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.

Filter by
Sorted by
Tagged with
2 votes
0 answers
21 views

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 ...
user avatar
  • 33
1 vote
1 answer
54 views

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\,...
user avatar
  • 313
1 vote
1 answer
87 views

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: ...
user avatar
2 votes
1 answer
95 views

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^{\...
user avatar
  • 857
1 vote
0 answers
36 views

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. ...
user avatar
0 votes
2 answers
60 views

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}(\...
user avatar
0 votes
0 answers
54 views

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 = ...
user avatar
0 votes
0 answers
20 views

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 ...
user avatar
0 votes
0 answers
25 views

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 ...
4 votes
0 answers
58 views

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 ...
user avatar
1 vote
0 answers
66 views

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}...
user avatar
0 votes
0 answers
24 views

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 ...
user avatar
1 vote
0 answers
25 views

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\...
user avatar
0 votes
1 answer
22 views

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 $\...
user avatar
0 votes
2 answers
77 views

Does the number of photons in a displaced coherent state is same as the original coherent state? [closed]

Lets say I receive a quantum state $|\alpha\rangle$ with number of photons $N$ and I displace this state by $\alpha$ $\hat D(\alpha)$ so the resultant state is $|2\alpha\rangle$ with same number of ...
user avatar
0 votes
1 answer
65 views

Why can we arbitrarily set the expectation value of a field operator by representing the field state as a product of coherent states?

In the paper "Unusual Transitions Made Possible by Superoscillations", the author begins by solving for a coherent state \begin{equation}|\alpha\rangle\end{equation} such that \begin{...
user avatar
2 votes
1 answer
73 views

Correspondence between terms in generic path integrals

In field theory, starting with a quantum Hamiltonian with field operator $c$, no matter its nature, one obtains the path integral formulation with partition function $$Z=\int DcDc^* \exp{ -S^1_E[c,c^*...
user avatar
0 votes
1 answer
59 views

Is $SU(2)$ coherent state normalized?

I know Glauber coherent state are normalized such that the inner product of < α|α > =1 where |α > is Glauber coherent state. My question is (is SU(2) COHERENT STATE NORMALIZED)? I MEAN IF |Z&...
user avatar
  • 1
0 votes
1 answer
81 views

How Do I Do This Integral? [closed]

I am trying to derive a boson coherent path integral and one part of the derivation is to evaluate/prove $$ \int d\Psi(\tau) d\Psi^*(\tau) |\Psi(\tau)|^{2n} \exp(-|\Psi(\tau)|^2) = (n!) \pi. $$ This ...
user avatar
3 votes
1 answer
71 views

What does "coherent evolution" of an $N$-body quantum system mean?

In classical physics we know of coherence of waves and in quantum physics we identify coherent states. While those are clearly defined concepts/terms, in literature we regularly encouter also that a $...
user avatar
  • 33
0 votes
1 answer
53 views

Angular momentum coherent states

$\renewcommand\bm[1]{\mathbf{#1}}$ $\renewcommand\h{\hbar}$ $\renewcommand\ket[1]{|#1\rangle}$ $\renewcommand\mean[1]{\langle #1 \rangle}$ $\renewcommand\norm[1]{||#1||}$ Let $\bm{J}$ be an angular ...
user avatar
  • 115
5 votes
2 answers
168 views

Why do coherent states behave semi-classically, but harmonic oscillator states do not?

A coherent state of the quantum harmonic oscillator is defined as an eigenvector $|\alpha\rangle$ of the annihilation operator $\hat a$ with eigenvalue $\alpha$ or as spatial translations of the ...
user avatar
1 vote
2 answers
35 views

Coherent Elastic Neutrino-Nucleus Scattering Energy Transfer

What is the meaning of coherent elastic in "coherent elastic neutrino-nucleus scattering"? What I understand is when a high energy particle such as neutrino interact with the nucleus as a ...
user avatar
0 votes
0 answers
11 views

Spin coherent state for periodic orbit

Usually the spin coherent state $|\theta,\phi\rangle$ represents a localized density centered around a point ($\theta,\phi$) in phase space, which is visible in the Husimi distribution of the ...
user avatar
1 vote
1 answer
72 views

Physical intuition for coherent states look like classical

In my course on quantum mechanics, we have seen that coherent states look classical. Since the expectation value of the electric field is similar as for the classical expression. Furthermore they look ...
user avatar
  • 109
1 vote
1 answer
40 views

If we have a state with 1/4 quadrature fluctuation, can we say it's a coherent state?

We know that the variances of quadrature components for a coherence state satisfies: $\langle(\Delta \hat{X}_{1})^2=\langle(\Delta \hat{X}_{2})^2 = \frac{1}{4}$ However, is its converse proposition ...
user avatar
  • 346
0 votes
1 answer
61 views

Coherent states - scalar product [closed]

$\newcommand\norm[1]{\lVert#1\rVert}$ $\newcommand\ket[1]{|#1\rangle}$ $\newcommand\mean[1]{\langle #1\rangle}$ $\newcommand\braket[2]{\langle #1|#2\rangle}$ $\newcommand\ketbra[2]{|#1\rangle\langle #...
user avatar
  • 115
1 vote
1 answer
62 views

Probability Distribution of a Coherent Harmonic Oscillator

I'm currently reading Quantum Optics by Scully and Zubairy and come across a derivation in which I am stuck as to what to do next. Starting with a general solution to the harmonic oscillator ...
user avatar
0 votes
0 answers
36 views

