gaussian state (related question).
One of them is given in the paper "Gaussian quantum channels" by J. Eisert and M.M. Wolf on page 3, equation 4....
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Tensor Inverse for Gaussian Quantum Fisher Information
I'm trying to calculate the Quantum Fisher Information (QFI) of a Gaussian state. In this case, I'm following the prescription outlined in this paper https://arxiv.org/abs/1407.7352, which was ...
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$(t-s)$ substitution in the derivation of Lindblad master equation
In the derivation of the Lindblad equation from first principles, on reaching the Redfield equation, for example Eq. 505 in D. Lidar's notes:
$$\frac{\mathrm{d}}{\mathrm{d}t} \tilde{\rho}(t) = - \text{...
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Fock State Generation in Trapped Ions
I am trying to understand the fock generation protocol explained here: https://amowiki.odl.mit.edu/index.php/Quantum_control_and_trapped_ions
What I am confused about is what experimental ...
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Resources with treatment of Quantum Optics as an application of Quantum Field Theory?
I am looking for resources which deal with Quantum Optics, with some rigor, as an application of Quantum Field Theory.
PS:I have read Introductory Quantum Optics by Gerry and Knight. So that is my ...
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Where did the time dependence go in the Jaynes-Cummings Hamiltonian?
In most references the Jaynes-Cummings Hamiltonian is always given as the following form
$$H_{JC} = \omega_0 a^\dagger a + \omega \sigma_z - g(a^\dagger + a)(\sigma_+ + \sigma_-)$$
I notice that the ...
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Explicit Expression of $S_2(\zeta)$ on a general Fock State?
I would like to know the explicit expression of the two-mode squeezing operator $\hat{S}_2(\zeta)$ acting on a general Fock state $|p,q\rangle$, without including any additional operators in the ...
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Two-Photon Interference But Different Global Phases
If two identical photons enter a beam splitter at the same time, they will always exit the beam splitter togheter (the Hong–Ou–Mandel effect), however small changes in timing can make them leave by ...
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Quantised electromagnetic field in quantum optics for an infinite quantiation volume
The electromagnetic field can be quantised by considering the allowed modes in a cube based on the periodic boundary conditions and then quantising those modes. Doing so, we find that the hamiltonian ...
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Why is PDC radiation someties emitted as a hollow cone and sometimes appears as a 2D gaussian?
Common depictions of PDC radiation depict it as a hollow cone being emitted. In the imaging plane, this then appears as a circle. See for example the following picture from this arXiv upload:
On the ...
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Is Hadamard gate considered a valid beam splitter when dealing with multiple beam splitters?
I have read that Hadamard gate can be a valid 50:50 beam splitter when dealing with one beam splitter , however when dealing with more than one beam splitter the hadamard gate is no longer valid and ...
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Probability distribution map for a diffraction experiment
Assume a single-photon propagates along $z$ in a glass fiber that terminates, creating an interface glass-vacuum. I'm interested in the diffraction pattern created after the fiber at a distance $z_s$.
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What are examples of (non-thermal) states with non-singular $P$ function?
We know that the $P$ function of (displaced) thermal states is smooth and positive. Indeed, as shown e.g. here, a thermal state $\rho_{\rm th}(x)\equiv (1-x)x^{a^\dagger a}$, $x\equiv e^{-\beta}$, has ...
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Using classical $g^{(1)}$ to calculate quantum $g^{(1)}$
Imagine a free space optical switch with several inputs and outputs. My question is: can we use the first order cross correlation between the complex amplitudes of two classical beams of light at the ...
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Phase of a coherent state in Quantum Mechanics
In the following image from Section II of the paper Mesoscopic Superposition of States with Sub-Planck Structures in Phase Space, the second state is designated by $\left|e^{i\theta}\alpha\right>$ ...
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Classical vs quantum field in beam-splitter [closed]
John F. Clauser's 1974 paper (https://doi.org/10.1103/PhysRevD.9.853), disproves the classical field theory model for light. In the experiment, a short burst of light from an excited Hg source passes ...
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How to find two-point correlators of field strength in Maxwell theory?
I know $\langle A_\mu \rangle=0$ by Lorentz symmetry. Here the expectation values $\langle . \rangle$ are taken w.r.t. the vacuum. Taking derivatives we have $\langle F_{\mu \nu} \rangle=0$. This ...
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Exploiting Creation Operator Commutation Relation in HOM Interference Calculation
In this paper where the authors derive the formula for coincidence probability in a Hong-Ou Mandel (HOM) interference effect as a function of time delay $\tau$, they arrive at an equation (15) with ...
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Fiber Beam Splitter for Quantum Optics
I am conducting an experiment involving HOM interference. I cannot find a definitive answer as to whether a free-space beam splitter will behave identically to a 50:50 fiber coupler, such as this one ...
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Hong-Ou-Mandel (HOM) effect - question on math of indistinguishability of photons
I’m working on the transformations of multi-photon states through a beam splitter, and I encountered confusion in some normalization factors . Using beam splitter transformations:
$$ \hat{a}^\dagger \...
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What is the difference between electro-optic sidebands and parametric down conversion sidebands?
I am trying to understand the difference between the modes generated via electro-optic modulation (EOM) and parametric down conversion (PDC) in the context of quantum optics. Throughout the literature,...
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Average field intensity in quantum optics [closed]
When we transform the electric field into operators $\mathbf{\hat{E}^{(+)}}$ and $\mathbf{\hat{E}^{(-)}}$ for the positive and negative frequency components, respectively, what is the correct ...
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Density matrix equations
I am studying a paper (http://dx.doi.org/10.1088/0022-3727/48/14/145301) in which the Hamiltonian is:
$$H = \sum_{i}\epsilon_{i}\sigma_{ii} - \hbar\omega_{p}\hat{a}_{p}\hat{\sigma}^{\dagger}_{ba}e^{-\...
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Relation Between Diagonal and Off-Diagonal Damping Elements
I was reading the 4th edition of "Nonlinear Optics" by Robert W. Boyd, more specifically chapter 3.3 - "Density Matrix Formulation of Quantum Mechanics". There, the author says ...
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Laser interference fringes fading in and out of view
I'm working in a lab this summer doing quantum optics, and my team is working on a Mach-Zehnder interferometer setup. We got it well aligned and interference fringes appeared as expected. However, ...
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Parametric down-conversion - QFT necessary?
In quantum optics, one ususally starts by quantizing the free electric field and obtains an expression for the electric field operators:
$$ E(\vec{r},t) = \sum_{\vec{k},p} C_{\vec{k}} \vec{e}_{\vec{k},...
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Dipole term in light-matter interaction
I have a question regarding the description of the term “dipole” in light-matter interactions.
If I understand it correctly, there are 3 different things that one can declare as a dipole during light-...
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What is the relation between the Faraday effect and the Zeeman effect?
The Faraday Effect basically says that certain materials under a magnetic field have different indexes of refraction for right and circular polarized light. Linear light which is a superposition of ...
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Scattering into an edge state
In the optical context, a photon can excite an electron from the valence band to the conduction band if the photon energy is higher than the gap. I would like to know is it possible to photoexcite an ...
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Quantum Optics - Output field of Spontaneous Parametric Down-Conversion (SPDC)
Following Ultrabright backward-wave biphoton source by Chih-Sung Chuu and S. E. Harris:
The output of a backward wave Spontaneous Parametric Down-Conversion (SPDC) is described by
$$ a_s(t, z) = b_s(t)...
