Molecules Atoms Ions Nuclei

Accurate measurements with implications in many branches in Physics have been accessed using Penning traps and conventional techniques within a temperature regime where each eigenmotion of a charged particle is still a classical harmonic oscillator. Cooling the particle directly or indirectly with lasers allows reaching the quantum regime of each oscillator, controlling subtle effects in the precision frontier by detecting photons instead of electric current. In this paper, we present a new in-vacuum optical system designed to detecting 397-nm fluorescence photons from individual calcium ions and Coulomb crystals in a 7-T Penning trap. Based on the outcome of computer simulations, our design shows diffraction-limited performance. The system has been characterized using a single laser-cooled ion as a point-like source, reaching a final resolution of 3.69(3) $μ$m and 2.75(3) $μ$m for the trap's axial and radial directions, respectively, after correcting aberrations.

We use an electric-dipole laser-driven transition to precisely measure the cyclotron-frequency ratios of the pairs $^{42}$Ca$^+$-$^{40}$Ca$^+$, $^{44}$Ca$^+$-$^{40}$Ca$^+$ and $^{48}$Ca$^+$-$^{40}$Ca$^+$ in a 7-tesla Penning trap. A single laser-cooled ($T\approx 1$~mK) ion serves, together with photon-counting and/or photon-imaging units, as a radiofrequency detector covering a broad-band frequency spectrum, in the present case from kHz to a few MHz. Such detectors ($^{40,42,44,48}$Ca$^{\scriptsize{+}}$) allow measuring extremely small forces, with measured normalized sensitivities down to $7.4(3.5)$ yN$/\sqrt{\text{Hz}}$ and $24.9(9.9)$ yN$/\sqrt{\text{Hz}}$ in the MHz and kHz regime, respectively. The direct determination of the ions' amplitudes makes a cyclotron-frequency measurement process more robust against inhomogeneities of the magnetic field and/or deviations of the electric quadrupole field due to mechanical imperfections of the trap.

Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing tools for verifying that a quantum device indeed performed the classically intractable sampling task are either impractical or not scalable to the quantum advantage regime. The verification problem thus remains an outstanding challenge. Here, we experimentally demonstrate efficiently verifiable quantum random sampling in the measurement-based model of quantum computation on a trapped-ion quantum processor. We create and sample from random cluster states, which are at the heart of measurement-based computing, up to a size of 4 x 4 qubits. By exploiting the structure of these states, we are able to recycle qubits during the computation to sample from entangled cluster states that are larger than the qubit register. We then efficiently estimate the fidelity to verify the prepared states -- in single instances and on average -- and compare our results to cross-entropy benchmarking. Finally, we study the effect of experimental noise on the certificates. Our results and techniques provide a feasible path toward a verified demonstration of a quantum advantage.

Transmon qubits are the predominant element in circuit-based quantum information processing, such as existing quantum computers, due to their controllability and ease of engineering implementation. But more than qubits, transmons are multilevel nonlinear oscillators that can be used to investigate fundamental physics questions. Here, they are explored as simulators of excited state quantum phase transitions (ESQPTs), which are generalizations of quantum phase transitions to excited states. We show that the spectral kissing (coalescence of pairs of energy levels) experimentally observed in the effective Hamiltonian of a driven SNAIL-transmon is an ESQPT precursor. We explore the dynamical consequences of the ESQPT, which include the exponential growth of out-of-time-ordered correlators, followed by periodic revivals, and the slow evolution of the survival probability due to localization. These signatures of ESQPT are within reach for current superconducting circuits platforms and are of interest to experiments with cold atoms and ion traps.

The novel application of a piezoelectric quartz resonator for the detection of trapped ions has developed in the observation of the quartz-ions interaction under non-equilibrium conditions, opening new perspectives for high-sensitive motional frequency measurements of radioactive particles. Energized quartz crystals have (long) constant-decay times in the order of milliseconds, permitting the coherent detection of charged particles within short times. In this publication we develop in detail a model governing the interaction between trapped $^{40}$Ca$^+$ ions and a quartz resonator connected to a low-noise amplifier. We apply this model to experimental data and extract relevant information like the coupling constant $g=2π\times 1.449(2)$~Hz and the ions' modified-cyclotron frequency in our 7-tesla Penning trap. The study on the latter is specially important for the use of this resonator in precision Penning-trap mass spectrometry. The improvement in sensitivity can be accomplished by increasing the coupling constant through the quality factor of the resonator. This can develop in the use of the hybrid quartz-ion system for other applications.

