We demonstrate the implementation of a spin qubit with a single Ca ion in a micro ion trap. The qubit is encoded in the Zeeman ground state levels mJ=+1/2 and mJ=-1/2 of the S1/2 state of the ion. We show sideband cooling close to the vibrational ground state and demonstrate the initialization and readout of the qubit levels with 99.5% efficiency. We employ a Raman transition close to the S1/2 - P1/2 resonance for coherent manipulation of the qubit. We observe single qubit rotations with 96% fidelity and gate times below 5mus. Rabi oscillations on the blue motional sideband are used to extract the phonon number distribution. The dynamics of this distribution is analyzed to deduce the trap-induced heating rate of 0.3(1) phonons/ms.
The analysis of traps, i.e., locally but not globally optimal controls, for quantum control systems has attracted a great interest in recent years. The central problem that has been remained open is to demonstrate for a given system either existence or absence of traps. We prove the absence of traps and hence completely solve this problem for the important tasks of unconstrained manipulation of the transition probability and unitary gate generation in the Landau-Zener system---a system with a wide range of applications across physics, chemistry and biochemistry. This finding provides the first…
The beam splitter and phase shifter, which are the key elements in the experiments of light interference, are realized in the motion of trapped ions. Some applications, such as the creation of quantum motional states and the realization of Mach-Zehnder interferometer, are illustrated. Several detection methods of motional states used in the interferometer are also discussed.
In this work we study extrema of objective functionals for ultrafast manipulation by a qubit. Traps are extrema of the objective functionals which are optimal for manipulation by quantum systems only locally but not globally. Much effort in prior works was devoted to the analysis of traps for quantum systems controlled by long enough laser pulses and, for example, manipulation by a qubit with long control pulses was shown to be trap-free. Ultrafast femtosecond and attosecond control becomes now widely applicable that motivates the necessity for the analysis of traps on the ultrafast time scale…
We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of 171Yb+, with a measured coherence time of 2.5 seconds. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.
We propose shortcuts to adiabaticity which achieve fast and stable control of the state of a charged particle in an electromagnetic field. In particular we design a non-adiabatic change of the magnetic field strength in a Penning trap which changes the radial spread without final excitations. We apply a streamlined version of the fast-forward formalism as well as an invariant based inverse engineering approach. We compare both methods and examine their stability.
We demonstrate Rabi flopping at MHz rates between ground hyperfine states of neutral $^{87}$Rb atoms that are trapped in two micron sized optical traps. Using tightly focused laser beams we demonstrate high fidelity, site specific Rabi rotations with crosstalk on neighboring sites separated by $8 μ\rm m$ at the level of $10^{-3}$. Ramsey spectroscopy is used to measure a dephasing time of $870 μ\rm s$ which is $\approx$ 5000 times longer than the time for a $π/2$ pulse.
We demonstrate a two-dimensional 11-zone ion trap array, where individual laser-cooled atomic ions are stored, separated, shuttled, and swapped. The trap geometry consists of two linear rf ion trap sections that are joined at a 90 degree angle to form a T-shaped structure. We shuttle a single ion around the corners of the T-junction and swap the positions of two crystallized ions using voltage sequences designed to accommodate the nontrivial electrical potential near the junction. Full two-dimensional control of multiple ions demonstrated in this system may be crucial for the realization of sc…
A single laser-cooled and trapped 9Be+ ion is used to investigate methods of coherent quantum-state synthesis and quantum logic. We create and characterize nonclassical states of motion including "Schroedinger-cat" states. A fundamental quantum logic gate is realized which uses two states of the quantized ion motion and two ion internal states as qubits. We explore some of the applications for, and problems in realizing, quantum computation based on multiple trapped ions.
