Hartmut Häffner

The exponential growth of many-body Hilbert space presents a fundamental barrier to quantum technology, obscuring the search for physically significant states within an astronomically vast landscape. Consequently, resources for quantum-enhanced metrology have been largely confined to the symmetric subspace whose dimensionality scales only polynomially with the particle number-leaving the vast majority of the Hilbert space largely unexplored and poorly understood. Here we challenge this paradigm by demonstrating that metrological advantage can arise as a ubiquitous feature across exponential-dimensional manifolds. By tailoring the first-moment structure of random unitaries, we uncover dense manifolds of engineered random states (ERSs) where Heisenberg-limited scaling emerges as a statistically generic property. This ubiquity endows these resource states with inherent resilience against parameter disorder. We experimentally validate this framework on a trapped-ion processor, achieving a metrological enhancement of $6.98 \pm 0.38$ dB beyond the standard quantum limit. Potential applications extend to diverse platforms, ranging from superconducting circuits and waveguide QED to solid-state spins and polar molecules. Our results establish a powerful paradigm where quantum-enhanced precision can be harvested from the exponential vastness of the Hilbert space.

We leverage recent advances in 3D-printing technology to design and fabricate a micro-ion trap with a spatially distinct loading zone for more efficient loading of ions from effusive thermal ovens. The design reduces the Mathieu-$q$ parameter in the loading zone by increasing the ion-electrode separation $r_0$, thereby potentially facilitating more effective laser cooling of hot ions. This circumvents the temporary thermal instability that arises when the rf potential is reduced during ion loading, a common practice to enable efficient laser cooling of hot ions. Simulations predict that expanding $r_0$ maintains a high trapped ion fraction from a simulated thermal source across a wide range of Mathieu-$q$ parameters. We demonstrate the manufacturability of this design by 3D-printing the rf rails of a four-rod ion trap and discuss the limitations imposed by state-of-the-art additive manufacturing techniques. We briefly compare hot-ion capture in the three-dimensional design presented here with that in a representative planar trap, illustrating one instance in which the former may be better for loading. The article concludes with an outlook for how this design may be incorporated into a quantum-CCD architecture to enhance ion loading and reduce associated experimental overheads.

We demonstrate the operation of a dual-frequency Paul trap and characterize its performance by storing either electrons or calcium ions while applying two quadrupole fields simultaneously which oscillate at $Ω_\textrm{fast} = 2π\times 1.6$ GHz and $Ω_\textrm{slow} = 2π\times 2$ MHz. The particles are loaded and stored in the trap under various conditions followed by detection employing an electron multiplier tube. We find that tens of electrons or ions can be trapped for up to ten milliseconds and a small fraction remains trapped even after hundreds of milliseconds. During dual-frequency operation we find that while the number of trapped electrons rapidly decreases with increase of the $Ω_\textrm{slow}$ field amplitude, the number of trapped ions shows no dependence on the $Ω_\textrm{fast}$ field amplitude as supported by our extensive numerical simulations. We aim to use a similar trap for synthesising antihydrogen from antiprotons and positrons. Accordingly, we discuss open challenges such as the co-trapping of oppositely charged species and particle trap duration.

Trapped-ion quantum computing requires precise optical control for individual qubit manipulation. However, conventional free-space optics face challenges in alignment stability and scalability as the number of qubits increases. Integrated photonics offers a promising alternative, providing miniaturized optical systems on a chip. Here, we propose a design for a multimode photonic circuit integrated with a surface-electrode ion trap capable of targeted and reconfigurable light delivery. Three closely positioned ions can be addressed using a focusing grating coupler that emits multimode light through electrode openings to ions trapped 80 $μ$m above the chip. Simulations show that the couplers achieve diffraction-limited spot with a 4.3 $μ$m beam waist along the trap axis and 2.2 $μ$m perpendicular to the trap axis. Controlled interference of the TE$_{\text{10}}$ and TE$_{\text{20}}$ modes results in crosstalk of -20 dB to -30 dB at ion separations of 5-8 $μ$m when addressing ions individually, and down to -60 dB when two of the three ions are addressed simultaneously. Additionally, the higher-order TE modes can offer a novel mechanism for driving spin-motion coupling transitions, potentially enabling alternative approaches to quantum gates and simulations. The proposed integrated platform offers a viable path for constructing large-scale trapped-ion systems, leveraging the benefits of nanophotonic design for precise and reliable ion manipulation.

