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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How to determine Collapse operator for Lindblad equation for a specific case
The general form of a Lindblad equation has the form
$$\frac{d\rho}{dt}=-i[H,\rho]+\sum\gamma(A{\rho}A^{\dagger}-\frac{1}{2}A^{\dagger}A\rho-\frac{1}{2}\rho{A}^{\dagger}A)$$
How can I find Collapse ...
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Polarization of light and transitions in a Magneto Optical Trap
After reading this question, I realized that I didn't really understand how a MOT works in detail. I was always relying on the simplistic picture given in textbooks which never addresses the actual ...
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Quantum phase transitions in a finite lattice
Sachdev begins his book on Quantum Phase Transitions by asserting that, for a system on a finite lattice, the ground state energy of a Hamiltonian H(g) (where g is some coupling) is a smooth, analytic ...
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Classical limit of coherent state in Jaynes–Cummings model
Im dealing with an exercise on the Jaynes Cummings model in a resonat single mode approximation. The interaction Hamiltonian in rotating wave approximation is
$$H_{int}=g\, \sigma_+\,a\,+g^*\,\sigma_-...
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Equivalence of quantum state diffusion and heterodyne trajectory
According to Breuer-Petruccione, the SDE quantum trajectory evolution for heterodyne detection
$$d\psi=-iH\psi dt-\frac{\gamma}{2}\left(C^\dagger C-\langle C^\dagger \rangle_{\psi} C+\frac{1}{2}\...
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Rationale for definition of input/output operators in quantum Langevin equations
I am going through Gardiner & Zoller's 'Quantum Noise', and following the derivation of the Langevin equations in terms of input/output operators. Let the bath Hamiltonian be:
$$H_B=\hbar\int_{-\...
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Spatial wave-function of a single photon and its measurement
In the last decade there were several papers claiming that they've measured a "transverse quantum state" / "quantum wave-function" / "spatial Wigner function" of a single photon:
Measurement of the ...
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Amplitude of single-mode field in a cavity
I have two contradictory result about the amplitude of single mode field when it is quantized
In C. Gerry and P. Knight's Introductory quantum optics, the amplitude is given by
$$\sqrt{\frac{2\omega^...
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How to understand the failure of Leibniz rule in Lindblad type Heisenberg equation?
Dual to the well-known Lindblad master equation for density matrices, the equation for operators (in the sense of Heisenberg equation) is written as
$$ \frac{d}{dt}\hat{A}=i[H,\; \hat{A}]+\sum_i \...
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Is it possible to prepare cat states of light over different frequencies?
Is it possible to form a superposition state of a single photon in multiple frequencies? As an archetypal example, consider the Schrödinger's-cat state
$$
|\psi\rangle = |1;\omega\rangle + |1;2\omega\...
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Quantization of electrodynamics in a nonlinear dielectric medium
Recently I read this paper https://doi.org/10.1103/PhysRevA.30.1860 by Hillery and Mlodinow about the (canonical) quantization of electrodynamics in nonlinear dielectric media. They assume that the ...
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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 ...
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Interference of single photons emitted from solid state sources
Solid state emitters such as quantum dots are thought of as being amongst the best single photon sources for quantum technology.
There have been impressive demonstrations of >10 photon experiments ...
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The Purcell effect, it's influence on the lifetime and quantum yield (of fluorophores)
So I've been looking into the Purcell effect and how it interacts with fluorophores (fluorescent molecules). The Purcell arises when you have a dipole in a cavity or even just near a dielectric or ...
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Modern axioms of quantum mechanics
Recently I have been learning a lot about what kind of axioms and mathematical formulations there are for non-relativistic quantum mechanics. Unfortunately, I am a little confused, because at first I ...
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Volkov States in Second Quantization
tl;dr: Is it possible to recover the semi-classical Volkov states from the full second quantized electron-photon Hamiltonian in the limit of large photon numbers? What could be an possible technical ...
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Recommended books that describe emission and absorption of light and light/matter interactions
Hello I am a Chemical Engineer that has ventured into the field of optics and I was wondering if there is any recommended book/books to understand the maths and also some answered exercises or ...
