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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21 views

What optical element can you use to implement a square root of NOT gate

How do you implement a square root of NOT gate in an optical quantum computing circuit? What optical element or combination of elements would you use - especially, if you want to manipulate ...
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39 views

$\sigma$ transition and angular momentum conservation

Suppose we have a box of atomic gas, where each atom has a upper $l=1$ level P and a lower $l=0$ state S. Suppose we then prepare the gas so that all atoms reside in the $l=1, m_z=1$ excited state. ...
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41 views

Proof of the similarity relations of the displacement operator and annihilation operator [closed]

I'm sure this has been asked here previously, but I seem to be having some trouble finding it, feel free to direct me to a popular reference. I was looking for a proof of the following let Let $|\...
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Markov approximation at low temperatures

I'm interested in a two-level system in contact with a reservoir of harmonic oscilators, described by the following Hamiltonian: $$ \hat{H}=\hat{H}_S+\hat{H}_R+\hat{H}_{RS}=\hbar\omega_0\hat{a}^\...
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19 views

Beam Spllitters

What is the difference between a symmetric, balanced and an asymmetric beam splitter? Which beam splitter should I use if I want one input state to be fully transmitted and the other to be fully ...
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Denotation for entangled photon pair by SPDC process

I have a question regarding the eqaution of entangled photon pairs obtained in the type-2 SPDC process. The subscripts 's' and 'i' stand for signal photon and idler photon. And, the states 'H' and 'V'...
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Photon Catalysis

I am doing my research in the field of Quantum Optics. My topic of interest is Photon Catalysis. In this process, a coherent state and a fock state |1> are incident on the "a" and "b&...
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36 views

CHSH Bell measurement, why is there difference between 45 and 135 degree?

Let assume BBO type-2 that simultaneously generates entangled photon pair in forms of horizontal polarization (H) and vertical polarization (V) of photon. One photon is going to Alice and the other is ...
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20 views

Polarizing beam splitter for diagonal polarization of photons?

If 4-fold photons which are bunched from an attenuated classical source are polarized at 45 degree (diagonally polarized) and put into polarizing beam splitter, two of them are reflected and the other ...
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18 views

Can this experimental setup generate a superposition of two distinguishable states?

Is it possible to generate a superposition state, $\hat{b}_1^{\dagger} = (\hat{a}_1^{\dagger}+\hat{a}_2^{\dagger})/\sqrt{2}$, in a way as demonstrated in this figure? Notice that this transformation ...
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3answers
100 views

Can laser light be described by individual photons?

If laser light is described by a coherent state, a macroscopic quantum state, to what extent does it make sense to speak of individual photons in laser light? And if the laser is attenuated to be a ...
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59 views

Momentum and photon indistinguishability

Suppose two photons have the same frequency and polarization, and their wavepackets also have identical temporal and spatial (along their propagation directions, respectively) profiles. The two ...
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Derivative of a multimode squeezed vacuum state

Let us suppose we have a multimode squeezed vacuum state of the form \begin{equation} |\psi\rangle = \exp[A]|0\rangle= \exp \big[\sum_{ij}G_{ij}(t) (a_i a_j -a_i^\dagger a_j^\dagger)\big] |0\rangle\...
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Quantum entanglement using a non-polarising beamsplitter [closed]

(1) Suppose you had an optical set up where 2 coherent laser beams (orthogonally polarised, and both having the same wavelength & amplitude; i.e. indistinguishable photons apart from their ...
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Entangled Photon Sources: how to choose the pump wavelength in SPDC?

I found several papers dealing with entangled pairs of photons generated by means of a setup consisting in a pump laser and a nonlinear crystal, such as BBO or KTP and here the incoming photons ...
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Is photon a wavepacket of electromagnetic field?