We use microwave induced adiabatic passages for selective spin flips within a string of optically trapped individual neutral Cs atoms. We position-dependently shift the atomic transition frequency with a magnetic field gradient. To flip the spin of a selected atom, we optically measure its position and sweep the microwave frequency across its respective resonance frequency. We analyze the addressing resolution and the experimental robustness of this scheme. Furthermore, we show that adiabatic spin flips can also be induced with a fixed microwave frequency by deterministically transporting the …
Methods for, and limitations to, the generation of entangled states of trapped atomic ions are examined. As much as possible, state manipulations are described in terms of quantum logic operations since the conditional dynamics implicit in quantum logic is central to the creation of entanglement. Keeping with current interest, some experimental issues in the proposal for trapped-ion quantum computation by I. Cirac and P. Zoller (University of Innsbruck) are discussed. Several possible decoherence mechanisms are examined and what may be the more important of these are identified. Some potential…
We trap individual $^{171}$Yb$^+$ ions in a surface trap microfabricated on a silicon substrate, and demonstrate a complete set of high fidelity single qubit operations for the hyperfine qubit. Trapping times exceeding 20 minutes without laser cooling, and heating rates as low as 0.8(0.1) quanta/ms indicate stable trapping conditions in these microtraps. A coherence time of more than one second, high fidelity qubit state detection and single qubit rotations are demonstrated.
We report new techniques for driving high-fidelity stimulated Raman transitions in trapped ion qubits. An electro-optic modulator induces sidebands on an optical source, and interference between the sidebands allows coherent Rabi transitions to be efficiently driven between hyperfine ground states separated by 14.53 GHz in a single trapped 111Cd+ ion.
We experimentally demonstrate the coherent manipulation of atomic states in far-detuned dipole traps and registers of dipole traps based on two-dimensional arrays of microlenses. By applying Rabi, Ramsey, and spin-echo techniques, we systematically investigate the dephasing mechanisms and determine the coherence time. Simultaneous Ramsey measurements in up to 16 dipole traps are performed and proves the scalability of our approach. This represents an important step in the application of scalable registers of atomic qubits for quantum information processing. In addition, this system can serve a…
We have cooled a two-ion-crystal to the ground state of its collective modes of motion. Laser cooling, more specific resolved sideband cooling is performed sympathetically by illuminating only one of the two $^{40}$Ca$^+$ ions in the crystal. The heating rates of the motional modes of the crystal in our linear trap have been measured, and we found them considerably smaller than those previously reported by Q. Turchette {\em et. al.} Phys. Rev. A 61, 063418 (2000) in the case of trapped $^9$Be$^+$ ions. After the ground state is prepared, coherent quantum state manipulation of the atomic popula…
We trap atoms in versatile two-dimensional (2D) arrays of optical potentials, prepare flexible 2D spin configurations, perform site-selective coherent manipulation, and demonstrate the implementation of simultaneous measurements of different system properties, such as dephasing and decoherence. This novel approach for the flexible manipulation of atomic quantum systems is based on the combination of 2D arrays of microlenses and 2D arrays of liquid crystal light modulators. It offers novel types of control for the investigation of quantum degenerate gases, quantum information processing, and qu…
We present an optical system designed to capture and observe a single neutral atom in an optical dipole trap, created by focussing a laser beam using a large numerical aperture N.A.=0.5 aspheric lens. We experimentally evaluate the performance of the optical system and show that it is diffraction limited over a broad spectral range (~ 200 nm) with a large transverse field (+/- 25 microns). The optical tweezer created at the focal point of the lens is able to trap single atoms of 87Rb and to detect them individually with a large collection efficiency. We measure the oscillation frequency of the…
Topological features in quantum computing provide controllability and noise error avoidance in the performance of logical gates. While such resilience is favored in the manipulation of quantum systems, it is very hard to identify topological features in nature. This paper proposes a scheme where holonomic quantum gates have intrinsic topological features. An ion trap is employed where the vibrational modes of the ions are coherently manipulated with lasers in an adiabatic cyclic way producing geometrical holonomic gates. A crucial ingredient of the manipulation procedures is squeezing of the v…
Physical systems must fulfill a number of conditions to qualify as useful quantum bits (qubits) for quantum information processing, including ease of manipulation, long decoherence times, and high fidelity readout operations. Since these conditions are hard to satisfy with a single system, it may be necessary to combine different degrees of freedom. Here we discuss a possible system, based on electronic and nuclear spin degrees of freedom in trapped ions. The nuclear spin yields long decoherence times, while the electronic spin, in a magnetic field gradient, provides efficient manipulation, an…
We consider an atomic Bose-Einstein condensate trapped in a symmetric one-dimensional double well potential in the four-mode approximation and show that the semiclassical dynamics of the two ground state modes can be strongly influenced by a macroscopic occupation of the two excited modes. In particular, the addition of the two excited modes already unveils features related to the effect of dissipation on the condensate. In general, we find a rich dynamics that includes Rabi oscillations, a mixed Josephson-Rabi regime, self-trapping, chaotic behavior, and the existence of fixed points. We inve…
We experimentally realize an enhanced Raman control scheme for neutral atoms that features an intrinsic suppression of the two-photon carrier transition, but retains the sidebands which couple to the external degrees of freedom of the trapped atoms. This is achieved by trapping the atom at the node of a blue detuned standing wave dipole trap, that acts as one field for the two-photon Raman coupling. The improved ratio between cooling and heating processes in this configuration enables a five times lower fundamental temperature limit for resolved sideband cooling. We apply this method to perfor…
A single Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.9% probability. Starting from this Fock state |n=0> we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations within 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the |n=1> Fock state. The coherence of optical state manipulation is only limited by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.