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A quantum mechanical description of a polarizing filter
When a single photon with polarization $\mathbf{a}$ arrives at a linear polarizing filter in the direction $\mathbf{p}$, the photon has a probability of $(\mathbf{a}\cdot\mathbf{p})^2$ to pass through ...
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How do I write the Hamiltonian for a 3-level system?
I came across following types of three-level systems like V-system, Λ-system and 2-photon absorption
It seems that their Hamiltonians can be written intuitively by checking out the coupled levels ...
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What happens if obstacles (walls) been put where destructive interference occurs in double slit experiment?
If photon doesn't have probability to be in dark (destructive interference) area, what will be the effect of adding obstacles (walls) in the dark (destructive interference) area for the double slit ...
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How does a broadband dielectric Mirror work?
It is widely known that dielectric mirrors work with several layers of at least two materials which differ in refractive index that are layered, such that partially reflected waves interfere ...
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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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Can the characteristic function $\chi_\rho(\beta)={\rm tr}[\rho D(\beta)]$ be an indicator function?
Given the characteristic function defined as:
$$\chi(\beta)=\text{tr}[\rho D(\beta)],$$
with $D(\alpha)=e^{\alpha a^\dagger-\bar\alpha a}$ the displacement operator. Is it possible that for some $\rho$...
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Unitary evolution of the displacement operator in terms of positions and momenta
Consider a set of $M$ signal modes described by the creation operators $\mathbf a^\dagger = (a_1^\dagger,...,a_M^\dagger)$, and let $\Phi_U$ be the channel defined by the conjugation $\Phi_U(\cdot)=U(\...
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Why in 2-level system can a diagonal Lindblad equation be used to describe decay, when $|0\rangle$ and $|1\rangle$ aren't energy eigenstates anymore?
Citing Wikipedia (https://en.wikipedia.org/wiki/Lindbladian), the Lindblad equation takes the following form:
\begin{align}
{\displaystyle {\dot {\rho }}=-{\frac {\mathrm {i} }{\hbar }}[H,\rho ]+\sum ...
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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
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Proving the uncertainty relation for the quantum covariance matrix
In quantum optics papers we often encounter this version of the Heisenberg uncertainly relation (for an $n$-mode quantum system):
$\sigma + \iota \Omega \ge 0$
Where $\sigma$ is the covariance matrix $...
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Why do we get rings in the Spontaneous Parametric Down conversion (SPDC) process?
In the SPDC process, the phase-matching conditions between the o-rays and/or e-rays have to hold for the down-conversion process to take place. Say we have a non-collinear phase-matching at the plane ...
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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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Continuous Valued POVMs
I'm thinking about the mathematical details of continuous variable QM, namely the infinite $|x\rangle$ and $|p\rangle$ bases. Is it possible (and should we) think of these bases and their measurements ...
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Can we create "asymmetric" EPR pairs in experiments?
Asymmetric here is just for lack of a better word.
What I am looking for are experiments that can create a simple EPR pair but without 50% 50% chance of each state.
As I understand from standard ...
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Derivation of Hamiltonian in non-linear optics
Update 2: one half of the answer to this question can be found here and the other half in the second half of this post.
I asked this question a few hours ago, but decided to re-post it because I think ...
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Coherent state under Kerr evolution
I have a bosonic mode associated to the usual operators $a$, $a^\dagger$. I'm interested in knowing the evolution of a coherent state $\vert \alpha \rangle = e^{\alpha a^\dagger - \alpha^\ast a}\vert ...
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Can we write the Quantum Fidelity between two density operators in terms of Quasi-Probability Distributions: $P$, $Q$ and $W$?
Quantum Fidelity between two density operators, $\hat{\rho}$ and $\hat{\sigma}$, is given by $F(\hat{\rho},\hat{\sigma})=\left(Tr\sqrt{\sqrt{\hat{\rho}}\hat{\sigma}\sqrt{\hat{\rho}}}\right)^2$, where $...
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What is the Bogoliubov transformation matrix for Fermions?
