Two-dimensional linear trap array for quantum information processing
Philip C. Holz, Silke Auchter, Gerald Stocker, Marco Valentini, Kirill Lakhmanskiy, Clemens Rössler, Paul Stampfer, Sokratis Sgouridis, Elmar Aschauer, Yves Colombe, Rainer Blatt
We present an ion-lattice quantum processor based on a two-dimensional arrangement of linear surface traps. Our design features a tunable coupling between ions in adjacent lattice sites and a configurable ion-lattice connectivity, allowing one, e.g., to realize rectangular and triangular lattices with the same trap chip. We present detailed trap simulations of a simplest-instance ion array with $2\times9$ trapping sites and report on the fabrication of a prototype device in an industrial facility. The design and the employed fabrication processes are scalable to larger array sizes. We demonstrate trapping of ions in rectangular and triangular lattices and demonstrate transport of a $2\times2$ ion-lattice over one lattice period.
One path to realizing systems of trapped atomic ions suitable for large-scale quantum computing and simulation is to create a two-dimensional array of ion traps. Interactions between nearest-neighbouring ions could then be turned on and off by tuning the ions' relative positions and frequencies. We demonstrate and characterize the operation of a planar-electrode ion-trap array. Driving the trap with a network of phase-locked radio-frequency (RF) resonators which provide independently variable voltage amplitudes we vary the position and motional frequency of a 40Ca+ ion in two dimensions within…
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 describe a new type of blue detuned optical lattice for atom trapping which is intrinsically two dimensional, while providing three-dimensional atom localization. The lattice is insensitive to optical phase fluctuations since it does not depend on field interference between distinct optical beams. The array is created using a novel arrangement of weakly overlapping Gaussian beams that creates a two-dimensional array of dark traps which are suitable for magic trapping of ground and Rydberg states. We analyze the spatial localization that can be achieved and demonstrate trapping and detection…
We investigate electrode geometries required to produce periodic 2-dimensional ion-trap arrays with the ions placed between two planes of electrodes. We present a generalization of previous methods for traps containing a single electrode plane to this new geometry, and show that for a given ion-electrode distance and applied voltages, the inter-ion distance can be reduced by a factor of up to 3 relative to single-plane traps. This represents an increase by a factor of 9 in the trap density and a factor of 27 in the exchange coupling between the oscillatory motion of neighboring ions. The resul…
We propose the use of 2-dimensional Penning trap arrays as a scalable platform for quantum simulation and quantum computing with trapped atomic ions. This approach involves placing arrays of micro-structured electrodes defining static electric quadrupole sites in a magnetic field, with single ions trapped at each site and coupled to neighbors via the Coulomb interaction. We solve for the normal modes of ion motion in such arrays, and derive a generalized multi-ion invariance theorem for stable motion even in the presence of trap imperfections. We use these techniques to investigate the feasibi…
Scaling quantum information processors is a challenging task, requiring manipulation of a large number of qubits with high fidelity and a high degree of connectivity. For trapped ions, this could be realized in a two-dimensional array of interconnected traps in which ions are separated, transported and recombined to carry out quantum operations on small subsets of ions. Here, we use a junction connecting orthogonal linear segments in a two-dimensional (2D) trap array to reorder a two-ion crystal. The secular motion of the ions experiences low energy gain and the internal qubit levels maintain …
We describe rapid, random-access loading of a two-dimensional (2D) surface-electrode ion-trap array based on two crossed photo-ionization laser beams. With the use of a continuous flux of pre-cooled neutral atoms from a remotely-located source, we achieve loading of a single ion per site while maintaining long trap lifetimes and without disturbing the coherence of an ion quantum bit in an adjacent site. This demonstration satisfies all major criteria necessary for loading and reloading extensive 2D arrays, as will be required for large-scale quantum information processing. Moreover, the alread…
In this work, we construct a polarization-mediated magic-intensity (MI) optical dipole trap (ODT) array, in which the detrimental effects of light shifts on the mixed-species qubits are efficiently mitigated so that the coherence times of the mixed-species qubits are both substantially enhanced and balanced for the first time. This mixed-species magic trapping technique relies on the tunability of the coefficient of the third-order cross term and ground state hyperpolarizability, which are inherently dependent on the degree of circular polarization of the trap laser. Experimentally, polarizati…