Photon is a "particle of light". Light is just a propagating EM field. Therefore photon is (at least intuitively) a localized EM field (i.e. wavepacket). In quantum optics, the Hamiltonian ...
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6answers
930 views

Is there a field of physics that attempts to understand the properties of light from a single perspective? [closed]

Hearing about the wave-particle duality of light, I can’t stop wondering whether there is a field of study that attempts to understand the properties of light from a single perspective. Is there such ...
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Phase/Intensity uncertainty relation

In quantum optic, we have the relationship: $$\Delta N\Delta \theta>1/2\tag 1$$ But to my knowledge, $\theta\in[0,2\pi[$ so $\Delta\theta$ is finite, then for example if we know perfectly the ...
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Derivation of Jump Operators in Master Equation

I'm trying to understand the process of deriving the master equation in this article. The system in general is composed of two interacting qubits each of which is coupled to their local thermal bath ...
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57 views

The “Algorithm” for Derivation of the Master Equation

I'm trying to come up with a master equation for a spin system. So, I'm trying to understand in general how can we derive the master equation and the Lindblad operators if we know the system, bath and ...
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100 views

Quantum and non-equilibrium properties of the radiation, emitted by “thermal light sources”

Free photon gas Let us consider different thermal light sources, such as the Sun, a incadescent lamp, or a fluorescent bulb. In elementary quantum mechanics and statistical physics one describes the ...
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Average photon number in the strongly correlated James-Cummings model

Looking for extensions of the so-called James-Cummings model, I found that the strongly correlated version uses a reservoir-Hamiltonian given by $$ H_R=\int_0^\infty \omega\hat{b}^\dagger(\omega)\hat{...
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43 views

Can separable states display statistical correlations between global observables

In the following the notation $|a\rangle$ represents one single particle in the spin state $a$, so that $|0+1\rangle$ represents one single particle in a spin state superposition. On the other hand $|...
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Transform two-mode squeezed state (TMSS) to its covariance matrix

The two-mode squeezed state can be written as: ${\left| \chi \right\rangle _{AB}} = \sqrt {1 - {\chi ^2}} \sum\nolimits_n^\infty {{\chi ^n}} {\left| n \right\rangle _A}{\left| n \right\rangle _B}$ ...
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Rotating wave approximation (RWA) in Dicke model

The interaction part of Rabi Hamiltonian is defined as $$H_I = g (a + a^{\dagger})(\sigma_{+}+\sigma_{-})$$ where $g$ is the coupling between atom and the field, the time dependencies of field and ...
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Possible mistake in Jaynes–Cummings' original ansatz of quantized electromagnetic field in a cavity

Starting from this paper, the eigenmode expansion of the electromagnetic field in a cavity is, $$\mathbf{E}(\mathbf{r},t) = -\sum_l p_l(t)\mathbf{E}_l(\mathbf{r}),$$ $$\mathbf{H}(\mathbf{r},t) = \...
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Master Equation Second Order Approximation

I have a problem deriving the master equation using projection operator technique. If we are given the master equation which reads: $$ \dot{\rho}= -\frac{i}{\hbar}[H_S+H_B+H_I,\rho]+\mathcal{D}\rho $$ ...
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2answers
83 views

What does it mean for $P$ functions to be “more singular than a delta”?

Consider the Glauber-Sudarshan $P$ representation of a state $\rho$, which is the function $\mathbb C\ni\alpha\mapsto P_\rho(\alpha)\in\mathbb R$ such that $$\rho = \int d^2\alpha \, P_\rho(\alpha) |\...
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1answer
48 views

Dipole moment in the Optical Interaction Hamiltonian [duplicate]

I've got a simple and fundamental question regarding the atom-light interaction Hamiltonian: How do we handle the dipole moment term in this expression? The atom-light interaction Hamiltonian, $H_{AL}$...
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Relationship between noise spectral density and quantum absorption/emission: I don't understand the derivation

In this paper, on page 57 he performs a calculation that I don't understand. Maybe there is an implicit physical assumption behind so this is why I am asking it here. The context (not necessary to ...
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25 views

Propagating fields: showing that $\hbar \omega_0 \langle b_{in}^{\dagger} b_{in} \rangle$ is the power

Let me consider a voltage propagating in a waveguide of impedance $Z_0$. It can be shown that the right movers verify, once quantized: $$V_{\rightarrow}(t-x/c)=-i \sqrt{\frac{\hbar Z_0}{4 \pi}}\int_0^{...
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Sketching dynamics of Bloch vector for ground state with dynamics induced by Hamiltonian

How can I sketch a Bloch vector for a system that is in the ground state |g> that is induced by Hamiltonian $ H_x = \frac{ω_x}{2}σ_z$? Is there a general method that I can follow for drawing Bloch ...
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Is anti-bunched light necessarily sub-Poissonian?

