Questions tagged [coherent-states]
The specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It obeys the minimal uncertainty relation in Heisenberg's uncertainty relationship.
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What is the state vector of a displaced (single-mode) squeezed vacuum state in the quadrature basis?
I've been hunting through the quantum optics literature for the displaced squeezed state written in the $q$-quadrature basis ($p$-quad would be fine too, since it's just a Fourier transform), but it ...
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Phase distribution of coherent states
I am studying the phase distribution for coherent states, as is defined in quantum optics. (See, for example, Introductory Quantum Optics by Gerry and Knight, pages 46–48).
In this situation, we seek ...
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Proof of coherent state displacement operator solution
In $3D$ space I have two $2\times2$ non-Hermitian matrix operators, $A$ and $A^\dagger$, of the form:
$$A=\begin{pmatrix}
A_{11}(x_j,\partial_j) & A_{12}(x_j,\partial_j)\\
A_{21}(x_j,\partial_j) &...
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Non-classicality of coherent state and squeezed states
Recently I have started studying about the coherent state and squeezed states of light. But I have a question about why do we call these states non classical? What are the things that deny their ...
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Is there any way to write eigenstates of infinite square well in terms of eigenstates of harmonic oscillator?
I wanted to find Husimi Q function using expression $Q= \langle \alpha|\rho|\alpha \rangle$, where $|\alpha \rangle $ is coherent states of harmonic oscillator. I want to consider system $\rho=|u_n\...
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Generalizing Harmonic oscillator to relativistic case
How can we generalize harmonic oscillator to relativistic case ?
One way (see here, here, and here) is simply to write a relativistic Lagrangian/Hamiltonian with a quadratic potential. Such an ...
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Finding an operator in terms of creation and annihilation operators that satisfy some conditions
I have a problem where I'm looking to find the following Hermitian operator $\hat{A}$ written in terms of the operators $\hat{a}^{\dagger}\hat{a}$, $\hat{a}^2$, $\hat{a}^{\dagger 2}$, $\hat{a}$, $\hat{...
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$U(1)$ symmetry transformations in second quantization confusion
I'm reading Chapter 18 (BEC and Superfluidity) of Girvin and Yang and ran into some confusion.
Let $|\alpha\rangle = e^{-|\alpha|^2}e^{\alpha b^†_0}|0\rangle $, where $\alpha$ is just a complex ...
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Large alpha coherent state almost eigenstate of creation operator?
I’m surveying the relation between quantum and classical mechanics. My interest is how a quantum coherent state approaches a classical state when the wave becomes bigger.
Regarding this, I have a ...
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Coherent States and Temperature for Scalar QFT with Source
This is a follow-up question on a question I previously asked, namely Coherent states and thermal properties. The authors of the article I am referring to in the previous question (Thermodynamics of ...
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Coherent states and thermal properties
I am reading a paper called Thermodynamics of Coherent States and Black Hole Entropy, written by Bashkirov and Sukhanov. If I understand correctly, they define a coherent state by the equation
$$a|d\...
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What defines "minimal coherence" as a condition for the emergence of stationary interference in a chaotic wave field?
Consider the following observations:
A superposition of two electromagnetic waves with different frequencies will never produce visible interference patterns. Such waveforms will produce ...
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Advantage of coherent path integral
I think(?) I am quite familiar with path integral over phase space, but not familiar with the coherent state path integral. What is the advantage of this coherent path integral besides the usual path ...
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Time evolution of a coherent state under displaced harmonic oscillator [closed]
Suppose we have a forced harmonic oscillator system with Hamiltonian:
$$H = \frac{P^2}{2m} + \frac{1}{2}m\omega^2 X^2 - FX = \frac{P^2}{2m} + \frac{1}{2}m\omega^2(X-\frac{F}{m\omega^2})^2 + \text{...
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Wigner function of a composite system consisting of two coherent states (Qutip weird result)
I have observed that when computing the Wigner function of a composite system consisting of two-coherent-state states using Qutip, the output is a negative Wigner function, which is unexpected as the ...
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Homodyne Detection of Photon Number States
I'm currently trying to understand why you can detect the signal of single photons with homodyne detection. I found that the difference current $i_{34}$ is given by
$$i_{34}\sim -2 ⟨\Psi|_1⟨\alpha|_2\...