We explain the meaning of dynamical manipulation, and we illustrate its mechanism by using a system composed of a charged particle in a Penning trap. It is shown that by means of appropriate electric shocks (delta-like pulses) applied to the trap walls one can induce the squeezing transformation. The geometric phases associated to some cyclic evolutions, induced either by the standard fields of the Penning trap or by the superposition of these plus a rotating magnetic field, are analysed
Advanced techniques for manipulation of internal states, standard in atomic physics, are demonstrated for a charged molecular species for the first time. We address individual hyperfine states of ro-vibrational levels of a diatomic ion by optical excitation of individual hyperfine transitions, and achieve controlled transfer of population into a selected hyperfine state. We use molecular hydrogen ions (HD^{+}) as a model system and employ a novel frequency-comb-based, continuous-wave 5 \mum laser spectrometer. The achieved spectral resolution is the highest obtained so far in the optical domai…
This article provides an introduction to one of the most efficient laser stabilization techniques - the Pound-Drever-Hall (PDH) method. The aim of the experiment is to build the PDH stabilization apparatus from scratch. I describe all the necessary theoretical treatment to formulate the technique and then describe it as I have experimentally implemented in the lab. All major sources of noise are discussed and noise tackling methods are implemented. All the equipments used are also described in detail for their principle and working.
Neutral atoms trapped by laser light are amongst the most promising candidates for storing and processing information in a quantum computer or simulator. The application certainly calls for a scalable and flexible scheme for addressing and manipulating the atoms. We have now made this a reality by implementing a fast and versatile method to dynamically control the position of neutral atoms trapped in optical tweezers. The tweezers result from a spatial light modulator (SLM) controlling and shaping a large number of optical dipole-force traps. Trapped atoms adapt to any change in the potential …
We propose to apply atom-chip techniques to the trapping of a single atom in a circular Rydberg state. The small size of microfabricated structures will allow for trap geometries with microwave cut-off frequencies high enough to inhibit the spontaneous emission of the Rydberg atom, paving the way to complete control of both external and internal degrees of freedom over very long times. Trapping is achieved using carefully designed electric fields, created by a simple pattern of electrodes. We show that it is possible to excite, and then trap, one and only one Rydberg atom from a cloud of groun…
This submission is an introduction to microfabricated ion traps. We cover the basics of Paul traps, various geometries for realizing the traps, a number of design considerations, and, finally, a review of existing microfabricated traps.