We explore the possibility of implementing a Heisenberg-limited Mach-Zehnder interferometry via an array of trapped ions, which obey a quantum Ising model within a transverse field. Based upon adiabatic processes of increasing the Ising interaction and then decreasing the transverse field, we demonstrate a perfect transition from paramagnetism to ferromagnetic states, which can be used as the beam splitter for the multi-ion Mach-Zehnder interferometry. The achieved NOON state of the ions enables the Heisenberg-limited interferometry. Using currently available techniques for ultracold ions, we …
Arrays of trapped atoms are the ideal starting point for developing registers comprising large numbers of physical qubits for storing and processing quantum information. One very promising approach involves neutral atom traps produced on microfabricated devices known as atom chips, as almost arbitrary trap configurations can be realised in a robust and compact package. Until now, however, atom chip experiments have focused on small systems incorporating single or only a few individual traps. Here we report experiments on a two-dimensional array of trapped ultracold atom clouds prepared using a…
We demonstrate single-atom trapping in two-dimensional arrays of microtraps with arbitrary geometries. We generate the arrays using a Spatial Light Modulator (SLM), with which we imprint an appropriate phase pattern on an optical dipole trap beam prior to focusing. We trap single $^{87}{\rm Rb}$ atoms in the sites of arrays containing up to $\sim100$ microtraps separated by distances as small as $3\;μ$m, with complex structures such as triangular, honeycomb or kagome lattices. Using a closed-loop optimization of the uniformity of the trap depths ensures that all trapping sites are equivalent. …
Single neutral atoms trapped in optical tweezers and laser-coupled to Rydberg states provide a fast and flexible platform to generate configurable atomic arrays for quantum simulation. The platform is especially suited to study quantum spin systems in various geometries. However, for experiments requiring continuous trapping, inhomogeneous light shifts induced by the trapping potential and temperature broadening impose severe limitations. Here we show how Raman sideband cooling allows one to overcome those limitations, thus, preparing the stage for Rydberg dressing in tweezer arrays.
We describe the advantages of 2-dimensional, addressable arrays of spherical Paul traps. They would provide for the ability to address and tailor the interaction strengths of trapped objects in 2D and could establish a valuable new tool for quantum information processing. Simulations of trapping ions are compared to first tests using printed circuit board trap arrays loaded with dust particles. Pair-wise interactions in the array are addressed by means of an adjustable radio-frequency (RF) electrode shared between trapping sites. By attenuating this RF electrode potential, neighboring pairs of…
We propose a hardware architecture and protocol for connecting many local quantum processors contained within an optical cavity. The scheme is compatible with trapped ions or Rydberg arrays, and realizes teleported gates between any two qubits by distributing entanglement via single-photon transfers through a cavity. Heralding enables high-fidelity entanglement even for a cavity of moderate quality. For processors composed of trapped ions in a linear chain, a single cavity with realistic parameters successfully transfers photons every few $μ$s, enabling the any-to-any entanglement of 20 ion ch…
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…
Neutral atom qubits with Rydberg-mediated interactions are a leading platform for developing large-scale coherent quantum systems. In the majority of experiments to date, the Rydberg states are not trapped by the same potential that confines ground state atoms, resulting in atom loss and constraints on the achievable interaction time. In this work, we demonstrate that the Rydberg states of an alkaline earth atom, ytterbium, can be stably trapped by the same red-detuned optical tweezer that also confines the ground state, by leveraging the polarizability of the Yb$^+$ ion core. Using the previo…
Ordered atomic arrays trapped in the vicinity of nanoscale waveguides offer original light-matter interfaces, with applications to quantum information and quantum non-linear optics. Here, we study the decay dynamics of a single collective atomic excitation coupled to a waveguide in different configurations. The atoms are arranged as a linear array and only a segment of them is excited to a superradiant mode and emits light into the waveguide. Additional atomic chains placed on one or both sides play a passive role, either reflecting or absorbing this emission. We show that when varying the geo…
We consider a system of particles in an array of microscopic traps, coupled to each other via electrostatic interaction, and pushed by an external state-dependent force. We show how to implement a two-qubit quantum gate between two such particles with a high fidelity.