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Evolution of Quantum Harmonic Oscillator into coherent state
Why does a quantum harmonic oscillator that is driven by an electromagnetic wave in cosine form with its frequency equal to the resonance frequency of the oscillator evolve from its groundstate into a ...
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Spin coherent state representation
In Fradkin book "Field Theories of condensed matter physics" he present the spin coherent state as follows: $|\vec{n} \rangle=exp(i \theta(\vec{n_0} \times \vec{n}) \cdot \vec{S})|S,S \...
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Coherent state basis
I'm learning about coherent states in a more in depth lesson the the quantum harmonic oscillator. Coherent states are eigenstates of the lowering operator. In my head this is just saying: since any ...
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Calculating free energy from coherent state path integral
Edit: It turns out that problem encountered in this question is not limited to BdG Hamiltonians.
I am having trouble in using the coherent state path integral approach to calculate the free energy. ...
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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 ...
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Driven Quantum Harmonic Oscillator
Consider the Hamiltonian
$$
H = \frac{p^2}{2} + \frac{ x^2}{2} - F(t) x.
$$
This is essentially a time dependent shifted harmonic oscillator, which can be represented as
$$
H' = \frac{p^2}{2} + \frac{...
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Is the wave function of a coherent state just a Gaussian density? [closed]
The formula giving the wavefunction of a coherent state looks pretty complicated, but am I correct in saying it is just a Gaussian distribution function? i.e.
$$\psi(x) = \frac{1}{\sigma \sqrt{2\pi} } ...
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Non-uniqueness of Glauber-Sudarshan $P$-function
For a state $\rho$ acting on single bosonic mode with coherent states $|\alpha\rangle$, one can always define a $P$-function to furnish a diagonal representation of the state in the coherent-state ...
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Quasi bell state relation for the two coherent states
I was reading out a research paper about two coherent states whose relative phase is equals to phase shift between them which was 3π/2.
Equation of quasi bell state for this state is added as a ...
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Trouble proving Wigner function identity [closed]
I am trying to prove $$\int d^2 \alpha W(\alpha)=1$$ where $W(\alpha)$ represents the Wigner funcion. However, I have trouble solving it. I tried solving it as follows but I think I have done some ...
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Application of Schur's lemma to proving the completeness of coherent states
I am studying many-body path integral through Altland & Simons's textbook called "Condensed Matter Field Theory," and the book states the completeness of the coherent states as below:
$$\...
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Overcompleteness of coherent states
I am trying to show that the basis of coherent states,
$$ |\phi\rangle =e^{-\sum_{\alpha'}\phi_{\alpha'}a^\dagger_{\alpha'}}|0\rangle, \quad\text{ where }\quad a_\alpha|\phi\rangle=\phi_\alpha|\phi\...
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Could one call eigenstates of $ \hat{a} = \hat{x} + i\hat{p}$ coherent states for other potentials than the harmonic oscillator?
Let's say I look at the quantum system of a particle in one dimension, subject to any other potential than the one of the harmonic oscillator, and I define $\hat{a}$ as stated above. I would find the ...
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Fermionic coherent state in Fock representation
The notes I follow define a Fermionic coherent state $|c\rangle$ as
\begin{equation}
\hat{c}|c\rangle=c|c\rangle
\end{equation}
where $\hat{c}$ is the Fermionic annihilation operator and $c$ is a ...
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SPDC One Arm vs Very Weak Coherent state
I know that SPDC(Spontaneous Parametric Down Conversion) is a method to generate heralded single photon source.
So If we do homodyne tomography of single photon fock state, another arm of SPDC is used ...
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Quantum Harmonic Oscillator density matrix in coherent states base [closed]
I was trying to calculate matrix elements of the density operator for a 1D QHO (with Hamiltonian $\mathcal H = \hbar\omega a^\dagger a $) in the base of coherent states $\{\vert\alpha\rangle\}$ and ...
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Normal ordering of an exponential [duplicate]
I would like to recalculate Eq.(2.4) in PRA, 31,4,(1985), which expresses the exponential of operators as a normal ordering form. This equation reads
\begin{equation}
D=e^{\alpha K_{+} - \alpha^{*} K_{...
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Decomposing a coherent state? [closed]
Can you decompose a coherent state $|\alpha\rangle$ into $p|p\rangle+q|q\rangle$, where $|p\rangle$ and $|q\rangle$ are eigenstates of the $P$ and $Q$ operators respectively with eigenvalues p and q?
...
