arXiv subjects

Tobias Schaetz

Publications and source records attributed to Tobias Schaetz.

35 records · Page 2Linked to original sources

arXiv2017

Optical trapping of ion Coulomb crystals

The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher dimensional systems. Here, we report on the trapping of multiple Barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields. We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal. As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap. Our system provides a platform which is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nano-scale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion. Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one- and two-dimensional crystals.

quant-ph↗

arXiv2017

Simulating spin-boson models with trapped ions

We propose a method to simulate the dynamics of spin-boson models with small crystals of trapped ions where the electronic degree of freedom of one ion is used to encode the spin while the collective vibrational degrees of freedom are employed to form an effective harmonic environment. The key idea of our approach is that a single damped mode can be used to provide a harmonic environment with Lorentzian spectral density. More complex spectral functions can be tailored by combining several individually damped modes. We propose to work with mixed-species crystals such that one species serves to encode the spin while the other species is used to cool the vibrational degrees of freedom to engineer the environment. The strength of the dissipation on the spin can be controlled by tuning the coupling between spin and vibrational degrees of freedom. In this way the dynamics of spin-boson models with macroscopic and non-Markovian environments can be simulated using only a few ions. We illustrate the approach by simulating an experiment with realistic parameters and show by computing quantitative measures that the dynamics is genuinely non-Markovian.

quant-ph↗

arXiv2017

Probing Quantum Memory Effects with High Resolution

Trapped atomic ions enable a precise quantification of the flow of information between internal and external degrees of freedom by employing a non-Markovianity measure [H.-P. Breuer et al., Phys. Rev. Lett. 103, 210401 (2009)]. We reveal that the nature of projective measurements in quantum mechanics leads to a fundamental, nontrivial bias in this measure. We observe and study the functional dependence of this bias to permit a demonstration of applications of local quantum probing. An extension of our approach can act as a versatile reference, relevant for understanding complex systems.

quant-ph↗

arXiv2016

Time-resolved observation of thermalization in an isolated quantum system

We use trapped atomic ions forming a hybrid Coulomb crystal, and exploit its phonons to study an isolated quantum system composed of a single spin coupled to an engineered bosonic environment. We increase the complexity of the system by adding ions and controlling coherent couplings and, thereby, we observe the emergence of thermalization: Time averages of spin observables approach microcanonical averages while related fluctuations decay. Our platform features precise control of system size, coupling strength, and isolation from the external world to explore the dynamics of equilibration and thermalization.

quant-ph↗

arXiv2016

Long lifetimes in optical ion traps

We report on single Barium ions confined in a near-infrared optical dipole trap for up to three seconds in absence of any radio-frequency fields. Additionally, the lifetime in a visible optical dipole trap is increased by two orders of magnitude as compared to the state-of-the-art using an efficient repumping method. We characterize the state-dependent potentials and measure an upper bound for the heating rate in the near-infrared trap. These findings are beneficial for entering the regime of ultracold interaction in atom-ion ensembles exploiting bichromatic optical dipole traps. Long lifetimes and low scattering rates are essential to reach long coherence times for quantum simulations in optical lattices employing many ions, or ions and atoms.

quant-ph↗

arXiv2016

Motional-Mode Analysis of Trapped Ions

We present two methods for characterization of motional-mode configurations that are generally applicable to the weak and strong-binding limit of single or multiple trapped atomic ions. Our methods are essential to realize control of the individual as well as the common motional degrees of freedom. In particular, when implementing scalable radio-frequency trap architectures with decreasing ion-electrode distances, local curvatures of electric potentials need to be measured and adjusted precisely, e.g., to tune phonon tunneling and control effective spin-spin interaction. We demonstrate both methods using single $^{25}$Mg$^+$ ions that are individually confined $40\,μ$m above a surface-electrode trap array and prepared close to the ground state of motion in three dimensions.

quant-ph↗

arXiv2016

Ion trap analogue of particle creation in black holes and cosmology

We consider the transversal modes of ions in a linear radio frequency (rf) trap where we control the time dependent axial confinement to show that we can excite quanta of motion via a two-mode squeezing process. This effect is analogous to phenomena predicted to occur during the evaporation of black holes and cosmological particle creation, in general out of reach for experimental investigation. As substantial advantage of this proposal in comparison to previous ones we propose to exploit radial and axial modes simultaneously to permit experimental access of these effects based on state-of-the-art technology. In addition, we propose to create and explore entanglement, starting with two ions, and relate the results to fundamental aspects of the entropy of black holes.

