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
1answer
45 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 ...
0
votes
0answers
31 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 $J^2_\phi(t)$ ...
0
votes
0answers
30 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\...
0
votes
0answers
40 views
Transform two-mode squeezed state (TMSS) to its covariance matrix
The two-mode squeezed state can be written as:
${\left| \chi \right\rangle _{AB}} = \sqrt {1 - {\chi ^2}} \sum\nolimits_n^\infty {{\chi ^n}} {\left| n \right\rangle _A}{\left| n \right\rangle _B}$
...
0
votes
2answers
43 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 ...
2
votes
1answer
52 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)
$$|0\rangle_{a}=\mathcal{N} \exp \left(\int_{0}^{\...
1
vote
0answers
37 views
Theoretical description of a two-mode squeezed state with continuous modes
Given two distinguishable modes $a$ and $b$ with $[a,a^\dagger]=1$ and $[b,b^\dagger]=1$ and $[a,b^\dagger]=0$, the two-mode squeezed vacuum state is given by
\begin{equation}
\exp (\zeta^* a b - \...
0
votes
0answers
48 views
two mode squeezed state in coherent state basis
It is known that, in the Fock basis, the two-mode squeezed state takes the form
$$
\vert TMSS \rangle = \sum_n \dfrac{(-e^{i\phi} \tanh(r))^n}{\cosh(r)} \vert n,n \rangle \;.
$$
An other possibility ...
2
votes
1answer
67 views
Interpreting Hamiltonian of single-mode squeezing
Hamiltonian represents energy. I can understand this when considering about harmonic oscillator, whose Hamiltonian is expressed as:
$$ \hat{H} = \frac{1}{2m}\hat{p}^2 + \frac{m\omega^2}{2}\hat{q}^2$$
...
0
votes
0answers
44 views
Is this two-mode squeezed vacuum state for a continuum of modes physical?
In the book 'Methods in theoretical quantum optics' the squeezing operator for a continuum of modes is given by
\begin{equation}
S \equiv S [\{ \zeta (\omega)\}] = \exp \bigg[ -\frac{1}{2} \int_0^ {2\...
3
votes
1answer
73 views
Can I create squeezing with a $P^2$ interaction?
One approach to squeeze light is through the one-mode squeezing operator, which can be written as $e^{-i H t}$ with $H \sim (a^2 - (a^\dagger)^2)$. My question is, can I create squeezing with $H \sim ...
2
votes
0answers
58 views
Photon number basis representation of a displaced single-mode squeezed thermal state
I am looking for a relatively clean expression for matrix elements for states of the form $$\rho_{\alpha,r,\bar{n}} = \hat{D}(\alpha)\hat{S}(r)\rho_{th}(\bar{n})\hat{S}^\dagger(r)\hat{D}^\dagger(\...
0
votes
1answer
102 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:
$$S(r)\hat{q}|q\rangle = S(r)...
2
votes
1answer
857 views
Derive explicit expression of squeezed vacuum state in the Fock basis
I'm learning quantum optics, and I'm starting to manage boson algebra.
In particular, as a pure exercise, I would like to express a squeezed vacuum state in the Fock basis, which, according to ...
6
votes
1answer
880 views
Find the Bogoliubov transformation $b=SaS^\dagger$ induced by the squeezed operator
A definition a bogoliubov transformation is defined as $$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]}$$ we ...
2
votes
2answers
414 views
Inverting squeezing and displacement operators: how do I turn $D(\alpha)S(\xi)$ into $S(\xi')D(\alpha')$?
This question is about inverting the product of squeezing operator and a displacement operator in the following way:
I have $D(\alpha)S(\xi)$ and I'd like to turn it into $S(\xi')D(\alpha')$,
where
$$...
