Questions tagged [squeezed-states]
Light with reduced quantum uncertainty: its electric field strength Ԑ for some phases ϑ has a quantum uncertainty smaller than that of a coherent state. Do not use for plain coherent states.
16
questions
2
votes
0
answers
37
views
Generalized squeezing operators: Are analytic vectors required for unitarity?
The paper Impossibility of naively generalizing squeezed coherent states
proves that the generalized squeezing operators
$$U_k(z)=\exp(z a^{\dagger k}-z^* a^k)$$ have some of their matrix elements ...
- 2,584
1
vote
0
answers
133
views
Wigner Function of Squeezed Vacuum state
I am trying to figure out how to derive the wigner function of the squeezed vacuum state,
\begin{align}
W(\alpha,\alpha^*)& =(2/{\pi})\times{e^{-2|\alpha'|^{2}}}\\
\alpha'& =\alpha \cosh{r}-\...
2
votes
1
answer
74
views
Squeezed quantum states of light
I am a beginner in quantum optics and started from reading the Fox's book. I got to Ch.7, where there is a discussion about the amplitude-squeezed states. I am really puzzled by the effect of phase ...
- 1,095
0
votes
0
answers
43
views
Finding expectation value of $J^2_\phi(t)$ to calculate the spin squeezing parameter for the One Axis Twisting (OAT) model hamiltonian
I am trying to calculate the spin squeezing parameter $\zeta = \frac{\Delta \hat J_\phi(t)_{min}}{\sqrt{J/2}}$ from this paper.
In order to calculate $\zeta$, the expectation value of $J^2_\phi(t)$ ...
- 21
0
votes
0
answers
33
views
Derivative of a multimode squeezed vacuum state
Let us suppose we have a multimode squeezed vacuum state of the form
\begin{equation}
|\psi\rangle = \exp[A]|0\rangle= \exp \big[\sum_{ij}G_{ij}(t) (a_i a_j -a_i^\dagger a_j^\dagger)\big]
|0\rangle\...
- 447
0
votes
2
answers
53
views
How to resolve the action of an operator in a power?
I'm deriving the action of the squeezing operator on a non-vacuum Fock state and I have almost finished but can't work out how to apply an operator that is stuck in the power of a constant, not an ...
- 37
2
votes
1
answer
64
views
Normalization of squeezed vacuum for QFT in the black hole background (Hawking radiation)
In the context of BH evaporation, one can represent an initial vacuum as the final state containing particles, following Polchcinski (2016, page 9)
$$|0\rangle_{a}=\mathcal{N} \exp \left(\int_{0}^{\...
- 319
1
vote
0
answers
69
views
Theoretical description of a two-mode squeezed state with continuous modes
Given two distinguishable modes $a$ and $b$ with $[a,a^\dagger]=1$ and $[b,b^\dagger]=1$ and $[a,b^\dagger]=0$, the two-mode squeezed vacuum state is given by
\begin{equation}
\exp (\zeta^* a b - \...
- 447
0
votes
0
answers
92
views
two mode squeezed state in coherent state basis
It is known that, in the Fock basis, the two-mode squeezed state takes the form
$$
\vert TMSS \rangle = \sum_n \dfrac{(-e^{i\phi} \tanh(r))^n}{\cosh(r)} \vert n,n \rangle \;.
$$
An other possibility ...
- 815
2
votes
1
answer
165
views
Interpreting Hamiltonian of single-mode squeezing
Hamiltonian represents energy. I can understand this when considering about harmonic oscillator, whose Hamiltonian is expressed as:
$$ \hat{H} = \frac{1}{2m}\hat{p}^2 + \frac{m\omega^2}{2}\hat{q}^2$$
...
- 21
3
votes
1
answer
75
views
Can I create squeezing with a $P^2$ interaction?
One approach to squeeze light is through the one-mode squeezing operator, which can be written as $e^{-i H t}$ with $H \sim (a^2 - (a^\dagger)^2)$. My question is, can I create squeezing with $H \sim ...
- 815
2
votes
0
answers
106
views
Photon number basis representation of a displaced single-mode squeezed thermal state
I am looking for a relatively clean expression for matrix elements for states of the form $$\rho_{\alpha,r,\bar{n}} = \hat{D}(\alpha)\hat{S}(r)\rho_{th}(\bar{n})\hat{S}^\dagger(r)\hat{D}^\dagger(\...
- 21
0
votes
1
answer
132
views
Normalising squeezed position eigenket?
I want to find the effect of squeezing operator $S(r) = \exp \big[r(\hat{a}^2 - \hat{a}^{{\dagger}^2})\big]$
on $|q\rangle$ i.e. $S(r)|q\rangle$.
I proceed as follows:
$$S(r)\hat{q}|q\rangle = S(r)...
- 179
2
votes
1
answer
1k
views
Derive explicit expression of squeezed vacuum state in the Fock basis
I'm learning quantum optics, and I'm starting to manage boson algebra.
In particular, as a pure exercise, I would like to express a squeezed vacuum state in the Fock basis, which, according to ...
- 410
6
votes
1
answer
1k
views
Find the Bogoliubov transformation $b=SaS^\dagger$ induced by the squeezed operator
A definition a bogoliubov transformation is defined as $$b=ua+va^\dagger~,~ b^\dagger=u^*a^\dagger+v^*a$$
But, using squeeze operator $$S=\exp{\left[\frac{1}{2}(z (a^\dagger)^2-z^*a^2)\right]}$$ we ...
- 1,142
2
votes
2
answers
559
views
Inverting squeezing and displacement operators: how do I turn $D(\alpha)S(\xi)$ into $S(\xi')D(\alpha')$?
This question is about inverting the product of squeezing operator and a displacement operator in the following way:
I have $D(\alpha)S(\xi)$ and I'd like to turn it into $S(\xi')D(\alpha')$,
where
$$...
- 133