1202.5397 (Søren Gammelmark et al.)

Interacting spins in a cavity: finite size effects and symmetry-breaking
dynamics    [PDF]

Søren Gammelmark, Klaus Mølmer

We calculate the ground state and simulate the dynamics of a finite chain of
spins with Ising nearest-neighbor interactions and a Dicke collective spin
interaction with a single mode cavity field. We recover the signatures of first
and second order phase transitions predicted by mean field theory, while for
small chains, we find significant and non-trivial finite size effects. Below
the first order phase transition, even quite large spin chains of 30-40 spins
give rise to a mean photon number and number fluctuations significantly above
the mean field vacuum result. Near the second order phase critical point, our
calculations reveal photon number fluctuations that grow beyond Poisson
statistics with the size of the spin chain. We simulate the stochastic
evolution of the system when the cavity output field is subject to homodyne
detection. For an initial state close to the first order phase-transition the
random character of the measurement process causes a measurement-induced
symmetry-breaking in the system. This symmetry-breaking occurs on the
time-scale needed for an observer to gather sufficient information to
distinguish between the two possible (mean-field) symmetry-broken states.

View original: http://arxiv.org/abs/1202.5397