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F. Schmidt-Kaler

Publications and source records attributed to F. Schmidt-Kaler.

At least 37 records · Page 2Linked to original sources
arXiv2016

Towards Rydberg quantum logic with trapped ions

We demonstrate the excitation of ions to the Rydberg state $22F$ by vacuum ultraviolet radiation at a wavelength of $123\,\text{nm}$ combined with the coherent manipulation of the optical qubit transition in $^{40}\text{Ca}^+$. With a tightly focused beam at $729\,\text{nm}$ wavelength we coherently excite a single ion from a linear string into the metastable $3D_{5/2}$ state before a VUV pulse excites it to the Rydberg state. In combination with ion shuttling in the trap, we extend this approach to the addressed excitation of multiple ions. The coherent initialization as well as the addressed Rydberg excitation are key prerequisites for more complex applications of Rydberg ions in quantum simulation or quantum information processing.

quant-ph↗
arXiv2015

Measurement of dipole matrix elements with a single trapped ion

We demonstrate a new method for the direct measurement of atomic dipole transition matrix elements based on techniques developed for quantum information purposes. The scheme consists of measuring dispersive and absorptive off-resonant light-ion interactions and is applicable to many atomic species. We determine the dipole matrix element pertaining to the Ca II H line, i.e. the 4$^2$S$_{1/2} \leftrightarrow $ 4$^2$P$_{1/2}$ transition of $^{40}$Ca$^+$, for which we find the value 2.8928(43) ea$_0$. Moreover, the method allows us to deduce the lifetime of the 4$^2$P$_{1/2}$ state to be 6.904(26) ns, which is in agreement with predictions from recent theoretical calculations and resolves a longstanding discrepancy between calculated values and experimental results.

quant-ph↗
arXiv2015

Rydberg excitation of a single trapped ion

We demonstrate excitation of a single trapped cold $^{40}$Ca$^+$ ion to Rydberg levels by laser radiation in the vacuum-ultraviolet at 122 nm wavelength. Observed resonances are identified as 3d$^2$D$_{3/2}$ to 51 F, 52 F and 3d$^2$D$_{5/2}$ to 64F. We model the lineshape and our results imply a large state-dependent coupling to the trapping potential. Rydberg ions are of great interest for future applications in quantum computing and simulation, in which large dipolar interactions are combined with the superb experimental control offered by Paul traps.

quant-ph↗
arXiv2015

Two-dimensional spectroscopy for the study of ion Coulomb crystals

Ion Coulomb crystals are currently establishing themselves as a highly controllable test-bed for mesoscopic systems of statistical mechanics. The detailed experimental interrogation of the dynamics of these crystals however remains an experimental challenge. In this work, we show how to extend the concepts of multi-dimensional nonlinear spectroscopy to the study of the dynamics of ion Coulomb crystals. The scheme we present can be realized with state-of-the-art technology and gives direct access to the dynamics, revealing nonlinear couplings even in the presence of thermal excitations. We illustrate the advantages of our proposal showing how two-dimensional spectroscopy can be used to detect signatures of a structural phase transition of the ion crystal, as well as resonant energy exchange between modes. Furthermore, we demonstrate in these examples how different decoherence mechanisms can be identified.

quant-ph↗
arXiv2014

Generalised Kronig-Penney model for ultracold atomic quantum systems

We study the properties of a quantum particle interacting with a one dimensional structure of equidistant scattering centres. We derive an analytical expression for the dispersion relation and for the Bloch functions in the presence of both even and odd scattering waves within the pseudopotential approximation. This generalises the well-known solid-state physics text-book result known as the Kronig-Penney model. Our generalised model can be used to describe systems such as degenerate Fermi gases interacting with ions or with another neutral atomic species confined in an optical lattice, thus enabling the investigation of polaron or Kondo physics within a simple formalism. We focus our attention on the specific atom-ion system and compare our findings with quantum defect theory. Excellent agreement is obtained within the regime of validity of the pseudopotential approximation. This enables us to derive a Bose-Hubbard Hamiltonian for a degenerate quantum Bose gas in a linear chain of ions.

