Quasi-adiabatic preparation of squeezed antiferromagnetic states

Abstract

Cavity-mediated interactions have recently been proposed as a route toward strongly correlated many-body regimes in atomic ensembles. The underlying mechanism is that an antiferromagnetic cavity-mediated interaction penalises total transverse spin fluctuations, pushing the system toward states of small total spin, where the physics is determined by the cavity fluctuations. Once the system reaches a degenerate singlet-like sector, additional spatially structured spin couplings lift the degeneracy and select specific many-body phases, such as quantum spin liquids. This thesis addresses the first of these steps: the quasi-adiabatic preparation of squeezed antiferromagnetic states in a collective cavity-QED setting. We consider two atomic sublattices initialised in a classical antiferromagnetic product state pinned by a staggered field, and ramp up a cavity-mediated interaction that generates correlations between the sublattices, suppressing their collective transverse fluctuations. Since the cavity is intrinsically lossy, we describe the dynamics with a Lindblad master equation for collective photon loss, which introduces a competition between diabatic excitations from fast ramps and dissipative degradation from slow ones. We solve this trade-off in the minimal two-atom case, where the target is the antisymmetric Bell state, and then extend the analysis to larger ensembles using linear spin-wave theory, where the target is a two-mode squeezed antiferromagnetic state. In both regimes, the optimal protocol is not the most adiabatic one, but the one that best balances diabatic and dissipative errors. As the atom number increases, the achievable squeezing improves monotonically despite collective dissipation, approaching Heisenberg-limited scaling (∝ 1/N) in the weakdissipation regime. These results show that squeezed antiferromagnetic states remain accessible under realistic cavity-QED conditions, supporting their role as a collective precursor toward richer, spatially structured many-body phases.