Is there any Bogoliubov transformation matrix for the operator $O=|g\rangle\langle e|$ where $|e\rangle$ and $|g\rangle$ are arbitrary states? I know that, for annihilation and creation operator $a$ ...
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„Linear Algebraic Explanation“ of Decay, Decoherence, Dephasing & Dissipation
In the literature one encounters many different versions/descriptions of general processes like decay, decoherence, dephasing and dissipation. Depending on the area (like condensed matter vs. quantum ...
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Quantum regression theorem/formula for Lindblad dynamics
I have been trying to understand the proof of the quantum regression theorem or formula for a Lindblad evolution.
If $V(t,0)$ is the propagator, $\rho_S(t) = V(t,0)\rho_S(0)$, the formula is:
$\...
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How do we write the state of a continuous-wave laser beam?
Many of us are probably familiar with the notion that the output of a laser is a coherent state $|\alpha\rangle$. But this simplistic description falls short in many respects. For instance, how can I ...
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Second Order Coherence of NOON State
Given the entangled state $\vert NOON \rangle =\frac{1}{\sqrt{2}}(\vert N,0\rangle + \vert 0,N\rangle)$ how can the second order coherence function at time $\tau$ and 0 be calculated?
I know that $g^{...
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Creating an arbitrary state of the quantum simple harmonic oscillator
Suppose $\mathcal{B}=\{|0\rangle, |1\rangle, |2\rangle, ... \}$ is the energy eigen-basis of a quantum simple harmonic oscillator. I want to create the state
\begin{equation}
|\Psi\rangle = c_{0}|0\...
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How do we show that photons generated by a constant electric current are distributed according to a Poisson distribution?
I saw the answer sometimes ago in a book "Quantum Electronics" or similar title. I don't remember the author since I lost the book. The book sets ( I believe so ) a constant electric current $I$ in a ...
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Pockels effect/Kerr effect
In Pockels electro-optic effect, change in Electric field produces change in refractive index/ birefringence. Moreover this effect becomes electric field squared in the case of Kerr effect. If we ...
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Dyson Series Second Order Term Importance vs. Time
Given a time ordered Dyson series expansion of
$$H_I=e^{-\frac{i}{\hbar}\sigma_3t}V_0\sin(\omega t)\sigma_1e^{\frac{i}{\hbar}\sigma_3t}$$
$${\cal T}\exp\left[-\frac{i}{\hbar}\int_0^tH_I(t')dt'\...
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uncertainty deviations for vacuum astronomy
Since i've done this question, i've been trying to improve and make more precise the statements regarding cosmic squeezed states and how different uncertainties affect the vacuum energy, but as it ...
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Resources with treatment of Quantum Optics as an application of Quantum Field Theory?
I am looking for resources which deal with Quantum Optics, with some rigor, as an application of Quantum Field Theory.
PS:I have read Introductory Quantum Optics by Gerry and Knight. So that is my ...
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What does the superposition of fields mean in the context of the convolution of two Glauber-Sudarshan $P$-representations?
In his 1963 paper, in which he introduces his formulation of the Glauber-Sudarshan $P$-representation (https://doi.org/10.1103/PhysRev.131.2766), Glauber refers to the convolution of the $P$-...
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Relation between spontaneous emission and natural linewidth
I have a question regarding the relation between the spontaneous emission and the corresponding natural linewidth of a two-level system. The way that I have seen people deriving the lineshape from the ...
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Trying to learn input-output formalism: 2-photon Fock state entering a cavity
I really don't understand the input-output formalism. I've gone through the 1985 paper, and I get completely lost when the following formula is written:
$$b_{out}(t)-b_{in}(t) = \sqrt{\gamma} c(t)$$
...
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What happens when two photon of same polarization enters in the polarizing beam-splitter(PBS)?
It is well established that if two photons of the same polarization, identical wavelength, phase, and spatial distribution of wavefunction enter a non-polarizing beam splitter (N-PBS), they exhibit ...
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Why does the spontaneous emission rate scale with energy?
Good afternoon,
the standard description of spontaneous emission in quantum optics is - to my knowledge - via coupling of an excited atom to vacuum modes of the em-field, which are still occupied at $...
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