Why 2D arrays? - The idea
In comparison to a string of ions typically used for trapped-ion quantum computers, a 2D architecture as realized in an array of individual ion traps allows for a more direct simulation of two-dimensional quantum models. Such are e.g. the Ising model [1,2], where each of the interacting spins could be described by the quantum state of a single ion trapped in an individual trapping site of the array.
A lattice of interacting spins could be simulated by single ions trapped in an array of individual Paul traps. The spin (up or down) is represented by the electronic qubit state of the respective ion. Coupling between two nearest-neighbours can be implemented by exploiting the Coulomb interaction between the ions [4-6].
Furthermore, arrays of ion traps are a possible architecture for a scalable quantum computer . Ion traps have already been used to demonstrate, in principle, all components necessary for building a quantum computer. This, however, is limited to a few ten ions so far. The scalability of ion traps to accommodate hundreds or thousands of ions is still a challenge which has to be solved towards a fully functional ion-based quantum computer.
To use 2D arrays of Paul traps as a tool for quantum simulation or computation, interactions between ions in different trapping sites have to be engineered. We aim at realising interactions whose strength can be controlled electronically. We use the fact that the Coulomb interaction scales as 1/d³ where d is the distance between two ions. To increase the coupling strength between a given pair of nearest-neighbours on the lattice, we shuttle ions by adjusting the RF amplitude on the electrode in between them .
Trap arrays in Innsbruck - The realisation
The trap array ‘Folsom’ shown below on the left was the first array used to trap ions in Innsbruck. It is a 4x4 array and allows to load up to 16 individual trapping sites. Folsom's purpose was to show that RF-controlled shuttling as described above works .
Left: The ‘Folsom’ trap. A 4x4 array, where each of the circular electrodes is an individual trapping site. The inset shows a trapped cloud of 40Ca+ ions.
Right: The trap array ‘Ziegelstadl’. Similarly to the Folsom design, the array has 16 independent trapping sites. But here the distance between adjacent trapping sites is only 100 µm – about the diameter of a human hair!
The new generation of 2D arrays is a microfabricated trap array called ‘Ziegelstadl’ shown above on the right. With a chip size of only about 1mm² and an ion-ion distance of only 100 µm, Ziegelstadl is by a factor 15 smaller than the old array Folsom. The reduced size should make coherent operations between adjacent ions possible. Ziegelstadl was produced in the Forschungszentrum Mikrotechnik of the Fachhochschule Vorarlberg, with whom we collaborate.
Philip Holz (PhD student)
Kirill Lakhmanskiy (PhD student)
Rainer Blatt (group leader)
Former members: Martin Meraner, Michael Brownnutt, Muir Kumph
Here’s the 2D team along with the other people from our laboratory – the CryoTrap and Nanofiber projects.
Mike, Muir, Philip, Kirill, Ben, Alex, Martin, Michi, Yves
 E. Ising, Beitrag zur Theorie des Ferromagnetismus, Zeitschrift für Physik 31, 253 (1925).
 J. W. Britton et al., Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins, Nature 84, 489 (2012).
 J. I. Cirac and P. Zoller, A scalable quantum computer with ions in an array of microtraps, Nature 404, 579 (2000).
 K. R. Brown et al., Coupled quantized mechanical oscillators, Nature 471, 196 (2011).
 M. Harlander et al., Trapped-ion antennae for the transmission of quantum information, Nature 471, 200 (2011).
 A. C. Wilson et al., Tunable spin–spin interactions and entanglement of ions in separate potential wells, Nature 512, 57 (2014).
 M. Kumph et al., Two-dimensional arrays of radio-frequency ion traps with addressable interactions, New J. Phys. 13, 073043 (2011).
 M. Kumph et al., Operation of a planar-electrode ion trap array with adjustable RF electrodes, arXiv:1402.0791.
- M. Niedermayr et al., Cryogenic surface ion trap based on intrinsic silicon, New J. Phys. 16, 113068 (2014).
- M. Brownnutt et al., Ion-trap measurements of electric-field noise near surfaces, arXiv:1409.6572 (2014).
- M. Kumph et al., Operation of a planar-electrode ion trap array with adjustable RF electrodes, arXiv:1402.0791 (2014).
- D. Gandolfi et al., Compact radio-frequency resonator for cryogenic ion traps, Rev. Sci. Instrum. 83, 084705 (2012).
- M. Brownnutt et al., Spatially-resolved potential measurement with ion crystals, Appl. Phys. B 107, 1125 (2012).