Boyan T. Torosov

In this work, we present a method for measuring the motional state of a two-level system coupled to a harmonic oscillator. Our technique uses ultra-narrowband composite pulses on the blue sideband transition to scan through the populations of the different motional states. Our approach does not assume any previous knowledge of the motional state distribution and is easily implemented. It is applicable both inside and outside of the Lamb-Dicke regime. For higher phonon numbers especially, the composite pulse sequence can be used as a filter for measuring phonon number ranges. We demonstrate this measurement technique using a single trapped ion and show good detection results with the numerically evaluated pulse sequence.

We propose a simple realization of a quantum simulator of the Riemann-Hurwitz (RH) ζ function based on a truncation of its Dirichlet representation. We synthesize a nearest-neighbour-interaction Hamiltonian, satisfying the property that the temporal evolution of the autocorrelation function of an initial bare state of the Hamiltonian reproduces the RH function along the line σ+i ωt of the complex plane, with σ>1. The tight-binding Hamiltonian with engineered hopping rates and site energies can be implemented in a variety of physical systems, including trapped ion systems and optical waveguide arrays. The proposed method is scalable, which means that the simulation can be in principle arbitrarily accurate. Practical limitations of the suggested scheme, arising from a finite number of lattice sites N and from decoherence, are briefly discussed.