Trapped-ion applications, such as in quantum information, precision measurements, optical clocks, and mass spectrometry, rely on specialized high-performance ion traps. The latter applications typically employ traditional machining to customize macroscopic 3D Paul traps, while quantum information processing experiments usually rely on photo-lithographic techniques to miniaturize the traps and meet scalability requirements. Using photolithography, however, it is challenging to fabricate the complex three-dimensional electrode structures required for optimal confinement. Here we address these limitations by adopting a high-resolution 3D printing technology based on two-photon polymerization supporting fabrication of large arrays of high-performance miniaturized 3D traps. We show that 3D-printed ion traps combine the advantages of traditionally machined 3D traps with the miniaturization provided by photolithography by confining single calcium ions in a small 3D-printed ion trap with radial trap frequencies ranging from 2 MHz to 24 MHz. The tight confinement eases ion cooling requirements and allows us to demonstrate high-fidelity coherent operations on an optical qubit after only Doppler cooling. With 3D printing technology, the design freedom is drastically expanded without sacrificing scalability and precision so that ion trap geometries can be optimized for higher performance and better functionality.

Most near-term quantum information processing devices will not be capable of implementing quantum error correction and the associated logical quantum gate set. Instead, quantum circuits will be implemented directly using the physical native gate set of the device. These native gates often have a parameterization (e.g., rotation angles) which provide the ability to perform a continuous range of operations. Verification of the correct operation of these gates across the allowable range of parameters is important for gaining confidence in the reliability of these devices. In this work, we demonstrate a procedure for sample-efficient verification of continuously-parameterized quantum gates for small quantum processors of up to approximately 10 qubits. This procedure involves generating random sequences of randomly-parameterized layers of gates chosen from the native gate set of the device, and then stochastically compiling an approximate inverse to this sequence such that executing the full sequence on the device should leave the system near its initial state. We show that fidelity estimates made via this technique have a lower variance than fidelity estimates made via cross-entropy benchmarking. This provides an experimentally-relevant advantage in sample efficiency when estimating the fidelity loss to some desired precision. We describe the experimental realization of this technique using continuously-parameterized quantum gate sets on a trapped-ion quantum processor from Sandia QSCOUT and a superconducting quantum processor from IBM Q, and we demonstrate the sample efficiency advantage of this technique both numerically and experimentally.

Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials, and for modeling next-generation non-linear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such light-matter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.

In this work, we derive analytic formulae that determine the effect of error mechanisms on one- and two-qubit gates in trapped ions and electrons. First, we analyze, and derive expressions for, the effect of driving field inhomogeneities on one-qubit gate fidelities. Second, we derive expressions for two-qubit gate errors, including static motional frequency shifts, trap anharmonicities, field inhomogeneities, heating, and motional dephasing. We show that, for small errors, each of our expressions for infidelity converges to its respective numerical simulation; this shows our formulae are sufficient for determining error budgets for high-fidelity gates, obviating numerical simulations in future projects. All of the derivations are general to any internal qubit state, and any mixed state of the ion crystal's motion that is diagonal in the Fock state basis. Our treatment of static motional frequency shifts, trap anharmonicities, heating, and motional dephasing apply to both laser-based and laser-free gates, while our treatment of field imhomogenieties applies to laser-free systems.

We demonstrate coupling between the motions of two independently trapped ions with a separation distance of 620 $μ$m. The ion-ion interaction is enhanced via a room-temperature electrically floating metallic wire which connects two surface traps. Tuning the motion of both ions into resonance, we show flow of energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by strong surface electric-field noise in our device. Our ion wire-ion system demonstrates that room-temperature conductors can be used to mediate and tune interactions between independently trapped charges over distances beyond those achievable with free-space dipole-dipole coupling. This technology may be used to sympathetically cool or entangle remotely trapped charges and enable coupling between disparate physical systems.

