Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions

Driving a homogeneous system across a quantum phase transition in a quench time tau(Q) generates excitations on wavelengths longer than the Kibble-Zurek (KZ) length (xi) over cap proportional to tau(nu/(1+z nu) )(Q)within the KZ time window (t) over cap proportional to tau(z nu/(1+z nu))(Q), where z and nu are the critical exponents. Quenches designed with local time-dependent inhomogeneity can introduce a gap in the spectrum. They can be parametrized by a time- and space-dependent distance epsilon from the critical point in the parameter space of the Hamiltonian: epsilon(t, x) = t-x/v/tau(Q) theta(vt - x). For a variety of setups with short-range interactions, they have been shown to suppress excitations if the spatial velocity v of the inhomogeneous front is below the characteristic KZ velocity (v) over cap proportional to (xi) over cap/(t) over cap. Ising-like models with long-range interactions can have no sonic horizon, spreading information instantaneously across the system. Usually, this should imply that inhomogeneous transitions will render the dynamics adiabatic regardless of the velocity of the front. However, we show that we get an adiabatic transition with no defects only when the inhomogeneous front moves slower than the characteristic crossover velocity (v) over tilde proportional to theta((z-1)nu/(1+nu)), where theta is the slope of the inhomogeneous front at the critical point. The existence of this crossover velocity and adiabaticity of the model results from the energy gap in the quasiparticle spectrum that is opened by the inhomogeneity. This effect can be employed for efficient adiabatic quantum state preparation in systems with long-range interactions.