Multiparticle decoherence-free subspaces in extended systems

We develop a method to determine spatial configurations to realize decoherence-free subspaces for spatially extended multiparticle systems. We have assumed normal reservoir behavior including translational invariance of the reservoir and preparation in stationary states or mixture thereof and weak Markovian system-reservoir coupling that requires energy transfer. One important outcome of our method is a proof that there does not exist a multiparticle decoherence-free subspace in such systems except in the limit that the spatial extent of the system becomes infinitesimal.

Figure 1

(Color online) (a) The system of two two-level atoms in a line with each dipole moment coaligned with the axis joining the atoms. (b) The system of four two-level atoms that lie on the corners of the square with each dipole moment coaligned with one specific side of the square. (c) The system of four two-level atoms in a line with each dipole moment coaligned with the axis connecting the atoms. (d) The system of four two-level atoms in a line with each dipole moment perpendicular to the axis connecting the atoms.

Figure 2

(Color online) Inverse lifetimes (relative to ${\gamma }_0$) for configurations shown in Fig. 1. The two plots in (a) correspond to the configuration of two atoms in Fig. 1a. The dash-dotted line corresponds to the symmetric state and the solid line to the antisymmetric state. The plots in (b)–(d) correspond to the configurations in Figs. 1b, 1c, 1d, respectively, and the four lines correspond to the collective states that arise when one atom is in the excited state and all other atoms are in the ground state.