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 report reliable transport of 9Be+ ions through a 2-D trap array that includes a separate loading/reservoir zone and an "X-junction". During transport the ion's kinetic energy in its local well increases by only a few motional quanta and internal-state coherences are preserved. We also examine two sources of energy gain during transport: a particular radio-frequency (RF) noise heating mechanism and digital sampling noise. Such studies are important to achieve scaling in a trapped-ion quantum information processor.
D1 magic wavelengths have been predicted for the alkali atoms but are not yet observed to date. We experimentally confirm a D1 magic wavelength that is predicted to lie at 615.87 nm for $^{23}$Na, which we then use to trap and image individual atoms with 80.0(6)% efficiency and without having to modulate the trapping and imaging light intensities. We further demonstrate that the mean loading efficiency remains as high as 74.2(7)% for a 1D array of eight atoms. Leveraging on the absence of trap intensity modulation and lower trap depths afforded by the D1 light, we achieve an order-of-magnitude…
State-of-the-art microfabricated ion traps for quantum information research are approaching nearly one hundred control electrodes. We report here on the development and testing of a new architecture for microfabricated ion traps, built around ball-grid array (BGA) connections, that is suitable for increasingly complex trap designs. In the BGA trap, through-substrate vias bring electrical signals from the back side of the trap die to the surface trap structure on the top side. Gold-ball bump bonds connect the back side of the trap die to an interposer for signal routing from the carrier. Trench…
We report on the trapping of single Rb atoms in tunable arrays of optical tweezers in a cryogenic environment at $\sim 4$ K. We describe the design and construction of the experimental apparatus, based on a custom-made, UHV compatible, closed-cycle cryostat with optical access. We demonstrate the trapping of single atoms in cryogenic arrays of optical tweezers, with lifetimes in excess of $\sim6000$ s, despite the fact that the vacuum system has not been baked out. These results open the way to large arrays of single atoms with extended coherence, for applications in large-scale quantum simula…
We present an approach for trapping cold atoms in a 2D optical trap array generated with a novel 4f filtering scheme and custom transmission mask without any active device. The approach can be used to generate arrays of bright or dark traps, or both simultaneously with a single wavelength for forming two-species traps. We demonstrate the design by creating a 2D array of 1225 dark trap sites, where single Cs atoms are loaded into regions of near-zero intensity in an approximately Gaussian profile trap. Moreover, we demonstrate a simple solution to the problem of out-of-focus trapped atoms, whic…
The optimisation of two-dimensional (2D) lattice ion trap geometries for trapped ion quantum simulation is investigated. The geometry is optimised for the highest ratio of ion-ion interaction rate to decoherence rate. To calculate the electric field of such array geometries a numerical simulation based on a "Biot-Savart like law" method is used. In this article we will focus on square, hexagonal and centre rectangular lattices for optimisation. A method for maximising the homogeneity of trapping site properties over an array is presented for arrays of a range of sizes. We show how both the pol…
We propose an architecture and methodology for large-scale quantum simulations using hyperfine states of trapped-ions in an arbitrary-layout microtrap array with laserless interactions. An ion is trapped at each site, and the electrode structure provides for the application of single and pairwise evolution operators using only locally created microwave and radio-frequency fields. The avoidance of short-lived atomic levels during evolution effectively eliminates errors due to spontaneous scattering; this may allow scaling of quantum simulators based on trapped ions to much larger systems than c…