quant-ph↗

arXiv2015

Freely configurable quantum simulator based on a two-dimensional array of individually trapped ions

A custom-built and precisely controlled quantum system may offer access to a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analog quantum simulator that makes the relevant observables, interactions, and states of a quantum model accessible could permit experimental insight into complex quantum dynamics that are intractable on conventional computers. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here we characterise two-dimensional arrays of three ions trapped by radio-frequency fields in individually controlled harmonic wells forming equilateral triangles with side lengths 40 and 80 micrometer. In our approach, which is scalable to arbitrary two dimensional lattices, we demonstrate individual control of the electronic and motional degrees of freedom, preparation of a fiducial initial state with ion motion close to the ground state, as well as tuning of crucial couplings between ions within experimental sequences. Our work paves the way towards an analog quantum simulator of two-dimensional systems designed at will.

quant-ph↗

arXiv2015

Quantum Transport of Energy in Controlled Synthetic Quantum Magnets

We introduce a scheme that exploits laser cooling and phonon-mediated spin-spin interactions in crystals of trapped atomic ions to explore the transport of energy through a quantum magnet. We show how to implement an effective transport window to control the flow of energy through the magnet even in the absence of fermionic statistics for the carriers. This is achieved by shaping the density of states of the effective thermal reservoirs that arise from the interaction with the external bath of the modes of the electromagnetic field, and can be experimentally controlled by tuning the laser frequencies and intensities appropriately. The interplay of this transport window with the spin-spin interactions is exploited to build an analogue of the Coulomb-blockade effect in nano-scale electronic devices, and opens new possibilities to study quantum effects in energy transport.

quant-ph↗

arXiv2014

A far-off-resonance optical trap for a Ba$^+$ ion

Optical trapping and ions combine unique advantages of independently striving fields of research. Light fields can form versatile potential landscapes, such as optical lattices, for neutral and charged atoms, avoiding detrimental implications of established radiofrequency (rf) traps while mediating interaction via long range Coulomb forces, controlling and detecting motional and electronic states on the quantum level. Here we show optical trapping of $^{138}$Ba$^{+}$ ions in the absence of rf fields in a far-detuned dipole trap, suppressing photon scattering by three and the related recoil heating by four orders of magnitude. To enhance the prospects for optical as well as hybrid traps, we demonstrate a novel method for stray electric field compensation to a level below 9 mV/m. Our results will be relevant, for example, for ion-atom ensembles, to enable four to five orders of magnitude lower common temperatures, accessing the regime of ultracold interaction and chemistry, where quantum effects are predicted to dominate.

physics.atom-ph↗

arXiv2014

Decoherence-assisted spectroscopy of a single Mg$^+$ ion

We describe a high-resolution spectroscopy method, in which the detection of single excitation events is enhanced by a complete loss of coherence of a superposition of two ground states. Thereby, transitions of a single isolated atom nearly at rest are recorded efficiently with high signal-to-noise ratios. Spectra display symmetric line shapes without stray-light background from spectroscopy probes. We employ this method on a $^{25}$Mg$^+$ ion to measure one, two, and three-photon transition frequencies from the 3S ground state to the 3P, 3D, and 4P excited states, respectively. Our results are relevant for astrophysics and searches for drifts of fundamental constants. Furthermore, the method can be extended to other transitions, isotopes, and species. The currently achieved fractional frequency uncertainty of $5 \times 10^{-9}$ is not limited by the method.

physics.atom-ph↗

arXiv2012

Single ions trapped in a one-dimensional optical lattice

We report on three-dimensional optical trapping of single ions in an optical lattice formed by two counter-propagating laser beams. We characterize the trapping parameters of the standing wave using the ion as a sensor stored in a hybrid trap consisting of a radio-frequency (rf), a dc, and the optical potential. When loading ions directly from the rf into the standing-wave trap, we observe a dominant heating rate. Monte Carlo simulations confirm rf-induced parametric excitations within the deep optical lattice as the main source. We demonstrate a way around this effect by an alternative transfer protocol which involves an intermediate step of optical confinement in a single-beam trap avoiding the temporal overlap of the standing wave and the rf field. Implications arise for hybrid (rf/optical) and pure optical traps as platforms for ultra-cold chemistry experiments exploring atom--ion collisions or quantum simulation experiments with ions, or combinations of ions and atoms.

