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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When is a state entangled?
I have read from What's the difference between an entangled state, a superposed state and a cat state? that an entangled state is one that cannot be expressed as product state. Suppose we have the ...
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"Deriving" Poisson bracket from commutator
This Q/A shows that deriving P.B.s from commutators is subtle. Without going into deep deformation quantization stuff, Yaffe manages to show that $$\lim_{\hbar \to 0}\frac{i}{\hbar}[A,B](p,q)=\{a(p,q),...
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Free evolution of coherent states
Is there a closed formula to express the time evolution of coherent states in absence of the potential term (only kinetic energy)?
The coherent state $|\alpha \rangle$ is defined by
$$\hat a|\alpha \...
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Coherent State as Eigenvector for some Observable?
A coherent state $|\alpha\rangle$ is an eingenvector of the operator $\hat{a}$, but this is not an observable (i.e., not an hermitian operator). But every vector is eigenvector of a complete set of ...
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Prove that integrating a displacement operator with a Gaussian gives $\int d^2\gamma e^{-|\gamma|^2/2}D(\gamma)=\pi|0⟩\!⟨0|$
I'm looking for "nice" ways to prove the following identity for displacement operators:
$$\int d^2\gamma e^{-|\gamma|^2/2}D(\gamma)=\pi|0⟩\!⟨0|,$$
with $|0\rangle$ the vacuum state and $D(\...
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Majorana Boson Coherent States
Consider $a$ be a bosonic operator, and we define $\Phi = a+a^{\dagger}$ and it is clear that $\Phi^{\dagger}=\Phi$ that implies "Majorana Boson". Now, i want to find the coherent states for ...
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Integration over the complex plane and the completeness relation of the coherent states [duplicate]
I am studying some of the properties of coherent states using the book "Introductory Quantum Optics" by C. Gerry & L. Knight. (C. Gerry & L. Knight, Chapter 3, Section 5) And when I ...
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Grassmann variables and orthogonality of coherent fermionic states
Let a coherent fermionic state
$$
\left|\phi\right> := \left|0\right> + \left|1\right> \phi,\tag{0}
$$
where $\phi$ is a Grassmann number (i.e. it anticommutes with other Grassmann numbers). ...
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Question about coherent population trapping
In coherent population trapping, if we denote the ground states in a $\Lambda$-like system as $|0\rangle$ and $|1 \rangle$ and the excited state $|2 \rangle$, there is a linear combination $|d \...
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How Does Laser Light Maintain Coherence Amid Photon-Atom Entanglement?
Laser light is known to produce "coherent state light," which consists of a superposition of different photon numbers. However, wouldn't the entanglement between the atoms and the light ...
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Coherent creation operator: unitary or not?
In Quantum Mechanics, for coherent states $|z\rangle$ it can be prooved that if $|0\rangle$ is the vacuum state for an harmonic oscillator, therefore:
\begin{equation}
|z\rangle=e^{za^{\dagger}-z^*a}|...
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Coherent spin state (CSS) for an electron with spin
Standard definition for the spin coherent state (CSS) for the system of $N$ identical particles reads
$$
|\theta, \phi\rangle = \bigotimes\limits_{k=1}^{N} \left[ \cos\frac{\theta}{2} |0\rangle_k + e^{...
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Paradox when expressing an operator in terms of creation/annihilation operators [duplicate]
I'm trying to expand an arbitrary operator using creation/annihilation operators following this post, where $|m\rangle \langle n|$ is expressed as
$$
|n\rangle \langle m|~=~\sum_{k\in\mathbb{N}_0} c^{...
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Existence of Glauber-Sudardhan $P$-representation of arbitrary given density operator for light field
In all textbooks on quantum optics I can reach (Scully, Leonhardt, Walls, etc), the Glauber-Sudardhan $P$-representation $P(\alpha)$ is introduced in the following two ways:
Fourier transform of $\...
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Operator acting on product of coherent states
My problem
Find $O_\phi|\psi\rangle$, where the state $|\psi\rangle$ is defined on a composite space $\mathcal H_A\otimes \mathcal H_B$ as
$$|\psi\rangle = \left(\bigotimes_{k=1}^N|\alpha_k'\rangle\...
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Identity of bosonic coherent states
I have a short question about the meaning of the identity of the bosonic coherent states.
Before I ask the question I will explain some background.
The eigenstate of the bosonic annihilation operator $...
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Can we treat Gazeau-Klauder coherent states for infinite potential well as a superposition of Fock states?
If we define coherent states of infinite potential well based on Gazeau-Klauder coherent states. Can we use ladder operators and bosonic algebra for them which we use for Glauber coherent states?
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Applying a phase shift to a coherent state vs a phase-space rotation (Mach-Zhender)
I'm having some trouble with the physical implementation of a phase vs rotation in phase-space for a coherent state.
Say I have a laser pulse which yields a coherent state $|\alpha\rangle$, I then put ...
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Prepration of a Gaussian modulated coherent state
In Continuous Variable -Quantum Key Distribution (CVQKD), usually Gaussian modulated coherent states are sent. This means both quadratures of a coherent state are chosen from two normal distribution. ...
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Finding the wavefunction of coherent state in 2D oscillator
Suppose I have a two-dimensional harmonic oscillator, $H= \hbar\omega(a_x^{\dagger}a_x+a_y^{\dagger}a_y)$. We define the operator $b=\frac{1}{\sqrt{2}}(a_x+ia_y)$.
If eigenkets of the hamiltonian are $...
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It seems that expectation value of $H$ on coherent states is independent of time? But why?
Let's say the particle is in the state $| \psi(0) \rangle = \exp(-i\alpha p/\hbar) |0 \rangle$, where $p$ is the momentum operator.
I have to show that $| \psi(0) \rangle$ is a coherent state and to ...
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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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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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