An array of planar Penning traps, holding single electrons, can realize an artificial molecule suitable for NMR-like quantum information processing. The effective spin-spin coupling is accomplished by applying a magnetic field gradient, combined to the Coulomb interaction acting between the charged particles. The system lends itself to scalability, since the same substrate can easily accommodate an arbitrary number of traps. Moreover, the coupling strength is tunable and under experimental control. Our theoretical predictions take into account a realistic setting, within the reach of current t…
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 trapp…
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…
We demonstrate Floquet engineering in a basic yet scalable 2D architecture of individually trapped and controlled ions. Local parametric modulations of detuned trapping potentials steer the strength of long-range inter-ion couplings and the related Peierls phase of the motional state. In our proof-of-principle, we initialize large coherent states and tune modulation parameters to control trajectories, directions and interferences of the phonon flow. Our findings open a new pathway for future Floquet-based trapped-ion quantum simulators targeting correlated topological phenomena and dynamical g…
We consider a coupled-cavity array (CCA), where one cavity interacts with a two-level atom under the rotating-wave approximation. We investigate the excitation transport dynamics across the array, which arises in the atom's emission process into the CCA vacuum. Due to the known formation of atom-photon bound states, partial field localization and atomic population trapping in general take place. We study the functional dependance on the coupling strength of these two phenomena and show that the threshold values beyond which they become significant are different. As the coupling strength grows …
We investigate the motional dynamics of single and multiple ions during transport between and separation into spatially distinct locations in a multi-zone linear Paul trap. A single 9Be+ ion in a 2 MHz harmonic well located in one zone was laser-cooled to near its ground state of motion and transported 370 micrometers by moving the well to another zone. This was accomplished in 8 microseconds, corresponding to 16 periods of oscillation. Starting from a state with n=0.1 quanta, during transport the ion was excited to a displaced coherent state with n=1.6 quanta but on completion was returned cl…
Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determi…
We report on the realization of large assembled arrays of more than 300 single $^{87}$Rb atoms trapped in optical tweezers in a cryogenic environment at $\sim4$~K. For arrays with $N_{\rm a}=324$ atoms, the assembly process results in defect-free arrays in $\sim37\%$ of the realizations. To achieve this high assembling efficiency, we equalize the loading probability of the traps within the array using a closed-loop optimization of the power of each optical tweezers, based on the analysis of the fluorescence time-traces of atoms loaded in the traps.
We propose a scheme for realizing quantum controlled phase gates with two nonidentical quantum dots trapped in two coupled photonic crystal cavities and driven by classical laser fields under the condition of non-small hopping limit. During the gate operation, neither the quantum dots are excited, while the system can acquire different phases conditional upon the different states of the quantum dots. Along with single-qubit operations, a two-qubit controlled phase gate can be achieved.
