# What Cat States of light have been experimentally produced?

I'm specifically looking for Schrödinger's Cat states involving superpositions of two, or if it's been done more, coherent states, i.e. monomodal states of the form $$|\psi\rangle=a|\alpha\rangle+b|\beta\rangle.$$ What states of this form have been produced in experiment? How even can the weights be? What regions of the $\hat{a}$-eigenvalue $\alpha$ and $\beta$ are accessible? If more than two coherent states can be superposed, how many? What phase-space geometries are possible so far?

I'm also interested in what techniques are currently used to generate these states.

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## 1 Answer

As far as I can tell, despite the recent achievements the experimental toolbox in this field is quite limited. The two main techniques are photon-subtraction from squeezed vaquum and generation from Fock states by conditional homodyne detection.

First technique is based on the fact, that an odd cat state may be expressed as: $$\left(\left|\alpha\right>-\left|-\alpha\right>\right)\propto \alpha\left|1\right>+\frac{\alpha^3}{\sqrt{6}}\left|3\right>+\ldots,$$ which for small $\alpha$ resembles squeezed vacuum state with one photon removed. Experimentally photon subtraction is realized with a low reflectivity beam splitter and single photon detection in the reflected port. Detecting a single photon in this port heralds the preparation of the desired state. This is only applicable for states with small $\alpha$ - so called "Schrödinger kittens". These kittens may be later "breeded" on a beamsplitter to increase $\alpha$.

Second technique uses homodyne detection of $p$ quadrature of a Fock state $\left|n\right>$ splitted on a 50/50 beamsplitter to conditionally prepare cats. A detection of $p\sim0$ heralds the preparation of a cat state with $\alpha=\sqrt{n}$.

The closest to arbitrary superposition preparation is described here. This is not exactly a cat state, but a superposition of a squeezed vacuum and squeezed single-photon states of the form: $$\left|\psi\right>=\cos\theta \hat{S}(r)\left|0\right>+e^{i\varphi}\sin\theta \hat{S}(r)\left|1\right>,$$ with $\hat{S}(r)$ being the squeezing operator. It is probably the most general continious-variable superposition experimentally generated so far.

I have to say that I do not specifically keep track of experiments in this field, that is just those which I heard of. As a good reference on experiemtal techniques I can recommend this review by Lvovsky and Raymer. This paper also contains a lot of references.

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