Electrons and ions trapped with electromagnetic fields have long served as important high-precision metrological instruments, and more recently have also been proposed as a platform for quantum information processing. Here we point out that these systems can also be used as highly sensitive detectors of passing charged particles, due to the combination of their extreme charge-to-mass ratio and low-noise quantum readout and control. In particular, these systems can be used to detect energy depositions many orders of magnitude below typical ionization scales. As illustrations, we suggest some applications in particle physics. We outline a non-destructive time-of-flight measurement capable of sub-eV energy resolution for slowly moving, collimated particles. We also show that current devices can be used to provide competitive sensitivity to models where ambient dark matter particles carry small electric millicharges $\ll e$. Our calculations may also be useful in the characterization of noise in quantum computers coming from backgrounds of charged particles.

We aim to illuminate how the microscopic properties of a metal surface map to its electric-field noise characteristics. In our system, prolonged heat treatments of a metal film can induce a rise in the magnitude of the electric-field noise generated by the surface of that film. We refer to this heat-induced rise in noise magnitude as a thermal transformation. The underlying physics of this thermal transformation process is explored through a series of heating, milling, and electron treatments performed on a single surface ion trap. Between these treatments, $^{40}$Ca$^+$ ions trapped 70~$μ$m above the surface of the metal are used as detectors to monitor the electric-field noise at frequencies close to 1~MHz. An Auger spectrometer is used to track changes in the composition of the contaminated metal surface. With these tools we investigate contaminant deposition, chemical reactions, and atomic restructuring as possible drivers of thermal transformations.

Trapped-ion quantum information processors store information in atomic ions maintained in position in free space via electric fields. Quantum logic is enacted via manipulation of the ions' internal and shared motional quantum states using optical and microwave signals. While trapped ions show great promise for quantum-enhanced computation, sensing, and communication, materials research is needed to design traps that allow for improved performance by means of integration of system components, including optics and electronics for ion-qubit control, while minimizing the near-ubiquitous electric-field noise produced by trap-electrode surfaces. In this review, we consider the materials requirements for such integrated systems, with a focus on problems that hinder current progress toward practical quantum computation. We give suggestions for how materials scientists and trapped-ion technologists can work together to develop materials-based integration and noise-mitigation strategies to enable the next generation of trapped-ion quantum computers.

Analog quantum simulation is expected to be a significant application of near-term quantum devices. Verification of these devices without comparison to known simulation results will be an important task as the system size grows beyond the regime that can be simulated classically. We introduce a set of experimentally-motivated verification protocols for analog quantum simulators, discussing their sensitivity to a variety of error sources and their scalability to larger system sizes. We demonstrate these protocols experimentally using a two-qubit trapped-ion analog quantum simulator and numerically using models of up to five qubits.

We probe electric-field noise in a surface ion trap for ion-surface distances $d$ between 50 and 300 $μ\mathrm{m}$ in the normal and planar directions. We find the noise distance dependence to scale as $d^{-2.6}$ in our trap and a frequency dependence which is consistent with $1/f$ noise. Simulations of the electric-field noise specific to our trap geometry provide evidence that we are not limited by technical noise sources. Our distance scaling data is consistent with a noise correlation length of about 100 $μ\mathrm{m}$ at the trap surface, and we discuss how patch potentials of this size would be modified by the electrode geometry.

We probe electric-field noise near the metal surface of an ion trap chip in a previously unexplored high-temperature regime. We observe a non-trivial temperature dependence with the noise amplitude at 1-MHz frequency saturating around 500~K. Measurements of the noise spectrum reveal a $1/f^{α\approx1}$-dependence and a small decrease in $α$ between low and high temperatures. This behavior can be explained by considering noise from a distribution of thermally-activated two-level fluctuators with activation energies between 0.35~eV and 0.65~eV. Processes in this energy range may be relevant to understanding electric-field noise in ion traps; for example defect motion in the solid state and surface adsorbate binding energies. Studying these processes may aid in identifying the origin of excess electric-field noise in ion traps -- a major source of ion motional decoherence limiting the performance of surface traps as quantum devices.

