Quantum Contact Processes on a Topological Lattice

Abstract

Contact processes play an important role in classical non-equilibrium dynamics, describing the spreading of diseases, the dynamics of earthquakes and forest fires, and the distribution of information through the internet. Here we show that their quantum counterpart, where the spreading occurs through coherent couplings, displays even richer dynamics and offers new means of control. A quantum contact process on a topologically non-trivial lattice can be confined to a protected subspace corresponding to either a single site or a fully excited lattice. Furthermore, excitation spreading can be controlled to occur in quantized steps and on demand when employing topological pumps. We show that the many-body dynamics of excited domains can be mapped to an effective single-particle model, which also determines the topological properties. Throughout this work, we consider a specific type of contact process corresponding to coherent Rydberg facilitation in a tweezer array of trapped atoms in a one-dimensional lattice.

Figures (5)

• Figure 1: QXP quantum contact process on a one-dimensional lattice. (a) In real space $\lambda_v = 1$ and $\lambda_w = 10$ denote alternating coherent excitation rates (Rabi frequencies) on even and odd sites. (b) In the basis of domains of length $m$ domain space these correspond to alternating hopping rates. Time and space resolved dynamics for the classical (c) and quantum (d) QXP contact process for four sites with open boundary conditions and with one initial seed excitation. The color code represents the excitation probability.
• Figure 2: Time resolved dynamics. Top row: real space, bottom row: domain space, for the trivial $\lambda_w = 1/10< \lambda_v = 1$ (left column) and topological cases $\lambda_w = 10 > \lambda_v = 1$ (right column). The dotted lines correspond to the analytically expected period $T_\mathrm{hyb} \propto (E_+ - E_-)^{-1}$, where $E_\pm$ are the corresponding energies of the two perfectly localized edge states.
• Figure 3: Hybridization of edge states. The states $\Psi_L = \ket{\bullet \circ \circ ... \circ}$ and $\Psi_R = \ket{\bullet \bullet \bullet ... \bullet}$ correspond to topological edge states in the limit $\lambda_w / \lambda_v \to \infty$. As the ratio $\lambda_w / \lambda_v$ increases, oscillations between $\Psi_L$ and $\Psi_R$ become clearer and the frequency approaches the analytical expectation $T_\mathrm{hyp}$ (see main text). Color code as in Fig. 2.
• Figure 4: Quantum control of domain size by manipulating AAH topological pump. In (a) the corresponding parameters $\lambda_2(t)$ and $\delta_2(t)$ are shown. (b) and (c) show the dynamics in real space and domain basis, respectively. The inset in (b) shows 3 periods of a time-evolution, with small detuning $\Delta_0 / \lambda_0 = -22$, where the mapping to the single-particle domain model fails. The inset in (c) shows the rapid transition between the domain sizes. To ensure the adiabaticity of the time-evolution, the frequency is chosen as $\omega = 0.02 \lambda_0$.
• Figure 5: Accuracy of the single-particle QXP model. For smaller detunings $\Delta_0/\lambda_0$ the QXP model of the facilitation breaks down. Top: Real space Rydberg excitation probability. Bottom: Population in domain picture. Color code is the same as in Fig. 2 of the main text.