Schaetz Abstract

"What's Up Spins? Simulating quantum systems in ion traps."

We study the building blocks for quantum simulations based on trapped ions. In the first part of the talk we focus on quantum spin-Hamiltonians simulated according to a protocol of Porras and Cirac (PRL 2004). Here, we experimentally simulated the adiabatic evolution of the smallest non-trivial spin system from para- into ferromagnetic order with a quantum magnetisation for two spins of 98%. We proved that the transition was not driven by thermal-fluctuations but of quantum mechanical origin, the source of quantum-fluctuations in quantum phase transitions. We observed a final superposition state of the two degenerate spin configurations for the ferromagnetic order corresponding to deterministic entanglement achieved with 88% fidelity. To calibrate the amplitudes of the simulated interactions, we performed a two-qubit phase-gate based on both axial motional modes with an entangling fidelity exceeding 95%. Currently, we explore the limits of quantum simulations in conventional traps, extending the operations to the radial degree of freedom, with a preliminary fidelity of the two-qubit phase-gate exceeding 97% and recently five ions cooled close to the motional ground state. In parallel we work on the realization of a surface-trap array that might allow for a 2D-lattice of ions (first of 2x2 – in principle scalable to >10x10 ions/spins). In a second part of the talk we want to present our experimental results of a quantum (random) walk of an ion – our protocol being close to the proposal of Travaglione and Milburn (PRA 2002).