We describe the design, fabrication, and operation of a novel surface-electrode Paul trap that produces a radio-frequency-null along the axis perpendicular to the trap surface. This arrangement enables control of the vertical trapping potential and consequentially the ion-electrode distance via dc-electrodes only. We demonstrate confinement of single $^{40}$Ca$^+$ ions at heights between $50~μ$m and $300~μ$m above planar copper-coated aluminium electrodes. We investigate micromotion in the vertical direction and show cooling of both the planar and vertical motional modes into the ground state. This trap architecture provides a platform for precision electric-field noise detection, trapping of vertical ion strings without excess micromotion, and may have applications for scalable quantum computers with surface ion traps.

We propose a scheme to read out the spin of a single electron quantum bit in a surface Paul trap using oscillating magnetic field gradients. The readout sequence is composed of cooling, driving, amplification and detection of the electron's motion. We study the scheme in the presence of noise and trap anharmonicities at liquid helium temperatures. An analysis of the the four procedures shows short measurement times ($25~μ$s) and high fidelities ($99.7\%$) are achievable with realistic experimental parameters. Our scheme performs the function of fluorescence detection in ion trapping schemes, highlighting the potential to built all-electric quantum computers based on trapped electron spin qubits.

The detailed characterization of non-trivial coherence properties of composite quantum systems of increasing size is an indispensable prerequisite for scalable quantum computation, as well as for understanding of nonequilibrium many-body physics. Here we show how autocorrelation functions in an interacting system of phonons as well as the quantum discord between distinct degrees of freedoms can be extracted from a small controllable part of the system. As a benchmark, we show this in chains of up to 42 trapped ions, by tracing a single phonon excitation through interferometric measurements of only a single ion in the chain. We observe the spreading and partial refocusing of the excitation in the chain, even on a background of thermal excitations. We further show how this local observable reflects the dynamical evolution of quantum discord between the electronic state and the vibrational degrees of freedom of the probe ion.

Electric field noise in proximity to metallic surfaces is a poorly understood phenomenon that appears in different areas of physics. Trapped ion quantum information processors are particular susceptible to this noise, leading to motional decoherence which ultimately limits the fidelity of quantum operations. On the other hand they present an ideal tool to study this effect, opening new possibilities in surface science. In this work we analyze and measure the polarization of the noise field in a micro-fabricated ion trap for various noise sources. We find that technical noise sources and noise emanating directly from the surface give rise to different degrees of polarization which allows us to differentiate between the two noise sources. Based on this, we demonstrate a method to infer the magnitude of surface noise in the presence of technical noise.

Atomic ions, confined in radio-frequency Paul ion traps, are a promising candidate to host a future quantum information processor. In this letter, we demonstrate a method to couple two motional modes of a single trapped ion, where the coupling mechanism is based on applying electric fields rather than coupling the ion's motion to a light field. This reduces the design constraints on the experimental apparatus considerably. As an application of this mechanism, we cool a motional mode close to its ground state without accessing it optically. As a next step, we apply this technique to measure the mode's heating rate, a crucial parameter determining the trap quality. In principle, this method can be used to realize a two-mode quantum parametric amplifier.

We experimentally study energy transport in chains of trapped ions. We use a pulsed excitation scheme to rapidly add energy to the local motional mode of one of the ions in the chain. Subsequent energy readout allows us to determine how the excitation has propagated throughout the chain. We observe energy revivals that persist for many cycles. We study the behavior with an increasing number of ions of up to 37 in the chain, including a zig-zag configuration. The experimental results agree well with the theory of normal mode evolution. The described system provides an experimental toolbox for the study of thermodynamics of closed systems and energy transport in both classical and quantum regimes.

We use a single ion as an movable electric field sensor with accuracies on the order of a few V/m. For this, we compensate undesired static electric fields in a planar RF trap and characterize the static fields over an extended region along the trap axis. We observe a strong buildup of stray charges around the loading region on the trap resulting in an electric field of up to 1.3 kV/m at the ion position. We also find that the profile of the stray field remains constant over a time span of a few months.

We consider interactions that generate a universal set of quantum gates on logical qubits encoded in a collective-dephasing-free subspace, and discuss their implementations with trapped ions. This allows for the removal of the by-far largest source of decoherence in current trapped-ion experiments, collective dephasing. In addition, an explicit parametrization of all two-body Hamiltonians able to generate such gates without the system's state ever exiting the protected subspace is provided.