It was recently proposed to use small groups of trapped ions as qubit carriers in miniaturized electrode arrays that comprise a large number of individual trapping zones, between which ions could be moved. This approach might be scalable for quantum information processing with a large numbers of qubits. Processing of quantum information is achieved by transporting ions to and from separate memory and qubit manipulation zones in between quantum logic operations. The transport of ion groups in this scheme plays a major role and requires precise experimental control and fast transport. In this pa…
Quantum mechanics dominates various effects in modern research from miniaturizing electronics, up to potentially ruling solid-state physics, quantum chemistry and biology. To study these effects experimental quantum systems may provide the only effective access. Seminal progress has been achieved in a variety of physical platforms, highlighted by recent applications. Atomic ions are known for their unique controllability and are identical by nature, as evidenced, e.g., by performing among the most precise atomic clocks and providing the basis for one-dimensional simulators. However, controllab…
In this study, we report the first Cu-filled through silicon via (TSV) integrated ion trap. TSVs are placed directly underneath electrodes as vertical interconnections between ion trap and a glass interposer, facilitating the arbitrary geometry design with increasing electrodes numbers and evolving complexity. The integration of TSVs reduces the form factor of ion trap by more than 80%, minimizing parasitic capacitance from 32 to 3 pF. A low RF dissipation is achieved in spite of the absence of ground screening layer. The entire fabrication process is on 12-inch wafer and compatible with estab…
We theoretically investigate the use of fast pulsed two-qubit gates for trapped ion quantum computing in a two-dimensional microtrap architecture. In one dimension, such fast gates are optimal when employed between nearest neighbours, and we examine the generalisation to a two-dimensional geometry. We demonstrate that fast pulsed gates are capable of implementing high-fidelity entangling operations between ions in neighbouring traps faster than the trapping period, with experimentally demonstrated laser repetition rates. Notably, we find that without increasing the gate duration, high-fidelity…
The coupling of atomic arrays and one-dimensional subwavelength waveguides gives rise to in- teresting photon transport properties, such as recent experimental demonstrations of large Bragg reflection and paves the way for a variety of potential applications in the field of quantum non-linear optics. Here, we present a theoretical analysis for the process of single-photon scattering in this configuration using a full microscopic approach. Based on this formalism, we analyze the spectral dependencies for different scattering channels from either ordered or disordered arrays. The de- veloped app…
Large arrays of individually controlled atoms trapped in optical tweezers are a very promising platform for quantum engineering applications. However, to date, only disordered arrays have been demonstrated, due to the non-deterministic loading of the traps. Here, we demonstrate the preparation of fully loaded, two-dimensional arrays of up to 50 microtraps each containing a single atom, and arranged in arbitrary geometries. Starting from initially larger, half-filled matrices of randomly loaded traps, we obtain user-defined target arrays at unit filling. This is achieved with a real-time contro…
We report techniques for the fabrication of multi-zone linear RF Paul traps that exploit the machinability and electrical conductivity of degenerate silicon. The approach was tested by trapping and laser cooling 24Mg+ ions in two trap geometries: a single-zone two-layer trap and a multi-zone surface-electrode trap. From the measured ion motional heating rate we determine an electric field spectral density at the ion's position of approximately 1E-10 (V/m)^2/Hz at a frequency of 1.125 MHz when the ion lies 40 micron above the trap surface. One application of these devices is controlled manipula…
We study the transverse expansion of arrays of ultracold $^{87}$Rb atoms weakly confined in tubes created by a 2D optical lattice, and observe that transverse expansion is delayed because of mutual atom interactions. A mean-field model of a coupled array shows that atoms become localized within a roughly square fort-like self-trapping barrier with time-evolving edges. But the observed dynamics is poorly described by the mean-field model. Theoretical introduction of random phase fluctuations among tubes improves the agreement with experiment, but does not correctly predict the density at which …
We propose a novel implementation of discrete time quantum walks for a neutral atom in an array of optical microtraps or an optical lattice. We analyze a one-dimensional walk in position space, with the coin, the additional qubit degree of freedom that controls the displacement of the quantum walker, implemented as a spatially delocalized qubit, i.e., the coin is also encoded in position space. We analyze the dependence of the quantum walk on temperature and experimental imperfections as shaking in the trap positions. Finally, combining a spatially delocalized qubit and a hyperfine qubit, we a…
In this chapter, we present an overview of experiments with trapped Rydberg ions and outline the advantages and challenges of developing applications of this new platform for quantum computing, sensing and simulation. Trapped Rydberg ions feature several important properties, unique in their combination: they are tightly bound in a harmonic potential of a Paul trap, in which their internal and external degrees of freedom can be controlled in a precise fashion. High fidelity state preparation of both internal and motional states of the ions has been demonstrated, and the internal states have be…
Fast, parallel, three-dimensional rearrangement of atom arrays using superpositions of elementary holograms
Institut für Quantenoptik, Leibniz Universität Hannover（汉诺威莱布尼茨大学量子光学研究所）；Centre for Cold Matter, Blackett Laboratory, Imperial College London（帝国理工学院布莱克特实验室冷物质中心）