First quantization Entropy of coherent state

I'm trying to follow the computations of example 5.1 in this paper. To begin with they have a symplectic Hilber space $(\mathcal{K},\tau,\sigma)$, where $(\mathcal{K},\tau)$ is a separable Hilbert ...
user avatar
1 vote
0 answers
63 views

Coherent state path integral for Dirac fermions

I’m trying to derive the fermionic path integral for the Dirac theory using the coherent state path integral, but I’m not able to get around the presence of a $\gamma_0$ making it look different from ...
user avatar
  • 930
2 votes
1 answer
197 views

Time evolution of a coherent state

$\newcommand\norm[1]{\lVert#1\rVert}$ $\newcommand\ket[1]{|#1\rangle}$ I consider an Hamiltonian of the Harmonic Oscillator $\hat{H} = \frac{P^2}{2m}+\frac{1}{2}m\omega^2 X^2$. I proved already if the ...
user avatar
  • 115
2 votes
1 answer
79 views

What is the relationship between "quantum coherence" and "coherent states"?

What is the relationship between Quantum coherence and Coherent States? I (almost) get the concept of Quantum Coherence when i think about it in the framework of density matrices. I also get the ...
user avatar
0 votes
1 answer
28 views

Decompose into a series of Coherent States [duplicate]

I was wondering if there was a method for decomposing a given quantum state into a series of coherent states. I know they form an overcomplete basis so the expression need not be unique but I was ...
user avatar
0 votes
0 answers
114 views

State mixtures at beam splitters

I am currently dealing with beam splitter transformations. As a little exercise, I wanted to calculate what happens if I mix states at a BS with transmission $T$. I derived a "general formula&...
user avatar
  • 387
0 votes
0 answers
58 views

The deriviation of displacement operator in Quantum Optics?

I've been studying coherent state, then I meet some problem. My teacher told me, one can derive displacement operator via complexify the parameter $\alpha$ in this formula: $$|\alpha\rangle=e^{\alpha( ...
user avatar
3 votes
0 answers
203 views

BCS groundstate as eigenstate of the Cooper pair annihilation operator

In section 3.7 of his book Introduction to Superconductivity (2nd Ed.), Tinkham states that [...] we note that S has the eigenvalue $e^{i\varphi}$ in a BCS state in which the the phase of $\Delta$ [.....
user avatar
  • 1,352
1 vote
0 answers
52 views

Questions of fermionic coherent states (page 166 of Atland and Simons)

This is quite a basic question but I just can not find the solution. The question is how do you show equation (2) below. Let me explain the details. From page 166 of condensed matter book by Atland ...
user avatar
2 votes
1 answer
74 views

Coherent state is maximally coherent

I read in a blog "The coherent state is called “coherent state” because all the states |n⟩ in its expansion have a fixed phase relation to each other. As a result, when we write down the density ...
user avatar
  • 123
3 votes
1 answer
132 views

Representing Green function as a coherent state path integral

I am working through the problem "self-consistent T-matrix approximation" in Altland and Simons (second edition) pg 234. One of the steps involves representing the Green function as a ...
user avatar
1 vote
0 answers
25 views

Coherent state and $m$-photon added coherent state

How is the coherent state differ from $m$-photon added coherent state? Because coherent state itself a state which is superposition of photons.
user avatar
  • 123
0 votes
0 answers
16 views

For coherent states, what does it mean to find information entropy. What will be "measure of disorder " or "measure of uncertainity" here?

We define Entropy as measure of uncertainty. We can relate entropy with available states directly of a system dirctly. Higher available states to occupy means high entropy. When we talk about ...
user avatar
  • 733
0 votes
0 answers
45 views

Coherent states and free motion on the circle

Consider the following formal implications: A quantum particle moving on the circle performs periodic motion even in the absence of an external potential. It can therefore be considered as a simple ...
user avatar
  • 3,761
0 votes
1 answer
76 views

Uniqueness of most classical state in quantum mechanics

Due to Heisenberg uncertainty relation $$(\Delta x)(\Delta p) \geq \frac{\hbar}{2}$$ there exist an uncertainty in measurement of displacement and momentum. The state reach minimum uncertainty $$(\...
user avatar
  • 475
2 votes
3 answers
131 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 ...
user avatar
0 votes
0 answers
63 views

Schroedinger cat states of the harmonic oscillator

I've found in an article that it is possible to prepare experimentally the superposition of two coherent (quasi-classical) states to obtain the Schroedinger cat state: $$ \left|\psi_{\pm}(t)\right\...
user avatar
1 vote
2 answers
97 views

Coherent States Path Integral of Harmonic Oscillators

I am studying the notes provided by Ben Simons in this link (http://www.tcm.phy.cam.ac.uk/~bds10/tp3.html). I am currently on Lecture 16 (Applications and Connections). The corresponding textbook is ...
user avatar
-2 votes
1 answer
94 views

Inner product of bosonic coherent states [closed]

In the notation of Altland and Simons, we have bosonic coherent state: $$ |\phi\rangle = \exp \left(\sum_i \phi_i a_i^\dagger\right) |0\rangle. $$ On page 159, they use $\langle0|\phi\rangle = 1$ ...
user avatar
0 votes
1 answer
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 ...
user avatar
  • 239
1 vote
0 answers
34 views

Is there symmetric form for statistical action?

In quantum statistical theory, for a given Hamiltonian $H$, one can express the partition function as \begin{equation} Z = \text{tr}\, e^{-\beta H} \end{equation} into the coherent path integral ...
user avatar
  • 11
0 votes
0 answers
93 views

How is it possible to find the Wigner function for spin coherent states?

I studied Wigner function distribution for Glauber coherent state and I know that by using this function we can find the probability distribution for particle's position, but How can me find and ...
user avatar
  • 1