quant-ph↗
arXiv2014

Observation of the Kibble-Zurek scaling law for defect formation in ion crystals

Traversal of a symmetry-breaking phase transition at a finite rate can lead to causallyseparated regions with incompatible symmetries and the formation of defects at their boundaries. The defect formation follows universal scaling laws prescribed by the Kibble-Zurek mechanism (KZM) important to the study of phase transitions in fields as diverse as quantum and statistical mechanics, condensed matter physics and cosmology. Here, we observe the KZM in a crystal of cold trapped ions, which is conducive to the precise control of structural phases and the detection of defects. The experiment confirms a scaling law with an exponent of 2.68 +/- 0.06, as predicted from the KZM in the finite inhomogeneous case. Such precision makes it feasible to use ion crystals for quantitative tests of classical and quantum statistical mechanics.

quant-ph↗
arXiv2014

Fast shuttling of a trapped ion in the presence of noise

We theoretically investigate the motional excitation of a single ion caused by spring-constant and position uctuations of a harmonic trap during trap shuttling processes. A detailed study of the sensitivity on noise for several transport protocols and noise spectra is provided. The effect of slow spring-constant drifts is also analyzed. Trap trajectories that minimize the excitation are designed combining invariant-based inverse engineering, perturbation theory, and optimal control.

quant-ph↗
arXiv2014

Dynamics and control of fast ion crystal splitting in segmented Paul traps

We theoretically investigate the process of splitting two-ion crystals in segmented Paul traps, i.e. the structural transition from two ions confined in a common well to ions confined in separate wells. The precise control of this process by application of suitable voltage ramps to the trap segments is non-trivial, as the harmonic confinement transiently vanishes during the process. This makes the ions strongly susceptible to background electric field noise, and to static offset fields in the direction of the trap axis. We analyze the reasons why large energy transfers can occur, which are impulsive acceleration, the presence of residual background fields and enhanced anomalous heating. For the impulsive acceleration, we identify the diabatic and adiabatic regimes, which are characterized by different scaling behavior of the energy transfer with respect to time. We propose a suitable control scheme based on experimentally accessible parameters. Simulations are used to verify both the high sensitivity of the splitting result and the performance of our control scheme. Finally, we analyze the impact of trap geometry parameters on the crystal splitting process.

physics.atom-ph↗
arXiv2013

Controlling the transport of an ion: Classical and quantum mechanical solutions

We investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

quant-ph↗
arXiv2013

Emulating Solid-State Physics with a Hybrid System of Ultracold Ions and Atoms

We propose and theoretically investigate a hybrid system composed of a crystal of trapped ions coupled to a cloud of ultracold fermions. The ions form a periodic lattice and induce a band structure in the atoms. This system combines the advantages of scalability and tunability of ultracold atomic systems with the high fidelity operations and detection offered by trapped ion systems. It also features close analogies to natural solid-state systems, as the atomic degrees of freedom couple to phonons of the ion lattice, thereby emulating a solid-state system. Starting from the microscopic many-body Hamiltonian, we derive the low energy Hamiltonian including the atomic band structure and give an expression for the atom-phonon coupling. We discuss possible experimental implementations such as a Peierls-like transition into a period-doubled dimerized state.

cond-mat.quant-gas↗
arXiv2013

Mode shaping in mixed ion crystals of 40Ca2+ and 40Ca+

We present studies of mixed Coulomb crystals of 40Ca+ and 40Ca2+ ions in a linear Paul trap. Doubly charged ions are produced by photoionisation of trapped 40Ca+ with a vacuum ultraviolet laser source and sympathetically cooled via Doppler cooled 40Ca+ ions. We investigate experimentally and theoretically the structural configurations and the vibrational modes of these mixed crystals. Our results with 40Ca2+ are an important step towards experimental realization of the proposals for mode shaping in a linear crystal and spin-dependent configuration changes from zigzag to linear as proposed by Li et al., Phys. Rev. A 87, (2013) 052304 and Phys. Rev. Lett 108, (2012) 023003 using ions excited to Rydberg states.

quant-ph↗
arXiv2013

Precise Experimental Investigation of Eigenmodes in a Planar Ion Crystal

The accurate characterization of eigenmodes and eigenfrequencies of two-dimensional ion crystals provides the foundation for the use of such structures for quantum simulation purposes. We present a combined experimental and theoretical study of two-dimensional ion crystals. We demonstrate that standard pseudopotential theory accurately predicts the positions of the ions and the location of structural transitions between different crystal configurations. However, pseudopotential theory is insufficient to determine eigenfrequencies of the two-dimensional ion crystals accurately but shows significant deviations from the experimental data obtained from resolved sideband spectroscopy. Agreement at the level of 2.5 x 10^(-3) is found with the full time-dependent Coulomb theory using the Floquet-Lyapunov approach and the effect is understood from the dynamics of two-dimensional ion crystals in the Paul trap. The results represent initial steps towards an exploitation of these structures for quantum simulation schemes.

