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.
Questions tagged [coherent-states]
251 questions
18
votes
2 answers
What is a coherent state?
In quantum mechanics, what exactly is a coherent state, and how does it differ from other states?
wrongusername
- 1,937
15
votes
2 answers
Countable basis of coherent states used to express coherent states
Let $|\alpha \rangle$ be coherent state in Fock space. According to the paper "Coherent-state representation for the photon density operator" by Cahill (Phys. Rev. 138, B1566 (1965), §VII), every convergent series $\{\alpha_j\}$ on the complex plane…
yasalami
- 487
15
votes
2 answers
How are coherent states in the real world made?
Coherent states are quantum states that are said to act "as classically as possible". You can define coherent states for the harmonic oscillator, or more generally for any collection of harmonic oscillators, such as a free quantum field. It is often…
knzhou
- 107,105
14
votes
3 answers
Is the vacuum state a coherent state?
I'm asking because I got introduced to the state $|0\rangle$ as a fock-state. Nevertheless:
$$
\hat{a} |0\rangle = 0 |0 \rangle
$$
It is an eigenstate of $\hat{a}$ with eigenvalue $0$, and it can be obtained the same way any other coherent states…
Quantumwhisp
- 7,095
13
votes
2 answers
Why use coherent state path integral? What is its motivation or goal?
In almost all textbooks of quantum field theory for high energy, they insert the position and momentum eigenstate to formulate the path integral. While in condensed matter field theory, they insert the coherent state to get the path integral. What's…
346699
- 6,211
12
votes
2 answers
Why is laser light described by a coherent state?
This is a follow-up to this recent answer by Wouter to this related question from 2015, and a comment by Emilio Pisanty underneath.
I have read the papers by Mølmer, Bartlett et al., Wiseman, and parts of van Enk and Fuchs referenced therein. I have…
The Vee
- 1,357
- 8
- 18
10
votes
4 answers
How to compute expectation value $\langle e^{iH}\rangle$ for quadratic Hamiltonians?
I have a rather basic, but actually non-trivial question:
We consider a bosonic system with creation operators $\hat{a}_i^\dagger$ and annihilation operators $\hat{a}_j$ and vacuum state $|0\rangle$ with $\hat{a}_i|0\rangle=0$. We consider a…
LFH
- 760
10
votes
2 answers
What does coherent superposition mean?
There is only one coherent state: $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle
$$
Also, a pure state does not mean a coherent state.
But what does one mean when they talk about a coherent…
Ka Wa Yip
- 1,057
9
votes
1 answer
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. For example, consider a Bogoliubov-de Gennes (BdG)…
Zhengyuan Yue
- 730
9
votes
3 answers
Eigenstates of the creation operator
We know that coherent states $\vert\alpha\rangle$ are eigenvectors of the annihilation operator $\hat{a}$, i.e.
$$
\hat{a} \vert\alpha\rangle = \alpha \vert\alpha\rangle
$$
while the creation operator $\hat{a}^\dagger$ has no eigenvector.
Now, I…
m137
- 1,241
9
votes
1 answer
Equivalence between grassmann fermion states and $SO(2N,\mathbb{R})$ fermion coherent states
I am importing this question from https://www.physicsoverflow.org/39342/equivalence-between-grassmann-fermion-mathbb-fermion-coherent
Cahill and Glauber in the paper 'Density operators for Fermions' construct Fermionic coherent state as the…
8
votes
4 answers
In what sense are spin coherent states "classical"?
Spin coherent states are often introduced as "the most classical states of a finite-dimensional system", or as the analogous of coherent states of light for finite-dimensional systems. See e.g. (Radcliffe 1971) and (Chryssomalakos et al. 2017).
One…
glS
- 15,488
- 5
- 42
- 114
8
votes
4 answers
Derivation of $P$ representation of the thermal density operator
I'm trying to derive the P representation for the thermal state
$$
\rho = \sum_{n=0}^\infty \frac{\mathrm{e}^{-\beta \omega n}}{Z} |n\rangle \langle n |
$$
where $\beta$ is the inverse temperature, $Z$ is the partition function, $\omega$ is the…
oweydd
- 505
8
votes
1 answer
Boundary conditions in holomorphic/coherent state path integral
Consider the holomorphic representation of the path integral (for a single degree of freedom):
$$ U(a^{*}, a, t'', t') = \int e^{\alpha^{*}(t'') \alpha(t'')} \exp\left\{\intop_{t'}^{t''} dt \left( -a^{*} \dot{a} - i h(a, a^{*}) \right) \right\}…
Prof. Legolasov
- 16,527
8
votes
2 answers
Definition of spatial and temporal coherence in QM?
It is often said that lasers are spatially and temporally coherent. Is there a simple definition of spatial and temporal coherence in the language of quantum mechanics? More specifically, can these be stated as constraints/measures on a certain…
zzz
- 2,987