It is well-known that sub-Poissonian photon statistics and light anti-bunching normally occur together, since both effects may be considered as a manifestation of photon streams being 'regular enough'....
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59 views

Phase transition in Dicke model

I have been reading about phase transition in Dicke model (Dimer). I have two conceptual questions How do steady state solutions gives us the critical point of phase transition? I understand the math,...
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1:1 Beam-splitter and the Hong-Ou-Mandel effect

We can write the state of two photons in different modes: $$\tag{1} \hat{\alpha}^{\dagger} \hat{b}^{\dagger}|0,0\rangle_{a b}=|1,1\rangle_{a b} $$ According to the Wiki page on the Hong-Ou-Mandel ...
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Intensity uncertainty, $\Delta \bar{I}(t) \approx \frac{1}{2}N \varepsilon_{0} c E_{0}^{2}$, of collisionally broadened source

According to my professor's notes, the intensity uncertainty of a collisionally broadened photon source is: $$\Delta \bar{I}(t) \approx \frac{1}{2}N \varepsilon_{0} c E_{0}^{2}$$ with N being the ...
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1answer
119 views

Understanding derivation of Wigner function for the Harmonic oscillator

In the document https://www.hep.anl.gov/czachos/aaa.pdf, they derive the Wigner functions, $f_n$ for the harmonic oscillator. However, I have some problems understanding some of the steps. On page 37 ...
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Why can't gases produce second harmonic generation (ie, why is $\chi^{(2)}$ always zero)?

To quote wikipedia on second-harmonic generation: Since media with inversion symmetry are forbidden from generating second-harmonic light via the leading-order electric dipole contribution (unlike ...
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Can EM wave “remember” a collision with another EM wave?

I’ve learned that when two EM waves pass each other they simply interfere at the region they cross but (before or) after that they continue their path as if nothing had happen. I know there must be ...
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46 views

Proof of relation with coherent quantum states

According to a Wikipedia article (https://en.wikipedia.org/wiki/Coherent_state), The quantum state of the harmonic oscillator that minimizes the uncertainty relation with uncertainty equally ...
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98 views

Input-output formalism of quantum optic for driven superconducting qubit in a waveguide

My question is about the input output formalism. In the original paper, the authors, Gardiner & Collet, describe the interaction of a system with a continuum of modes via the Hamiltonian: $$H=H_S+\...
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1answer
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About two photon interference in nanophotonics

Within the standard model, photons are point particles, i.e., with no spatial distribution. On the other hand, classical electromagnetic modes have field distributions. Suppose there are two different ...
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Source for “nice” properties for bosonic and fermionic operators

I am looking for a book, or a PDF in which all the "nice" properties about creation and annihilation operators would be written. One example would be the general expression of $[a^n,a^{\...
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What is the length of a photon?

Some questions that look kind of similar have been asked before, and I find the answers quite confusing. I intend to ask this question in a way that clearly shows what I'm asking. Imagine the ...
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Quantization of electromagnetic field: from free-space to media

When studying the quantization of the electromagnetic field, one seems to always derive everything for free space (no charges/currents). This involves solving Maxwell's equations to find modes (in ...
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Lie Superoperator Algebra Commutation relations

I am trying to derive commutation relation of Lindblad Superoperator relations. They are defined as: $$\cdot a^{\dagger}a=\mathcal{L}$$ $$a^{\dagger}a\cdot =\mathcal{R}$$ $$a\cdot a^{\dagger}=\mathcal{...
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47 views

Glauber Surdarshan $P$ Representation Normalizaion

I am studying Scully and Zubiary's quantum optics book currently, and I ran across their definition of the P representation as: $$P(\alpha,\alpha^*) = Tr[\rho \delta(\alpha^* - a^\dagger) \delta(\...
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Intuition behind Huygens-Fresnel formula

I'm currently studying Optics, and I stumbled upon another alternative way in which to derive the Intensity Distribution of light through a slit. My question is, why does the formula work. $U(r_{0}) \...
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2answers
56 views

Is it possible to laser cool without using spatially-varying magnetic fields and above zero degrees?

As the title says, is it possible to laser cool without generating a weak quadrupolar magnetic field? Also, if I wasn't trying to achieve extremely low temperatures is it possible to use laser cooling ...
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What does a complex electric field covariance mean?

Assume that one is working with a zero mean state $|\psi\rangle$. The quantum covariance is given by: $$\text{Cov}(X,Y) = \frac{1}{2}\langle\{A,B\}\rangle-\langle A \rangle\langle B \rangle=\frac{1}{...

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