T. Schätz

Quantum Walk of a Trapped Ion in Phase Space

We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its classical counterpart if we allow the walker or ion to take all classical paths simultaneously. Quantum interferences enforce asymmetric, nonclassical distributions in the highly entangled degrees of freedom (of coin and position states). We theoretically study and experimentally observe the limitation in the number of steps of our approach that is imposed by motional squeezing. We propose an altered protocol based on methods of impulsive steps to overcome these restrictions, allowing to scale the quantum walk to many, in principal to several hundreds of steps.

Dirac equation and quantum relativistic effects in a single trapped ion

We present a method of simulating the Dirac equation in 3+1 dimensions for a free spin-1/2 particle in a single trapped ion. The Dirac bispinor is represented by four ionic internal states, and position and momentum of the Dirac particle are associated with the respective ionic variables. We show also how to simulate the simplified 1+1 case, requiring the manipulation of only two internal levels and one motional degree of freedom. Moreover, we study relevant quantum-relativistic effects, like the Zitterbewegung and Kleins paradox, the transition from massless to massive fermions, and the relativistic and nonrelativistic limits, via the tuning of controllable experimental parameters.

Quantum information processing with trapped ions

Experiments directed towards the development of a quantum computer based on trapped atomic ions are described briefly. We discuss the implementation of single–qubit operations and gates between qubits. A geometric phase gate between two ion qubits is described. Limitations of the trapped–ion method such as those caused by Stark shifts and spontaneous emission are addressed. Finally, we describe a strategy to realize a large–scale device.

Crystalline Ion Beams

By freezing out the motion between particles in a high-energy storage ring, it should be possible to create threads of ions, offering research opportunities beyond the realm of standard accelerator physics. The usual heating due to intra-beam collisions should completely vanish, giving rise to a state of unprecedented brilliance. Despite a continuous improvement of beam cooling techniques, such as electron cooling and laser cooling, the ultimate goal of beam crystallization has not yet been reached in high-energy storage rings. Electron-cooled dilute beams of highly charged ions show liquid-like order with unique applications. An experiment using laser cooling suggested a reduction of intra-beam heating, although the results were ambiguous. Here we demonstrate the crystallization of laser-cooled Mg+ beams circulating in the radiofrequency quadrupole storage ring PALLAS at a velocity of 2,800 m s-1, which corresponds to a beam energy of 1 eV. A sudden collapse of the transverse beam size and the low longitudinal velocity spread clearly indicate the phase transition. The continuous ring-shaped crystalline beam shows exceptional stability, surviving for more than 3,000 revolutions without cooling.

Analogue of Cosmological Particle Creation in an Ion Trap

We study phonons in a dynamical chain of ions confined by a trap with a time-dependent (axial) potential strength and demonstrate that they behave in the same way as quantum fields in an expanding or contracting Universe. Based on this analogy, we present a scheme for the detection of the analogue of cosmological particle creation which should be feasible with present day technology. In order to test the quantum nature of the particle creation mechanism and to distinguish it from classical effects such as heating, we propose to measure the two-phonon amplitude via the 2nd red sideband transition and to compare it with the one-phonon amplitude (1st red sideband).

Towards (scalable) quantum simulations in ion traps

Experiments directed towards the development of an analogue quantum simulator based on trapped atomic magnesium ions are described. We report on the required initialization including ground state cooling of 25Mg+ ions for the first time—parallel to the group at NIST/Boulder. We discuss basic operations to implement quantum spin Hamiltonians like a one-dimensional quantum Ising model and some challenges to be addressed in reaching for larger scale and higher dimensional devices.

Single Ions Trapped in a One-Dimensional Optical Lattice

We report on three-dimensional optical trapping of single ions in a one-dimensional optical lattice formed by two counterpropagating laser beams. We characterize the trapping parameters of the standing-wave using the ion as a sensor stored in a hybrid trap consisting of a radio-frequency (rf), a dc, and the optical potential. When loading ions directly from the rf into the standing-wave trap, we observe a dominant heating rate. Monte Carlo simulations confirm rf-induced parametric excitations within the deep optical lattice as the main source. We demonstrate a way around this effect by an alternative transfer protocol which involves an intermediate step of optical confinement in a single-beam trap avoiding the temporal overlap of the standing-wave and the rf field. Implications arise for hybrid (rf-optical) and pure optical traps as platforms for ultracold chemistry experiments exploring atom-ion collisions or quantum simulation experiments with ions, or combinations of ions and atoms.

Quantum Information Processing with Trapped Ions

We summarize two experiments on the creation and manipulation of multi‐particle entangled states of trapped atomic ions — quantum dense coding and quantum teleportation. The techniques used in these experiments constitute an important step toward performing large‐scale quantum information processing. The techniques also have application in other areas of physics, providing improvement in quantum‐limited measurement and fundamental tests of quantum mechanical principles, for example.

Photon-assisted-tunneling toolbox for quantum simulations in ion traps

We describe a versatile toolbox for the quantum simulation of many-body lattice models, capable of exploring the combined effects of background Abelian and non-Abelian gauge fields, bond and site disorder and strong on-site interactions. We show how to control the quantum dynamics of particles trapped in lattice potentials by the photon-assisted tunneling induced by periodic drivings. This scheme is general enough to be applied to either bosons or fermions with the additional advantage of being non-perturbative. It finds an ideal application in microfabricated ion trap arrays, where the quantized vibrational modes of the ions can be described by a quantum lattice model. We present a detailed theoretical proposal for a quantum simulator in that experimental setup, and show that it is possible to explore phases of matter that range from the fractional quantum Hall effect, to exotic strongly correlated glasses or flux-lattice models decorated with arbitrary patterns of localized defects.

Particle physics with petawatt class lasers

With a Petawatt class CPA laser of the LLNL Livermore or the proposed GSI (Darmstadt) type laser interactions with matter can be studied in the upper 10 20 W/cm 2 regime. For such a laser focused into an underdense plasma strong electron bursts with energies up to several 100 MeV are ejected in forward direction leading to a comparable burst of bremsstrahlung radiation in the presence of high Z material. Here we discuss the corresponding-induced nuclear reactions including secondary particle production including pions. Due to the threshold behaviour in the production and the advantage of delayed detection, we propose to employ these reactions for probing the initial plasma conditions.