Michael Johanning

Quantum simulations with cold trapped ions

The control of internal and motional quantum degrees of freedom of laser-cooled trapped ions has been subject to intense theoretical and experimental research for about three decades. In the realm of quantum information science, the ability to deterministically prepare and measure quantum states of trapped ions is unprecedented. This expertise may be employed to investigate physical models conceived to describe systems that are not directly accessible for experimental investigations. Here, we give an overview of current theoretical proposals and experiments for such quantum simulations with trapped ions. This includes various spin models (e.g. the quantum transverse Ising model or a neural network), the Bose?Hubbard Hamiltonian, the Frenkel?Kontorova model, and quantum fields and relativistic effects.

Quantum gates and memory using microwave-dressed states

Trapped atomic ions have been used successfully to demonstrate basic elements of universal quantum information processing. Nevertheless, scaling up such methods to achieve large-scale, universal quantum information processing (or more specialized quantum simulations) remains challenging. The use of easily controllable and stable microwave sources, rather than complex laser systems, could remove obstacles to scalability. However, the microwave approach has drawbacks: it involves the use of magnetic-field-sensitive states, which shorten coherence times considerably, and requires large, stable magnetic field gradients. Here we show how to overcome both problems by using stationary atomic quantum states as qubits that are induced by microwave fields (that is, by dressing magnetic-field-sensitive states with microwave fields). This permits fast quantum logic, even in the presence of a small (effective) Lamb–Dicke parameter (and, therefore, moderate magnetic field gradients). We experimentally demonstrate the basic building blocks of this scheme, showing that the dressed states are long lived and that coherence times are increased by more than two orders of magnitude relative to those of bare magnetic-field-sensitive states. This improves the prospects of microwave-driven ion trap quantum information processing, and offers a route to extending coherence times in all systems that suffer from magnetic noise, such as neutral atoms, nitrogen-vacancy centres, quantum dots or circuit quantum electrodynamic systems.

Individual Addressing of Trapped Ions and Coupling of Motional and Spin States Using rf Radiation

Individual electrodynamically trapped and laser cooled ions are addressed in frequency space using radio-frequency radiation in the presence of a static magnetic field gradient. In addition, an interaction between motional and spin states induced by an rf field is demonstrated employing rf optical double resonance spectroscopy. These are two essential experimental steps towards realizing a novel concept for implementing quantum simulations and quantum computing with trapped ions.

Error-resistant Single Qubit Gates with Trapped Ions

This study presents single qubit gates with trapped ions that are robust against experimental imperfections over a wide range of parameters. In particular it is shown that errors caused by an inaccurate setting of either frequency, amplitude, or duration of the driving field, or of a combination of these errors are tolerable when a suitable sequence of radiation pulses, or a shaped pulse is applied instead of, for instance, a single rectangular pi-pulse. Thus an essential prerequisite for scalable quantum computation with trapped ions is demonstrated.

Adiabatic quantum simulation with a segmented ion trap: Application to long-distance entanglement in quantum spin systems

We investigate theoretically systems of ions in segmented linear Paul traps for the quantum simulation of quantum spin models with tunable interactions. The scheme is entirely general and can be applied to the realization of arbitrary spin-spin interactions. As a specific appl ication we discuss in detail the quantum simulation of models that exhibit long-distance entanglement in the ground state. We show how tailoring of the axial trapping potential allows for generating spin-spin coupling patter ns that are suitable to create long-distance entanglement. We discuss how suitable sequences of microwave pulses can implement Trotter expansions and realize various kinds of effective spin-spin interactions. The corresponding Hamiltonians can be varied on adjustable time scales, thereby allowing the controlled adiabatic pre paration of their ground states.

A planar ion trap chip with integrated structures for an adjustable magnetic field gradient

We present the design, fabrication, and characterization of a segmented surface ion trap with integrated current-carrying structures. The latter produce a spatially varying magnetic field necessary for magnetic-gradient-induced coupling between ionic effective spins. We demonstrate trapping of strings of 172Yb+ ions and characterize the performance of the trap and map magnetic fields by radio frequency-optical double-resonance spectroscopy. In addition, we apply and characterize the magnetic gradient and demonstrate individual addressing in a string of three ions using RF radiation.

Ion trajectory analysis for micromotion minimization and the measurement of small forces

For experiments with ions confined in a Paul trap, minimization of micromotion is often essential. In order to diagnose and compensate micromotion we have implemented a method that allows for finding the position of the radio-frequency (rf) null reliably and efficiently, in principle, without any variation of direct current (dc) voltages. We apply a trap modulation technique and focus-scanning imaging to extract three-dimensional ion positions for various rf drive powers and analyze the power dependence of the equilibrium position of the trapped ion. In contrast to commonly used methods, the search algorithm directly makes use of a physical effect as opposed to efficient numerical minimization in a high-dimensional parameter space. Using this method we achieve a compensation of the residual electric field that causes excess micromotion in the radial plane of a linear Paul trap down to

Analog quantum simulation of (1+1)-dimensional lattice QED with trapped ions

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A scalable, fast, and multichannel arbitrary waveform generator

. Additionally, the precise position determination of a single harmonically trapped ion employed here can also be utilized for the detection of small forces. This is demonstrated by determining light pressure forces with a precision of 135 yN. As the method is based on imaging only, it can be applied to several ions simultaneously and is independent of laser direction and thus well suited to be used with, for example, surface-electrode traps.

High-Fidelity Preservation of Quantum Information During Trapped-Ion Transport

nite-size scaling, we demonstrate that this model recovers Wilson’s lattice gauge theory in a controlled way. Its implementation can be scaled up to tens of ions in an array of micro-traps. The second scheme represents the gauge elds by spins 1/2, and thus simulates a quantum link model. As we show, this allows the fermionic matter to be replaced by bosonic degrees of freedom, permitting smallscale implementations in a linear Paul trap. Both schemes work on energy scales signicantly larger than typical decoherence rates in experiments, thus enabling the investigation of phenomena such as string breaking, Coleman’s quantum phase transition, and false-vacuum decay. The underlying ideas of the proposed analog simulation schemes may also be adapted to other platforms, such as superconducting qubits.