A digital quantum simulation for the extended Agassi model is proposed using a quantum platform with eight trapped ions. The extended Agassi model is an analytically solvable model including both short range pairing and long range monopole-monopole interactions with applications in nuclear physics and in other many-body systems. In addition, it owns a rich phase diagram with different phases and the corresponding phase transition surfaces. The aim of this work is twofold: on one hand, to propose a quantum simulation of the model at the present limits of the trapped ions facilities and, on the other hand, to show how to use a machine learning algorithm on top of the quantum simulation to accurately determine the phase of the system. Concerning the quantum simulation, this proposal is scalable with polynomial resources to larger Agassi systems. Digital quantum simulations of nuclear physics models assisted by machine learning may enable one to outperform the fastest classical computers in determining fundamental aspects of nuclear matter.

Two-ion crystals constitute a platform for investigations of quantum nature that can be extended to any ion species or charged particle provided one of the ions in the crystal can be directly laser-cooled and manipulated with laser radiation. This paper presents the formation of two-ion crystals for quantum metrology in a 7-tesla open-ring Penning trap. $^{40}$Ca$^+$ ions are produced either internally by photoionization or externally in a (Paul-trap) source, transported through the strong magnetic field gradient of the superconducting solenoid, and captured in-flight with a mean kinetic energy of a few electronvolts with respect to the minimum of the Penning-trap potential well. Laser cooling of the two-ion crystal in a strong magnetic field towards reaching the quantum regime is also presented with particular emphasis on the cooling of the radial modes.

We present a protocol to produce a class of non-thermal Fock state mixtures in trapped ions. This class of states features a clear metrological advantage with respect to the ground state, thus overcoming the standard quantum limit without the need for full sideband cooling and Fock-state preparation on a narrow electronic transition. The protocol consists in the cyclic repetition of red-sideband, measurement and preparation laser pulses. By means of the Kraus map representation of the protocol, it is possible to relate the length of the red sideband pulses to the specific class of states that can be generated. With the help of numerical simulations, we analyze the parametric regime where these states can be reliably reproduced.

The coherent coupling between a quartz electro-mechanical resonator at room temperature and trapped ions in a 7-tesla Penning trap has been demonstrated for the first time. The signals arising from the coupling remain for integration times in the orders of seconds. From the measurements carried out, we demonstrate that the coupling allows detecting the reduced-cyclotron frequency ($ν_+$) within times below 10~ms and with an improved resolution compared to conventional electronic detection schemes. A resolving power $ν_+/Δν_+=2.4\times10^{7}$ has been reached in single measurements. In this publication we present the first results, emphasizing the novel features of the quartz resonator as fast non-destructive ion-trap detector together with different ways to analyze the data and considering aspects like precision, resolution and sensitivity.

In this article, the dynamics of an unbalanced two-ion crystal comprising the 'target' and the 'sensor' ions confined in a Penning trap has been studied. First, the low amplitude regime is addressed. In this regime, the overall potential including the Coulomb repulsion between the ions can be considered harmonic and the axial, magnetron and reduced-cyclotron modes split up into the so-called 'stretch' and 'common' modes, that are generalizations of the well-known 'breathing' and 'center-of-mass' motions of a balanced crystal made of two ions. By measuring the frequency modes of the crystal and the sensor ion eigenfrequencies using optical detection, it will be possible to determine the target ion's free-cyclotron frequency. The measurement scheme is described and the non-harmonicity of the Coulomb interaction is discussed since this might cause large systematic effects.

Despite its importance to experiments, numerical simulations, and the development of theoretical models, self-averaging in many-body quantum systems out of equilibrium remains underinvestigated. Usually, in the chaotic regime, self-averaging is taken for granted. The numerical and analytical results presented here force us to rethink these expectations. They demonstrate that self-averaging properties depend on the quantity and also on the time scale considered. We show analytically that the survival probability in chaotic systems is not self-averaging at any time scale, even when evolved under full random matrices. We also analyze the participation ratio, Rényi entropies, the spin autocorrelation function from experiments with cold atoms, and the connected spin-spin correlation function from experiments with ion traps. We find that self-averaging holds at short times for the quantities that are local in space, while at long times, self-averaging applies for quantities that are local in time. Various behaviors are revealed at intermediate time scales.