physics.atom-ph↗

arXiv2012

Photon-Assisted-Tunneling Toolbox for Quantum Simulations in Ion Traps

We describe a versatile toolbox for the quantum simulation of many-body lattice models, capable of exploring the combined effects of background Abelian and non-Abelian gauge fields, bond and site disorder, and strong on-site interactions. We show how to control the quantum dynamics of particles trapped in lattice potentials by the photon-assisted tunneling induced by periodic drivings. This scheme is general enough to be applied to either bosons or fermions with the additional advantage of being non-perturbative. It finds an ideal application in microfabricated ion trap arrays, where the quantized vibrational modes of the ions can be described by a quantum lattice model. We present a detailed theoretical proposal for a quantum simulator in that experimental setup, and show that it is possible to explore phases of matter that range from the fractional quantum Hall effect, to exotic strongly-correlated glasses, or flux-lattice models decorated with arbitrary patterns of localized defects.

quant-ph↗

arXiv2011

Influence of static electric fields on an optical ion trap

We recently reported on a proof-of-principle experiment demonstrating optical trapping of an ion in a single-beam dipole trap superimposed by a static electric potential [Nat. Photonics 4, 772--775 (2010)]. Here, we first discuss the experimental procedures focussing on the influence and consequences of the static electric potential. These potentials can easily prevent successful optical trapping, if their configuration is not chosen carefully. Afterwards, we analyse the dipole trap experiments with different analytic models, in which different approximations are applied. According to these models the experimental results agree with recoil heating as the relevant heating effect. In addition, a Monte-Carlo simulation has been developed to refine the analysis. It reveals a large impact of the static electric potential on the dipole trap experiments in general. While it supports the results of the analytic models for the parameters used in the experiments, the analytic models cease their validity for significantly different parameters. Finally, we propose technical improvements for future realizations of experiments with optically trapped ions.

physics.atom-ph↗

arXiv2011

Experimental simulation and limitations of quantum walks with trapped ions

We examine the prospects of discrete quantum walks (QWs) with trapped ions. In particular, we analyze in detail the limitations of the protocol of Travaglione and Milburn (PRA 2002) that has been implemented by several experimental groups in recent years. Based on the first realization in our group (PRL 2009), we investigate the consequences of leaving the scope of the approximations originally made, such as the Lamb--Dicke approximation. We explain the consequential deviations from the idealized QW for different experimental realizations and an increasing number of steps by taking into account higher-order terms of the quantum evolution. It turns out that these become dominant after a few steps already, which is confirmed by experimental results and is currently limiting the scalability of this approach. Finally, we propose a new scheme using short laser pulses, derived from a protocol from the field of quantum computation. We show that the new scheme is not subject to the above-mentioned restrictions, and analytically and numerically evaluate its limitations, based on a realistic implementation with our specific setup. Implementing the protocol with state-of-the-art techniques should allow for substantially increasing the number of steps to 100 and beyond and should be extendable to higher-dimensional QWs.

quant-ph↗

arXiv2011

Many-Body Physics with Trapped Ions

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.

quant-ph↗

arXiv2011

Trapping ions with lasers

This work theoretically addresses the trapping an ionized atom with a single valence electron by means of lasers, analyzing qualitatively and quantitatively the consequences of the net charge of the particle. In our model, the coupling between the ion and the electromagnetic field includes the charge monopole and the internal dipole, within a multipolar expansion of the interaction Hamiltonian. Specifically, we perform a Power-Zienau-Woolley transformation, taking into account the motion of the center of mass. The net charge produces a correction in the atomic dipole which is of order $m_e/M$ with $m_e$ the electron mass and $M$ the total mass of the ion. With respect to neutral atoms, there is also an extra coupling to the laser field which can be approximated by that of the monopole located at the position of the center of mass. These additional effects, however, are shown to be very small compared to the dominant dipolar trapping term.

quant-ph↗