Nitrogen vacancy (NV) centers in diamond are promising elemental blocks for quantum optics [1, 2], spin-based quantum information processing [3, 4], and high-resolution sensing [5-13]. Yet, fully exploiting these capabilities of single NV centers requires strategies to accurately manipulate them. Here, we use optical tweezers as a tool to achieve deterministic trapping and 3D spatial manipulation of individual nano-diamonds hosting a single NV spin. Remarkably, we find the NV axis is nearly fixed inside the trap and can be controlled in-situ, by adjusting the polarization of the trapping light…
Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap is the prerequisite for quantum information experiments with trapped ions. With resolved sideband cooling on the optical S1/2 - D5/2 quadrupole transition we have cooled one and two 40Ca+ ions to the ground state of vibration with up to 99.9% probability. With a novel cooling scheme utilizing electromagnetically induced transparency on the S1/2 - P1/2 manifold we have achieved simultaneous ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the motional ground state we have demonstrated coherent…
Ion traps offer the opportunity to study fundamental quantum systems with high level of accuracy highly decoupled from the environment. Individual atomic ions can be controlled and manipulated with electric fields, cooled to the ground state of motion with laser cooling and coherently manipulated using optical and microwave radiation. Microfabricated ion traps hold the advantage of allowing for smaller trap dimensions and better scalability towards large ion trap arrays also making them a vital ingredient for next generation quantum technologies. Here we provide an introduction into the princi…
We characterise the performance of a surface-electrode ion "chip" trap fabricated using established semiconductor integrated circuit and micro-electro-mechanical-system (MEMS) microfabrication processes which are in principle scalable to much larger ion trap arrays, as proposed for implementing ion trap quantum information processing. We measure rf ion micromotion parallel and perpendicular to the plane of the trap electrodes, and find that on-package capacitors reduce this to <~ 10 nm in amplitude. We also measure ion trapping lifetime, charging effects due to laser light incident on the trap…
A new scheme for the individual addressing of ions in a trap is described that does not rely on light beams tightly focused onto only one ion. The scheme utilizes ion micromotion that may be induced in a linear trap by dc offset potentials. Thus coupling an individual ion to the globally applied light fields corresponds to a mere switching of voltages on a suitable set of compensation electrodes. The proposed scheme is especially suitable for miniaturized rf (Paul) traps with typical dimensions of about 20-40 microns.
We examine the validity of the harmonic approximation, where the radio-frequency ion trap is treated as a harmonic trap, in the problem regarding the controlled collision of a trapped atom and a single trapped ion. This is equivalent to studying the effect of the micromotion since this motion must be neglected for the trapped ion to be considered as a harmonic oscillator. By applying the transformation of Cook and Shankland we find that the micromotion can be represented by two periodically oscillating operators. In order to investigate the effect of the micromotion on the dynamics of a trappe…
The prospect of building a quantum information processor underlies many recent advances ion trap fabrication techniques. Potentially, a quantum computer could be constructed from a large array of interconnected ion traps. We report on a micrometer-scale ion trap, fabricated from bulk silicon using micro-electromechanical systems (MEMS) techniques. The trap geometry is relatively simple in that the electrodes lie in a single plane beneath the ions. In such a trap we confine laser-cooled 24Mg+ ions approximately 40 microns above the surface. The fabrication technique and planar electrode geometr…
We investigate single ions of $^{40}Ca^+$ in Paul traps for quantum information processing. Superpositions of the S$_{1/2}$ electronic ground state and the metastable D$_{5/2}$ state are used to implement a qubit. Laser light on the S$_{1/2} \leftrightarrow$ D$_{5/2}$ transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state $|n=0>$, we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is ob…
We describe the design, fabrication and testing of a surface-electrode ion trap, which incorporates microwave waveguides, resonators and coupling elements for the manipulation of trapped ion qubits using near-field microwaves. The trap is optimised to give a large microwave field gradient to allow state-dependent manipulation of the ions' motional degrees of freedom, the key to multiqubit entanglement. The microwave field near the centre of the trap is characterised by driving hyperfine transitions in a single laser-cooled 43Ca+ ion.
Recent experiments [K. R. Brown, et al., Nature 471, 196 (2011); and M. Harlander, et al., Nature 471, 200 (2011)] have demonstrated the coherent manipulations on the external vibrations of two ions, confined individually in the separated ion traps. Using these recently developed techniques, we propose here an approach to realize the coherent operations, e.g., the universal quantum gates, between the separated ion-trap qubits encoded by two internal atomic states of the trapped ions. Our proposal operates beyond the usual Lamb-Dicke limits, and could be applied to the scalable ion traps couple…
Many proposals for quantum information processing require precise control over the motion of neutral atoms, as in the manipulation of coherent matter waves or the confinement and localization of individual atoms. Patterns of micron-sized wires, fabricated lithographically on a flat substrate, can conveniently produce large magnetic-field gradients and curvatures to trap cold atoms and to facilitate the production of Bose-Einstein condensates. This paper describes tools and techniques for the construction of such devices.
