Classical first-passage time distributions have been extensively studied both theoretically and experimentally. Their quantum counterparts—quantum first-passage time distributions (QFPTDs)—remain largely unexplored and have deep implications for both fundamental physics and the development of emerging quantum technologies. We measure the first QFPTDs using a motional mode of a single trapped ion. We develop a composite-phase laser pulse sequence to perform tunable stroboscopic single-shot projective measurements of the motional state of a trapped ion. We measure QFPTDs of the ion energy when coupled to electric-field noise. The measurement protocol developed here is broadly applicable to other quantum systems and provides a powerful method for exploring a broad range of QFPTD phenomena. With these results, we open a field of experimental investigations of QFPT processes with potential future relevance to quantum search algorithms, unraveling connections between classical and quantum dynamics, and study of the quantum measurement problem.
Classical first-passage time distributions have been extensively studied both theoretically and experimentally. Their quantum counterparts—quantum first-passage time distributions (QFPTDs)—remain largely unexplored and have deep implications for both fundamental physics and the development of emerging quantum technologies. We measure the first QFPTDs using a motional mode of a single trapped ion. We develop a composite-phase laser pulse sequence to perform tunable stroboscopic single-shot projective measurements of the motional state of a trapped ion. We measure QFPTDs of the ion energy when coupled to electric-field noise. The measurement protocol developed here is broadly applicable to other quantum systems and provides a powerful method for exploring a broad range of QFPTD phenomena. With these results, we open a field of experimental investigations of QFPT processes with potential future relevance to quantum search algorithms, unraveling connections between classical and quantum dynamics, and study of the quantum measurement problem.
First-passage phenomena play a fundamental role in classical stochastic processes. We here exactly solve a quantum first-passage time problem for quantum diffusion driven by measurement noise, a generalization of classical Brownian motion. Such continuous monitoring may trap the measured quantum system in a decoherence-free subspace, a fraction of the available state space that is isolated from the surroundings, and thus plays an important role in quantum information science. We analytically determine the first-passage time distribution, whose form neither depends on the system Hamiltonian nor on the measurement operator, and is therefore universal. These results provide a general framework to investigate the first-passage statistics of diffusive quantum trajectories.
The quantum first-passage problem involves stochastic trajectories conditioned on measurement outcomes. The timing statistics of such trajectories remain largely unexplored in open quantum systems. Here, we investigate the first-passage time to an energy threshold for a ubiquitous model: a harmonic oscillator driven by classical additive noise. We find that projective measurements and energy quantization lead to substantial differences between the quantum and classical first-passage-time distributions at low thresholds, while these differences gradually diminish as the threshold energy increases. We treat the problem using both ensemble-averaged conditioned density-matrix dynamics and trajectory-resolved stochastic pure-state dynamics. The two descriptions yield indistinguishable timing statistics. Quantization effects appear in the ensemble-level phase-space distributions of the surviving states and vanish at larger threshold energies. Individual trajectories reveal emergent quantum signatures from the repeated measurements, such as persistent Wigner negativity. Our results provide a framework for using first-passage processes to create measurement-induced nonclassical resource states and to study the quantum-classical crossover of monitored systems.
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.
We present experimental results of using trapped ions for the study of energy transport and quantum correlations in many-body systems. We investigate energy propagation by locally exciting one end of an ion chain and then observing the subsequent dynamics. The experimental results agree with the presented normal mode model of ion motion, and signify the first steps towards realizing theoretical proposals of studying many-body physics with the motional degree of freedom of trapped ions. Additionally, we present a method for detecting correlations between an open quantum system and its environment by acting only locally on the open system. We implement this method using a single trapped ion and discuss our current work towards extending the results to larger systems. Lastly, we demonstrate how the presented method for local detection of quantum correlations can be used for detection of quantum phase transitions.
Quantum noise is a fundamental limitation for quantum sensors and results in the so-called shot-noise limit. Nowadays, several systems such as optical clocks or gravitational wave detectors approach measurement sensitivities where this limitation poses a major contribution to the total statistical uncertainty. It is known that this limit can be overcome by preparing the probe in a non-classical state. We will give an overview over the different non-classical states that have been implemented in the motion of single trapped ions and discuss their individual advantages and limitations in metrology. Possible applications for the presented experiments are the measurement of small oscillating electric fields and trapping frequencies. The Focus will be on our experimental work on Fock states, where quantum-enhanced sensing in both scenarios is possible with the same quantum state.
In this work, we present a method for measuring the motional state of a two-level system coupled to a harmonic oscillator. Our technique uses ultranarrowband composite pulses on the blue sideband transition to scan through the populations of the different motional states. Our approach does not assume any previous knowledge of the motional state distribution and is easily implemented. It is applicable both inside and outside of the Lamb-Dicke regime. For higher phonon numbers especially, the composite pulse sequence can be used as a filter for measuring phonon number ranges. We demonstrate this measurement technique using a single trapped ion and show good detection results with the numerically evaluated pulse sequence. Published by the American Physical Society 2024