quant-ph↗
arXiv2012

Shot-noise limited monitoring and phase locking of the motion of a single trapped ion

We perform high-resolution real-time read-out of the motion of a single trapped and laser-cooled Ba ion. By using an interferometric setup we demonstrate shot-noise limited measurement of thermal oscillations with resolution of 4 times the standard quantum limit. We apply the real-time monitoring for phase control of the ion motion through a feedback loop, suppressing the photon recoil-induced phase diffusion. Due to the spectral narrowing in phase-locked mode, the coherent ion oscillation is measured with resolution of about 0.3 times the standard quantum limit.

quant-ph↗
arXiv2012

Quantum Magnetism of Spin-Ladder Compounds with Trapped-Ion Crystals

The quest for experimental platforms that allow for the exploration, and even control, of the interplay of low dimensionality and frustration is a fundamental challenge in several fields of quantum many-body physics, such as quantum magnetism. Here, we propose the use of cold crystals of trapped ions to study a variety of frustrated quantum spin ladders. By optimizing the trap geometry, we show how to tailor the low dimensionality of the models by changing the number of legs of the ladders. Combined with a method for selectively hiding of ions provided by laser addressing, it becomes possible to synthesize stripes of both triangular and Kagome lattices. Besides, the degree of frustration of the phonon-mediated spin interactions can be controlled by shaping the trap frequencies. We support our theoretical considerations by initial experiments with planar ion crystals, where a high and tunable anisotropy of the radial trap frequencies is demonstrated. We take into account an extensive list of possible error sources under typical experimental conditions, and describe explicit regimes that guarantee the validity of our scheme.

quant-ph↗
arXiv2012

A bosonic Josephson junction controlled by a single trapped ion

We theoretically investigate the properties of a double-well bosonic Josephson junction coupled to a single trapped ion. We find that the coupling between the wells can be controlled by the internal state of the ion, which can be used for studying mesoscopic entanglement between the two systems and to measure their interaction with high precision. As a particular example we consider a single $^{87}$Rb atom and a small Bose-Einstein condensate controlled by a single $^{171}$Yb$^+$ ion. We calculate inter-well coupling rates reaching hundreds of Hz, while the state dependence amounts to tens of Hz for plausible values of the currently unknown s-wave scattering length between the atom and the ion. The analysis shows that it is possible to induce either the self-trapping or the tunneling regime, depending on the internal state of the ion. This enables the generation of large scale ion-atomic wavepacket entanglement within current technology.

quant-ph↗
arXiv2012

Entangled states of trapped ions allow measuring the magnetic field gradient of a single atomic spin

Using trapped ions in an entangled state we propose detecting a magnetic dipole of a single atom at distance of a few $μ$m. This requires a measurement of the magnetic field gradient at a level of about 10$^{-13}$ Tesla/$μ$m. We discuss applications e.g. in determining a wide variation of ionic magnetic moments, for investigating the magnetic substructure of ions with a level structure not accessible for optical cooling and detection,and for studying exotic or rare ions, and molecular ions. The scheme may also be used for measureing spin imbalances of neutral atoms or atomic ensembles trapped by optical dipole forces. As the proposed method relies on techniques well established in ion trap quantum information processing it is within reach of current technology.

quant-ph↗
arXiv2011

Frustrated Quantum Spin Models with Cold Coulomb Crystals

We exploit the geometry of a zig-zag cold-ion crystal in a linear trap to propose the quantum simulation of a paradigmatic model of long-ranged magnetic frustration. Such a quantum simulation would clarify the complex features of a rich phase diagram that presents ferromagnetic, dimerized antiferromagnetic, paramagnetic, and floating phases, together with previously unnoticed features that are hard to assess by numerics. We analyze in detail its experimental feasibility, and provide supporting numerical evidence on the basis of realistic parameters in current ion-trap technology.

quant-ph↗