**ICE1 2014
**Workshop “Información Cuántca en España-1” - Zaragoza,
2014

**Entanglement
of atomic spins beyond simple spin squeezing**

**Robert
Sewell**

*Instituto
de Ciencias Fotónicas*

I describe our recent work in generating exotic entangled states a sample of laser-cooled atomic spins. We use quantum non-demolition (QND) measurement techniques [1] to prepare entangled spin states. In the simplest case, we measure a single spin component and generate spin-squeezing in a sample of highly polarised atoms - a useful resource for quantum-enhanced atomic magnetometry [2]. More recently, we have developed techniques for squeezing all three spin components of an unpolarised sample of atoms. This generates a highly entangled macroscopic spin singlet (MSS) [3,4], analogous to the ground state of many fundamental spin models in condensed matter physics. The state we generate is SU(2) invariant, so it is directly useful for background-free measurement of magnetic field gradients, and may be useful for quantum information tasks such as storing information in a decoherence free subspace. Combining this with quantum feedback control [5] should allow us to deterministically prepare a MSS. In the outlook I discuss prospects for using these techniques for quantum state engineering of quantum lattice gases [6].

[1]
Nat. Photon. 7, 517 (2013).

[2] PRL 109, 253605 (2012).

[3] NJP
12, 053007 (2010).

[4] arXiv:1403.1964 [quant-ph].

[5] Phys.
Rev. Lett., 111,103601 (2013).

[6] PRA 87, 021601 (2013).