Spin squeezing is a quantum process that decreases the variance of one of the angular momentum components in an ensemble of particles with a spin.
[1] Such states have been proposed for quantum metrology, to allow a better precision for estimating a rotation angle than classical interferometers.
[2] However a wide body of work contradicts this analysis.
[3][4][5] In particular, these works show that the estimation precision obtainable for any quantum state
can be expressed solely in terms of the state response to the signal.
As squeezing does not increase the state response to the signal, it cannot fundamentally improve the measurement precision.
Spin squeezed states for an ensemble of spins have been defined analogously to squeezed states of a bosonic mode.
are the collective angular momentum components defined as
are the single particle angular momentum components.
-component is smaller than the square root of the right-hand side of the inequality above
A different definition was based on using states with a reduced spin-variance for metrology.
It has also been shown that a higher and higher level of multipartite entanglement is needed to achieve a larger and larger degree of spin squeezing.
[9] Experiments have been carried out with cold or even room temperature atomic ensembles.
Hence, in order to entangle them, they make them interact with light which is then measured.
A 20 dB (100 times) spin squeezing has been obtained in such a system.
[14] Cold gas experiments have also been carried out with Bose-Einstein Condensates (BEC).
[15][16][17] In this case, the spin squeezing is due to the interaction between the atoms.
Most experiments have been carried out using only two internal states of the particles, hence, effectively with spin-
[18][19] Nuclear-electron spin squeezing within the atoms, rather than interatomic spin squeezing, has also been created in room temperature gases.
[20] Experiments with atomic ensembles are usually implemented in free-space with Gaussian laser beams.
To enhance the spin squeezing effect towards generating non-Gaussian states,[21] which are metrologically useful, the free-space apparatuses are not enough.
Cavities and nanophotonic waveguides have been used to enhance the squeezing effect with less atoms.
[22] For the waveguide systems, the atom-light coupling and the squeezing effect can be enhanced using the evanescent field near to the waveguides, and the type of atom-light interaction can be controlled by choosing a proper polarization state of the guided input light, the internal state subspace of the atoms and the geometry of the trapping shape.
By optimizing the optical depth or cooperativity through controlling the geometric factors mentioned above, the Faraday protocol demonstrates that, to enhance the squeezing effect, one needs to find a geometry that generates weaker local electric field at the atom positions.
[24] This is counterintuitive, because usually to enhance atom-light coupling, a strong local field is required.
But it opens the door to perform very precise measurement with little disruptions to the quantum system, which cannot be simultaneously satisfied with a strong field.
In entanglement theory, generalized spin squeezing also refers to any criterion that is given with the first and second moments of angular momentum coordinates, and detects entanglement in a quantum state.
[9][27] Some of the generalized spin-squeezing entanglement criteria have also a relation to quantum metrological tasks.
For instance, planar squeezed states can be used to measure an unknown rotation angle optimally.