H. Häffner

Quantum statistics have a profound impact on the properties of systems composed of identical particles. In this Letter, we demonstrate that the quantum statistics of a pair of identical massive particles can be probed by a direct measurement of the exchange symmetry of their wave function even in conditions where the particles always remain spatially well separated and thus the exchange contribution to their interaction energy is negligible. We present two protocols revealing the bosonic or fermionic nature of a pair of particles and discuss possible implementations with a pair of trapped atoms or ions.

We report on the design of a cryogenic setup for trapped ion quantum computing containing a segmented surface electrode trap. The heat shield of our cryostat is designed to attenuate alternating magnetic field noise, resulting in 120~dB reduction of 50~Hz noise along the magnetic field axis. We combine this efficient magnetic shielding with high optical access required for single ion addressing as well as for efficient state detection by placing two lenses each with numerical aperture 0.23 inside the inner heat shield. The cryostat design incorporates vibration isolation to avoid decoherence of optical qubits due to the motion of the cryostat. We measure vibrations of the cryostat of less than $\pm$20~nm over 2~s. In addition to the cryogenic apparatus, we describe the setup required for an operation with $^{\mathrm{40}}$Ca$^{\mathrm{+}}$ and $^{\mathrm{88}}$Sr$^{\mathrm{+}}$ ions. The instability of the laser manipulating the optical qubits in $^{\mathrm{40}}$Ca$^{\mathrm{+}}$ is characterized yielding a minimum of its Allan deviation of 2.4$\cdot$10$^{\mathrm{-15}}$ at 0.33~s. To evaluate the performance of the apparatus, we trapped $^{\mathrm{40}}$Ca$^{\mathrm{+}}$ ions, obtaining a heating rate of 2.14(16)~phonons/s and a Gaussian decay of the Ramsey contrast with a 1/e-time of 18.2(8)~ms.

Electric noise from metallic surfaces is a major obstacle towards quantum applications with trapped ions due to motional heating of the ions. Here, we discuss how the same noise source can also lead to pure dephasing of motional quantum states. The mechanism is particularly relevant at small ion-surface distances, thus imposing a new constraint on trap miniaturization. By means of a free induction decay experiment, we measure the dephasing time of the motion of a single ion trapped 50~$μ$m above a Cu-Al surface. From the dephasing times we extract the integrated noise below the secular frequency of the ion. We find that none of the most commonly discussed surface noise models for ion traps describes both, the observed heating as well as the measured dephasing, satisfactorily. Thus, our measurements provide a benchmark for future models for the electric noise emitted by metallic surfaces.

We present measurements of resistive and sympathetic cooling of ion clouds confined in a Penning trap. For resistive cooling of a cloud consisting of one ion species, we observe a significant deviation from exponential cooling behavior which is explained by an energy-transfer model. The observed sympathetic cooling of simultaneously confined ion species shows a quadratic dependence on the ion charge state and is hence in agreement with expectations from the physics of dilute non-neutral plasmas.

We report room-temperature electric field noise measurements combined with in-situ surface characterization and cleaning of a microfabricated ion trap. We used a single-ion electric field noise sensor in combination with surface cleaning and analysis tools, to investigate the relationship between electric field noise from metal surfaces in vacuum and the composition of the surface. These experiments were performed in a novel setup that integrates ion trapping capabilities with surface analysis tools. We find that surface cleaning of an aluminum-copper surface significantly reduces the level of electric field noise, but the surface does not need to be atomically clean to show noise levels comparable to those of the best cryogenic traps. The post-cleaning noise levels are low enough to allow fault-tolerant trapped-ion quantum information processing on a microfabricated surface trap.

We report heating rate measurements in a microfabricated gold-on-sapphire surface electrode ion trap with trapping height of approximately 240 micron. Using the Doppler recooling method, we characterize the trap heating rates over an extended region of the trap. The noise spectral density of the trap falls in the range of noise spectra reported in ion traps at room temperature. We find that during the first months of operation the heating rates increase by approximately one order of magnitude. The increase in heating rates is largest in the ion loading region of the trap, providing a strong hint that surface contamination plays a major role for excessive heating rates. We discuss data found in the literature and possible relation of anomalous heating to sources of noise and dissipation in other systems, namely impurity atoms adsorbed on metal surfaces and amorphous dielectrics.

Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate within a decoherence-free, scalable quantum computer.

There has been much interest in developing methods for transferring quantum information. We discuss a way to transfer quantum information between two trapped ions through a wire. The motion of a trapped ion induces oscillating charges in the trap electrodes. By sending this current to the electrodes of a nearby second trap, the motions of ions in the two traps are coupled. We investigate the electrostatics of a set-up where two separately trapped ions are coupled through an electrically floating wire. We also discuss experimental issues, including possible sources of decoherence.

We propose the implementation of a geometric-phase gate on magnetic-field-insensitive qubits with $\hatσ^z$-dependent forces for trapped ion quantum computing. The force is exerted by two laser beams in a Raman configuration. Qubit-state dependency is achieved by a small frequency detuning from the virtually-excited state. Ion species with excited states of long radiative lifetimes are used to reduce the chance of a spontaneous photon emission to less than 10$^{-8}$ per gate-run. This eliminates the main source of gate infidelity of previous implementations. With this scheme it seems possible to reach the fault tolerant threshold.

We report measurements of the lifetimes of the 3d $^2$D$_{5/2}$ and 3d $^2$D$_{3/2}$ metastable states of a single laser-cooled $^{40}$Ca$^+$ ion in a linear Paul trap. We introduce a new measurement technique based on high-efficiency quantum state detection after coherent excitation to the D$_{5/2}$ state or incoherent shelving in the D$_{3/2}$ state, and subsequent free, unperturbed spontaneous decay. The result for the natural lifetime of the D$_{5/2}$ state of 1168(9) ms agrees excellently with the most precise published value. The lifetime of the D$_{3/2}$ state is measured with a single ion for the first time and yields 1176(11) ms which improves the statistical uncertainty of previous results by a factor of four. We compare these experimental lifetimes to high-precision ab initio all order calculations and find a very good agreement. These calculations represent an excellent test of high-precision atomic theory and will serve as a benchmark for the study of parity nonconservation in Ba$^+$ which has similar atomic structure.

We report the realization of an elementary quantum processor based on a linear crystal of trapped ions. Each ion serves as a quantum bit (qubit) to store the quantum information in long lived electronic states. We present the realization of single-qubit and of universal two-qubit logic gates. The qwo-qubit operation relies on the coupling of the ions through their collective quantized motion. A detailed description of the setup and the methods is included.