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Confusion with two-mode bra-ket notation [closed]
Let us consider some abstract two-mode bosonic model with a conserved total number of quanta (i.e. eigenvalue $N$ of the operator $\hat{N} = a^\dagger a + b^\dagger b$ remains constant with ...
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Heisenberg picture and time dependence of a wave function
I'll try to give you a quick background of what I'm doing, then the question will come: I'm studying an EFT where a coherent state of a scalar field $\Phi$ reproduces a static potential $V(r)$ through ...
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How is continuous variable quantum key distribution safe against tapping some photons?
As far as I understand, CV-QKD (also here) uses coherent states to send a key, that is encoded in amplitude and phase quadratures. When someone tries to eavesdrop, this will introduce an error and ...
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Equation of motion for space and momentum of a $\textbf{coherent state}$ [closed]
Given the coherent states
$$| \alpha \rangle\, e^{\textstyle -|\alpha|^2/2}\,\sum_{n = 0}^\infty \dfrac{\alpha^n}{\sqrt{n!}}\,|n\rangle$$
that satisfy the eigenvalue-equation: $A|\alpha\rangle=\alpha\,...
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Master equation with a coherent bath
When we consider an oscillator $a$ acting with a bath of oscillators $b_i$ with the interaction Hamiltonian reads
$$H_{int}=\sum_{i}g_ia b_i^{\dagger}+g_i^*a^{\dagger}b_i,$$ with the free Hamiltonian:
...
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Fock Space and Coherent state
Can a coherent photon state also belong to the Fock space? If yes, under what conditions? For example I read that
$$\exp\bigg\{-\frac{1}{2}\sum_i|\alpha_i|^2\bigg\}\exp\bigg\{-\sum_i\alpha_ia_i^{\...
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Is it possible to define the operator similar to the Displacement $|\alpha\rangle = \hat D|0\rangle$ but from the coherent state to the Fock space?
I am looking for the theory of electro-optical modulator with Fock states as an input and I know how the modulator acts on the coherent states. Knowing the connection between coherent and Fock states. ...
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Number and phase operators in superconductors
It is stated in many texts that the number operator $N$ which counts the number of Cooper pairs and the phase operator $\phi$ which counts the superconducting order parameter's phase $\text{Arg}(\...
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Number-Phase uncertainty relation
I was trying to understand the Number-Phase uncertainty mainly following "A. Duncan, The Conceptual Framework of QFT", pages 223-233 and I got stuck into the definition of the operator
$$E = ...
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If I split coherent state light in half (by a beam splitter) are the 2 output intensities correlated?
From what I have been told and understand, if I use a simple beamsplitter to split coherent state light, I will obtain 2 coherent states as a result.
Are the intensities of these two output states ...
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References on coherent states
I've begun my Master degree final work and I was asked to study in details coherent states. The goal is to apply them to a QFT formalism for a scalar potential effectively decribing the weak field ...
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What is the best way to describe a classical field in quantum field theory (coherent state)?
In quantum field theory, we have the following expansion on a scalar field (I follow the convention of Schwarz's book)
$$\phi(\vec{x},t)=\int d^3 p \frac{a_p exp(-ip_\mu x^\mu)+a_p^{\dagger}exp(ip_\mu ...
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What is the meaning of the time evolution of a product of coherent states of the QHO?
I am trying to analyze the dynamics of a coupled quantum harmonic oscillator (cQHO) system. The Hamiltonian of the system is given by:
\begin{equation}
\hat{H}_{Coupled}=\frac{1}{2m}\sum_{j}\hat{p}_{j}...
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What does "Coherent" mean in coherent spectroscopy?
I find this on wiki: "Coherent or resonance spectroscopy are techniques where the radiative energy couples two quantum states of the material in a coherent interaction that is sustained by the ...
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Off-diagonal elements of density matrix in three-level system
given is a three-level system, let's say an atom with three possible states 1 being the lowest and 3 the highest ($E_1<E_2<E_3$), where
$$
\Psi(t)= C_1(t)|1\rangle+C_2(t)|2\rangle+C_3(t)|3\...
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Difference between Wigner function in coherent space and coordinate space
Such a density operator $\hat{\rho}$ match with a Wigner function in coherent space: $$W(\alpha,\alpha^{*})$$
$\alpha$ and $\alpha^{*}$ are $C-number$ ( $\alpha^{*}$ denotes complex conjugate of $\...
