We demonstrate that the radial degree of freedom of strings of trapped ions in the quantum regime may be prepared and controlled accurately through the variation of the external trapping potential while at the same time its properties are measurable with high spatial and temporal resolution. This provides a new testbed giving access to static and dynamical properties of the physics of quantum-many-body systems and quantum phase transitions that are hard to simulate on classical computers. Furthermore, it allows for the creation of double well potentials with experimentally accessible tunneling rates, with applications in testing the foundations of quantum physics and precision sensing.
We demonstrate that the radial degree of freedom of strings of trapped ions in the quantum regime may be prepared and controlled accurately through the variation of the external trapping potential while at the same time its properties are measurable with high spatial and temporal resolution. This provides a new testbed giving access to static and dynamical properties of the physics of quantum-many-body systems and quantum phase transitions that are hard to simulate on classical computers. Furthermore, it allows for the creation of double well potentials with experimentally accessible tunneling rates, with applications in testing the foundations of quantum physics and precision sensing.
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. We report on the progress in experimentally simulating quantum many-body physics with trapped ions.
Double-well potentials have extensive applications in many branches of physics and have resulted in devices that are useful for precision sensing as well as quantum information processing. Here, we present a theoretical analysis of the transverse phonon coupling between a pair of trapped ions as described by a double-well system. Typically the phonons in trapped ions are used as an intermediary in quantum information processing, but here we focus on the dynamics of the phonons themselves. The double-well system is a special case of the more generalized Bose-Hubbard Model, with exactly two sites available to store particles. We draw an analogy to another double-well system in solid state physics: a Josephson junction containing a thin insulating barrier between two superconductors. Applications of the Josephson junction include superconducting quantum interference devices (SQUIDs), which have emerged as sensitive magnetometers and also as qubits for quantum computation. Another analogy is the recent demonstrations of matter-wave interference with Bose-Einstein condensates in double-well traps, which have also shown great promise for applications in precise inertial and gravitational field sensing. We will also discuss experimental techniques that can be applied to control and manipulate this double-well system.
Trapped laser-cooled atoms and ions are quantum systems which can be experimentally controlled with an as yet unmatched degree of precision. Due to the control of the motion and the internal degrees of freedom, these quantum systems can be adequately described by a well-known Hamiltonian. In this colloquium, powerful numerical tools for the optimization of the external control of the motional and internal states of trapped neutral atoms, explicitly applied to the case of trapped laser-cooled ions in a segmented ion-trap are presented. Inverse problems when optimizing trapping potentials for ions, are solved. The presentation is complemented by a quantum-mechanical treatment of the wave-packet dynamics of a trapped ion. Efficient numerical solvers for both time-independent and time-dependent problems are provided. Shaping the motional wave functions and optimizing a quantum gate is realized by the application of quantum optimal control techniques. The numerical methods presented can also be used to gain an intuitive understanding of quantum experiments with trapped ions by performing virtual simulated experiments on a personal computer. Code and executables are supplied as supplementary online material.
Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology.
Achieving control over physical systems down to individual quanta is central for advancing our understanding of nature and enabling emerging quantum technologies. Trapped-ion systems provide a powerful platform offering exceptional control over internal and external degrees of freedom and allowing the study of both fundamental and applied aspects of quantum dynamics. This thesis introduces an experimental toolbox, centered on problem-tailored modifications of Ramsey interferometry, for observing and manipulating dynamic processes with high temporal and spatial resolution, showcased in a trapped-ion quantum simulator. Using this versatile approach, we bridge quantum metrology and quantum thermodynamics – from tracking the motional wave packet evolution of a single ion in phase space to observing time-(in)dependent energy-level renormalizations in ultra-strongly coupled open systems. A central innovation of this thesis is the development of a stroboscopic measurement technique that establishes and maintains coherence among four oscillators: a global microwave reference, an ultraviolet polarization-gradient traveling-wave light field, and the spin and motional states of a single trapped ion. This architecture, spanning a phase-stable frequency range of more than nine orders of magnitude, enables superresolved, back-action-free tracking of motional wave packets in phase-space. In this way, we achieve noise floors of 1.8(2) nm for position and 8(2) zN μs for momentum on sub-100-nanosecond timescales. This precision enables quantum-enhanced diagnostics, non-classical state preparation, and fine-grained phase-space control, with broad implications for entanglement generation, quantum interferometry, and quantum sensing. In a complementary study, we exploit the trapped-ion system as a testbed for probing fundamental quantum interactions: We experimentally simulate a strongly coupled open quantum system, where dressed electronic states represent the system and a single motional mode serves as its environment. We observe time-dependent energy shifts up to 15% of the bare transition frequency, induced solely by ultra-strong system-environment coupling. These shifts, anticipated to be a general feature of all quantum platforms across all coupling regimes, are accurately described by the minimal-dissipation ansatz and interpreted as generalized, time-resolved Lamb shifts. Together, the results of this thesis extend the frontier of trapped-ion quantum simulation: The integration of Ramsey interferometry, stroboscopic techniques, and strong-coupling simulations offers a high-resolution window into diverse aspects of quantum dynamics. This work enables advanced studies – including squeezed states, analogues of relativistic effects such as Hawking radiation and the physics of the early universe, and autonomous quantum engines.