Spin gases as microscopic models for non-Markovian decoherence

We analyze a microscopic decoherence model in which the total system is described as a spin gas. A spin gas consists of $N$ classically moving particles with additional, interacting quantum degrees of freedom (e.g., spins). For various multipartite entangled probe states, we analyze the decoherence induced by interactions between the probe and environmental spins in such spin gases. We can treat mesoscopic environments ($\approx {10}^5$ particles). We present results for a lattice gas, which could be realized by neutral atoms hopping in an optical lattice, and show the effects of non-Markovian and correlated noise, as well as finite-size effects.

Figure 1

(Color online) (a) Concurrence of two probe particles prepared in a maximally entangled Bell state $\mid {\varphi }^{+}⟩\propto \mid 00⟩+\mid 11⟩$ in a $100\times 3200$ lattice gas with $N=8\times {10}^4$ for $g_o=0.8\eta$ and fixed probes (solid ); and fast moving probes (dashed). The solid, light curve corresponds to an analytical result obtained in a Markovian regime. (b) Concurrence of two probe particles at time $t_1=25{\eta }^{-1}$ for different initial entangled states as a function of distance $d$ between the probes: $\mid {\psi }^{+}⟩\propto \mid 01⟩+\mid 10⟩$ (dashed-dark), $\mid {\varphi }^{+}⟩$ (solid-light), and $\mid G⟩\propto \mid +0⟩+\mid -1⟩$ (dotted).

Figure 2

(Color online) (a) Log-linear plot showing the decay of the average negativity $\overline{\mathcal{N}}$ for six-qubit linear cluster state (solid), $W$ state (short-dashed), and GHZ states $\mid \Psi ⟩$ (dotted), $\mid {\Psi }^{\prime }⟩$ (dash-dotted), and $\mid {\Psi }^{″}⟩$ (long-dashed) in a lattice gas with 400 spins in a $40\times 40$ lattice and coupling constant $g_0=0.8\eta$. (b) Entanglement decay of four-qubit GHZ (long-dashed) and $W$ (dotted) states in $20\times 20$ lattice with 25 spins and $g_0=8\times {10}^{-3}\eta$ illustrating finite-size effects. Single-parameter $\left({\alpha }^{\prime }s\right)$ analytical fits are also shown (thin lines).