Paula  Linear QuantumSpin Systems
Govinda Clos, Matthias Wittemer, JanPhilipp Schröder, Frederick Hakelberg, Philip Kiefer, Ulrich Warring, and Tobias Schaetz
introduction
quantum simulation with trapped ions
Richard Feynman originally proposed to use a wellcontrolled quantum system to efficiently tackle problems that are too complex to be addressed with classical computers, such as quantum dynamics of many body systems; he called his hypothetical device a quantum computer (QC). Today, we classify it as an analog quantum simulator (AQS) to distinguish it from a QC, in which the dynamics of a system are implemented via algorithms of gate operations on subsets of qubits. In an AQS the strategy is to adiabatically evolve a quantum system from an experimentally wellprepared (initial) state to a new state by changing its Hamiltonian in a controlled manner, to reveal, for example, highly nontrivial dynamics, such as quantum phase transitions. Either device, QC and AQS, may help to develop insights into underlying physics. In addition, wellcontrolled quantum systems may enable to simulate processes in quantum chemistry and (quantum) biology, such as photosynthesis, where it is under debate whether the laws of quantum mechanics could also influence biological and other macroscopic objects. In any cases, we may gain a deeper understanding of the essential ingredients by directly observing a controlled model quantum system.laser cooled trapped ions form complex 3D (cp. KINKS) and more simple linear Coulomb crystals
Currently there are efforts to implement QC/AQS in many different physical systems; we purse an approach with trapped ions: In the past, spectacular progress has been achieved in controlling the dynamics of such isolated quantum systems, as highlighted with the award of the 2012 Physics Nobel Prize to S. Haroch and D. J. Wineland: ”for groundbreaking experimental methods that enable measuring and manipulation of individual quantum systems” [Nobel prize website]. Nonetheless such controlled quantum systems (cp. tools below) have been limited to only a few constituents to permit mitigating residual decoherence effects. Methods for implementing largescale devices/systems are still in the developmental phase. One of our goals is to contribute to a substantially more robust implementation of such systems to enable and to drive progress toward larger quantum systems (cp. BERMUDA project). While another mission of the PAULA apparatus is to study couplings of isolated quantum systems to wellcontrolled environments (openquantum systems).
impressions from a quantum simulator: ion trap, dyelaser system, and secondharmonicgeneration stage
In the past, PAULA has been used to demonstrate the first optical trap for ions (now a dedicated spinoff project: OPIAT) and proofofprinciple quantum simulation experiments, e.g.: simulation of a quantum phase transition [Nature Physics 4, 757  761 (2008)] and quantum walk [Phys. Rev. Lett. 103, 090504 (2009)].
our tools in the lab
conventional linear Paul trap for linear ion chains



further reading
 Measurement of quantum memory effects and its fundamental limitations
M. Wittemer, G. Clos, H.P. Breuer, U. Warring, T. Schaetz
Phys. Rev. A 97, 020102(R) (2018)  arXiv: 1702.07518 (2017)  The new thermodynamics: how quantum physics is bending the rules
Nature 551, 20–22 (2017)
 Timeresolved observation of thermalization in an isolated quantum system
G. Clos, D. Porras, U. Warring, T. Schaetz
Phys. Rev. Lett. 117, 170401 (2016)  arXiv: 1509.07712 (2015)  Decoherenceassisted spectroscopy of a single Mg+ ion
G. Clos, M. Enderlein, U. Warring, T. Schaetz, D. Leibfried
Phys. Rev. Lett. 112, 113003 (2014)  arXiv:1402.1678 (2014)  Quantum walk with nonorthogonal position states
R. Matjeschk, A. Ahlbrecht, M. Enderlein, Ch. Cedzich, A. H. Werner, M. Keyl, T. Schaetz, R. F. Werner
Phys. Rev. Lett. 109, 240503 (2012)  arXiv:1206.0220 (2012)  Experimental simulation and limitations of quantum walks with trapped ions
R. Matjeschk, Ch. Schneider, M. Enderlein, T. Huber, H. Schmitz, J. Glueckert, T. Schaetz
New J. Phys. 14, 035012 (2012)  arXiv:1108.0913 (2011)  Quantum Odyssey of Photons
T. Schaetz, Ch. Schneider, M. Enderlein, T. Huber and R. Matjeschk
ChemPhysChem 12, 7174 (2011)  The quantum Walk of a trapped Ion in phase space
H. Schmitz, R. Matjeschk, Ch. Schneider, J. Glueckert, M. Enderlein, T. Huber and T. Schaetz
Phys. Rev. Lett. 103, 090504 (2009)
 pdf
 Pressemitteilung
 arXiv:0904.4214
 APSSynopsis: Quantum walking the line
 Selected for Virtual Journal of Quantum Information  The 'arch' of simulating quantum spin systems with trapped ions
H. Schmitz, A. Friedenauer, Ch. Schneider, R. Matjeschk, M. Enderlein, T. Huber, J. Glueckert, D. Porras and T. Schaetz
Appl. Phys. B 95, 195 (2009)  Simulating a quantum magnet with trapped ions
A. Friedenauer, H. Schmitz, J. Glueckert, D. Porras and T. Schaetz
Nature Physics 4, 757  761 (2008)
 pdf
 Pressemitteilung
 arXiv:0802.4072v1 (pdf)
 ScienceNews (174, 5, August the 30th)