The LPCTrap experiment uses an open Paul trap which was built to enable precision measurements in the beta decay of radioactive ions. The initial goal was the precise measurement of the beta-neutrino angular correlation coefficient in the decay of 6He. Its geometry results from a careful optimization of the harmonic potential created by cylindrical electrodes. It supersedes previously considered geometries that presented a smaller detection solid angle to the beta particle and the recoiling ion. We describe here the methods which were used for the potential optimization, and we present the measured performances in terms of trapping time, cloud size and temperature, and space charge related limits. The properties of the ion cloud at equilibrium are well reproduced by a simple numerical simulation using hard sphere collisions, which additionally gives insights on the trapping loss mechanism. The interpretation for the observed trapping liftetimes is further corroborated by a model recently developed for ion clouds in Paul traps. The open trap shall serve other projects. It is currently used for commissioning purpose in the TRAPSENSOR experiment and is also considered in tests of the Standard Model involving the beta decay of polarized $^{23}$Mg and $^{39}$Ca ion in the frame of the MORA experiment. The latter tests require in-trap polarization of the ions and further optimization of the trapping and detection setup. Based on the results of the simulations and of their interpretations given by the model, different improvements of the trapping setup are discussed.

The Penning-trap electronic-detection technique that offers the precision and sensitivity requested in mass spectrometry for fundamental studies in nuclear and particle physics has not been proven yet to be universal. This has motivated the construction of a Penning-trap facility aiming at the implementation of a novel detection method, consisting in measuring motional frequencies of singly-charged trapped ions in strong magnetic fields, through the fluorescence photons from the 4s$^2$S$_{1/2}\rightarrow $4p$^2$P$_{1/2}$ atomic transition in $^{40}$Ca$^+$. The key element of this facility is an open-ring Penning trap, built and fully characterized, which is coupled upstream to a preparation Penning trap similar to those built at Radioactive Ion Beam facilities. Motional frequency measurements of trapped ions stored in the open-ring trap have been carried out by applying external dipolar and quadrupolar fields in resonance with the ions' eigenmotions, in combination with time-of-flight identification. The infrastructure to observe the fluorescence photons from $^{40}$Ca$^+$, comprising the twelve laser beams needed in 7~Tesla, and a two-meters long system to register the image in a high-sensitive CCD sensor, has also been successfully tested by observing optically the trapped $^{40}$Ca$^+$ ions. This demonstrates the capabilities of this facility for the proposed laser-based mass-spectrometry technique, and introduces it as a unique platform to perform laser-spectroscopy experiments with implications in different fields of physics.

A single-ion reservoir has been tested, and characterized in order to be used as a highly sensitive optical detector of electric signals arriving at the trapping electrodes. Our system consists of a single laser-cooled $^{40}$Ca$^+$ ion stored in a Paul trap with rotational symmetry. The performance is observed through the axial motion of the ion, which is equivalent to an underdamped and forced oscillator. Thus, the results can be projected also to Penning traps. We have found that, for an ion oscillator temperature $T_{\scriptsize{\rm axial}}\lesssim 10$~mK in the forced-frequency range $ω_z =2π\times (80,200$~kHz), the reservoir is sensitive to a time-varying electric field equivalent to an electric force of $5.3(2)$~neV/$μ$m, for a measured quality factor $Q=3875(45)$, and a decay time constant $γ_z=88(2)$~s$^{-1}$. This method can be applied to measure optically the strength of an oscillating field or induced (driven) charge in this frequency range within times of tens of milliseconds. Furthermore the ion reservoir has been proven to be sensitive to electrostatic forces by measuring the ion displacement. Since the heating rate is below $0.3$~$μ$eV/s, this reservoir might be used as optical detector for any ion or bunch of charged particles stored in an adjacent trap.

An open-ring ion trap, also referred to as transparent trap was initially built up to perform $β$-$ν$ correlation experiments with radioactive ions. This trap geometry is also well suited to perform experiments with laser-cooled ions, serving for the development of a new type of Penning trap, in the framework of the project TRAPSENSOR at the University of Granada. The goal of this project is to use a single $^{40}$Ca$^+$ ion as detector for single-ion mass spectrometry. Within this project and without any modification to the initial electrode configuration, it was possible to perform Doppler cooling on $^{40}$Ca$^+$ ions, starting from large clouds and reaching single ion sensitivity. This new feature of the trap might be important also for other experiments with ions produced at Radioactive Ion Beam (RIB) facilities. In this publication, the trap and the laser system will be described, together with their performance with respect to laser cooling applied to large ion clouds down to a single ion.