We experimentally demonstrate novel structures for the realisation of registers of atomic qubits: We trap neutral atoms in one and two-dimensional arrays of far-detuned dipole traps obtained by focusing a red-detuned laser beam with a microfabricated array of microlenses. We are able to selectively address individual trap sites due to their large lateral separation of 125 mu m. We initialize and read out different internal states for the individual sites. We also create two interleaved sets of trap arrays with adjustable separation, as required for many proposed implementations of quantum gate…
We describe a novel high aspect ratio radiofrequency linear ion trap geometry that is amenable to modern microfabrication techniques. The ion trap electrode structure consists of a pair of stacked conducting cantilevers resulting in confining fields that take the form of fringe fields from parallel plate capacitors. The confining potentials are modeled both analytically and numerically. This ion trap geometry may form the basis for large scale quantum computers or parallel quadrupole mass spectrometers. PACS: 39.25.+k, 03.67.Lx, 07.75.+h, 07.10+Cm
We have generated multiple micron-sized optical dipole traps for neutral atoms using holographic techniques with a programmable liquid crystal spatial light modulator. The setup allows the storing of a single atom per trap, and the addressing and manipulation of individual trapping sites.
We present theoretical and experimental progress towards a new approach for the precision spectroscopy, coherent manipulation and state-to-state chemistry of single isolated molecular ions in the gas phase. Our method consists of a molecular beam for creating packets of rotationally cold neutrals from which a single molecule is state-selectively ionized and trapped inside a radiofrequency ion trap. In addition to the molecular ion, a single co-trapped atomic ion is used to cool the molecular external degrees of freedom to the ground state of the trap and to detect the molecular state using sta…
We demonstrate the use of high-Q superconducting coplanar waveguide (CPW) microresonators to perform rapid manipulations on a randomly distributed spin ensemble using very low microwave power (400 nW). This power is compatible with dilution refrigerators, making microwave manipulation of spin ensembles feasible for quantum computing applications. We also describe the use of adiabatic microwave pulses to overcome microwave magnetic field ($B_{1}$) inhomogeneities inherent to CPW resonators. This allows for uniform control over a randomly distributed spin ensemble. Sensitivity data are reported …
We consider manipulation of the transmission coefficient for a quantum particle moving in one dimension where the shape of the potential is taken as the control. We show that the control landscape---the transmission as a functional of the potential---has no traps, i.e., any maxima correspond to full transmission.
Microfabricated ion traps are a major advancement towards scalable quantum computing with trapped ions. The development of more versatile ion-trap designs, in which tailored arrays of ions are positioned in two dimensions above a microfabricated surface, would lead to applications in fields as varied as quantum simulation, metrology and atom-ion interactions. Current surface ion traps often have low trap depths and high heating rates, due to the size of the voltages that can be applied to them, limiting the fidelity of quantum gates. Here we report on a fabrication process that allows for the …
In order to study interactions of atomic ions with ultracold neutral atoms, it is important to have sub-$μ$m control over positioning ion crystals. Serving for this purpose, we introduce a microfabricated planar ion trap featuring 21 DC electrodes. The ion trap is controlled by a home-made FPGA voltage source providing independently variable voltages to each of the DC electrodes. To assure stable positioning of ion crystals with respect to trapped neutral atoms, we integrate into the overall design a compact mirror magneto optical chip trap (mMOT) for cooling and confining neutral $^{87}$Rb at…
We present a multilayer surface-electrode ion trap with embedded 3D microwave circuitry for implementing entangling quantum logic gates. We discuss the electromagnetic full-wave simulation procedure that has led to the trap design and the characterization of the resulting microwave field-pattern using a single ion as a local field probe. The results agree with simulations within the uncertainty; compared to previous traps, this design reduces detrimental AC Zeeman shifts by three orders of magnitude. The design presented here can be viewed as an entangling gate component in a library for surfa…
We show that the physical system consisting of trapped ions interacting with lasers may undergo a rich variety of quantum phase transitions. By changing the laser intensities and polarizations the dynamics of the internal states of the ions can be controlled, in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analogue quantum simulator of spin systems with trapped ions, and observe and analyze quantum phase transitions with unprecedent opportunities for the measurement and manipulation of spins.
Three-dimensional (3D) micro-electromagnets were developed to control particle motion in magnetic field landscapes in vacuum near a chip. Multiple layers of micron-scale conductors separated by transparent insulators create particle containers with deep, symmetric and time-dependent potentials, suitable for integration in quantum circuits. Single and coupled multiple 3D traps, integrated 3D traps with a mirror, 3D guides for neutral particles with spin, and traps for electrons in vacuum are described.
