Scaling of quantum simulations in ion traps
Final Report Abstract
We were able to demonstrate that a rich spectrum of problems, intractable on classical computers, can be addressed in a quantum simulator based on trapped ions. Several groups followed our approach and currently try to scale the method. We studied the limitations of the protocol on the amount of steps that still allow the walker to interfere with himself taking all possible paths simultaneously and proposed a new scheme allowing for scaling to an amount for this quantum walk to become a tool for the subsequent investigation of unexplored quantum phenomena. The achieved fidelities exceeding 99% are the basis of several experiments we are actually planning to implement. For example exploring entangled quantum walkers and their interactions during a common walk. Furthermore, the prospect was proposed to simulate the constructive influence of de-coherence in (biological) systems on the efficiency of energy transfer, predicted to be achievable by quantum walks at ambient temperature. We achieved the trapping of a single ion in an optical dipole potential. After more than 60 years of successfully trapping ions in Paul traps and more than 30 years of confining atoms in optical dipole traps we were able to do the first step to combine these fields by "optical trapping of an ion". This allows for completely new concepts: 1) simulating complex spin systems with ions trapped in an optical lattice. 2) A new class of quantum simulations, combining atoms and ions in a common lattice. 3) Furthermore, ions could be embedded into quantum degenerate gases avoiding the inevitable excess kinetic energy in conventional rf-traps, currently limiting cold chemistry experiments. We recently demonstrated the trapping of an ion in a 1D-optical lattice. We observed the creation of structural defects in more-dimensional Coulomb crystals within "conventional" rf-potentials. These had been predicted by theory, if a non-adiabatic transition from a one-dimensional to a two-dimensional crystalline structure of a Coulomb crystal is enforced. If the two-dimensional zigzag structure is formed on time scales that do not allow the transmission of information between the two ends of the crystal (via phonons), two (several) domains can occur, separated by a defect ("frustrated" between a zigzag and a zagzig configuration). We performed systematic studies on these systems and found, in addition to the proposed defects, various new defects. In parallel we started collaborations with several leading theoreticians of the field to address questions on the control of quantum effects occurring in our experiment that turned out to be interesting by their own or will become substantial for the scaling of quantum simulations.
Publications
- Analogue of cosmological particle creation in an ion trap. Phys. Rev. Lett. 99, 201301 (2007)
R. Schuetzhold, M. Uhlmann, L. Petersen, A. Friedenauer, H. Schmitz, and T. Schaetz
- Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion. Phys. Rev. Lett. 98, 253005 (2007)
L. Lamata, J. Leon, T. Schaetz, E. Solano
- Simulating the quantum magnet with trapped ions. Nature Physics 4, 757 (2008)
A. Friedenauer, H. Schmitz, J. Glueckert, D. Porras, and T. Schaetz
- The quantum Walk of a trapped Ion in phase space. Phys. Rev. Lett. 103, 090504 (2009)
H. Schmitz, R. Matjeschk, Ch. Schneider, J. Glueckert, M. Enderlein, T. Huber, T. Schaetz
- Optical trapping of an ion. Nature Photonics 4, 772 (2010)
Ch. Schneider, M. Enderlein, T. Huber, and T. Schaetz
- Synthetic Gauge Fields for Vibrational Excitations of Trapped Ions. Phys. Rev. Lett. 107, 150501 (2011)
A. Bermudez, T. Schaetz, D. Porras
- Dissipation-Assisted Quantum Information Processing with Trapped Ions
A. Bermudez, T. Schaetz, M.B. Plenio
(See online at https://doi.org/10.1103/PhysRevLett.110.110502) - Experimental quantum simulations of many-body physics with ions. Rep. Prog. Phys. 75, 024401 (2012)
Ch. Schneider, D. Porras, T. Schaetz
- Quantum walk with non-orthogonal position states
R. Matjeschk, A. Ahlbrecht, M. Enderlein, Ch. Cedzich, A.H. Werner, M. Keyl, T. Schaetz, R.F. Werner
(See online at https://doi.org/10.1103/PhysRevLett.109.240503) - Single ions trapped in a one-dimensional optical lattice. Phys. Rev. Lett.
M. Enderlein, T. Huber, Ch. Schneider, T. Schaetz
(See online at https://doi.org/10.1103/PhysRevLett.109.233004)
