Abstract Cryogenic ion traps offer substantial advantages over their room-temperature counterparts, particularly in terms of stable ion confinement and cooling. However, this technological advancement has introduced a significant challenge, namely the generation of additional vibrational noise. This noise is pronounced during the compression and expansion phases of the Gifford–McMahon cycle refrigerator and stems from the mechanical operation of the cold head. The residual vibrational noise can modulate the Rabi oscillation frequency, thereby compromising the fidelity of the quantum logic gate. In this study, we quantitatively assess the impact of residual vibrational noise and introduce an innovative strategy for its mitigation. This strategy was designed to reduce superimposed potential fluctuations within a cryogenic surface electrode ion trap. The measured residual vibrational noise was used for real-time feedback control. Addressing the inverse determination of the compensating potential for a stable superimposed trapping potential is an inherently ill-posed problem considering known measurement noise results. By applying quadratic programming, we numerically calculated the optimal time series for the compensation potential. An ensemble of these compensation voltages was applied in real time to the static compensation electrodes. Although this method is in the theoretical stage, we believe that it can effectively suppress the translation induced by vibrational noise and foster the creation of a stable superimposed harmonic potential. The deployment of this technique is expected to substantially improve the accuracy of quantum operations, thereby fueling the evolution of quantum technologies.
Abstract Cryogenic ion traps offer substantial advantages over their room-temperature counterparts, particularly in terms of stable ion confinement and cooling. However, this technological advancement has introduced a significant challenge, namely the generation of additional vibrational noise. This noise is pronounced during the compression and expansion phases of the Gifford–McMahon cycle refrigerator and stems from the mechanical operation of the cold head. The residual vibrational noise can modulate the Rabi oscillation frequency, thereby compromising the fidelity of the quantum logic gate. In this study, we quantitatively assess the impact of residual vibrational noise and introduce an innovative strategy for its mitigation. This strategy was designed to reduce superimposed potential fluctuations within a cryogenic surface electrode ion trap. The measured residual vibrational noise was used for real-time feedback control. Addressing the inverse determination of the compensating potential for a stable superimposed trapping potential is an inherently ill-posed problem considering known measurement noise results. By applying quadratic programming, we numerically calculated the optimal time series for the compensation potential. An ensemble of these compensation voltages was applied in real time to the static compensation electrodes. Although this method is in the theoretical stage, we believe that it can effectively suppress the translation induced by vibrational noise and foster the creation of a stable superimposed harmonic potential. The deployment of this technique is expected to substantially improve the accuracy of quantum operations, thereby fueling the evolution of quantum technologies.
Cryogenic trapped-ion systems (CTISs) have emerged as indispensable platforms for the advancement of quantum computation and precision measurement techniques. However, the sensitivity of these systems to vibrational noise, especially during the compression and expansion cycles of the cold head in a Gifford-McMahon cycle refrigerator (GMCR), poses a significant challenge. To mitigate this, we have crafted an innovative methodology for characterizing low-frequency residual vibrational noise in closed-cycle cryogenic trapped-ion systems. Our methodology is underpinned by a compact homodyne quadrature laser interferometer (HQLI) vibrometer system that boasts nanometer-scale accuracy. This state-of-the-art system leverages elliptic curve fitting to rectify nonlinear noise artifacts and applies an inverse tangent function to demodulation phase techniques, enabling accurate vibrational displacement measurements. Unlike the conventional approach, our scheme circumvents the introduction of extraneous vibrational noise associated with piezoelectric ceramic mirrors, which are conventionally employed to track target vibrations for locking the interference signal intensity in the reference arm. This innovation not only improves the overall CTIS performance but is also significantly applied to characterize the practical realization of quantum computation and precision measurement.
Trapped ions are one of the leading platforms for building scalable quantum information processors. Current ion traps run on less than 100 qubits. A useful quantum computer needs to operate thousands or even millions of qubits. If systems reach gate fidelities that allow for quantum error correction, gate errors below the physical fidelity can be reached, which is important for scaling. The most promising platform for scaling up ion-based quantum computers are surface electrode traps in connection with the so-called QCCD (Quantum Charge Coupled Device) architecture. In an evolution of the standard (laser-based) approach to quantum logic gates, gates can be performed by applying an oscillating magnetic near-field gradient to the ions. Current fidelities are about one order of magnitude away from reaching the fault tolerant threshold with no fundamental limitations in sight. Scaling QCCDs is impeded by heating rates of the ions as well as vacuum quality. Ions have to be stored for at least as long as it takes for an algorithm to run and subsequent readout. Collisions with background gas and heating can expel ions from the trap. The microwave near-field approach of driving gates benefits from ions that are trapped close to the trap surface. Unfortunately, heating becomes more prominent near the surface. A cryogenic environment reduces the background pressure by several orders of magnitude and the kinetic energy of gas molecules by two orders of magnitude. Heating rates in a cryogenic trap are about two orders of magnitude lower than in a room temperature trap with otherwise equal physical properties. To operate a QCCD processor, it is required to employ phase-stable Raman laser beams. The cryogenic design of the apparatus needs to take into account the resulting requirements for ultra-low vibration amplitudes. This is particularly relevant for closed-cycle cooling systems, which are desirable from an economic point of view compared to liquid cryostats that boil off helium, but which also feature moving mechanical parts that can introduce a serious amount of vibrations. Here, we present a vibration isolated closed cycle Gifford-McMahon cryocooler with record low vibration amplitudes of 29 nm (RMS=7.8 nm) in the vertical and 51 nm (RMS=13.5 nm) in the horizontal direction. It contains a self-sustained inner vacuum chamber that houses the trap. It features 100 DC connections, 10 of which are able to carry up to 1 A of current and 8 high frequency lines. At 5 K, we can apply continuous 3.4 W of microwave power continuously at 1 GHz to the trap electrodes without heating the system. This is about 5.8 times more than state of the art near-field gates require. We also present the laser systems required to for single-shot ablation loading and Doppler cooling of Be ions: a 70 mW 313 nm Dopper cooling laser, a 1064 nm ns-pulse laser for ablation of neutral beryllium atoms and a 235 nm laser for ionizing them. The detection system features an in vacuum imaging system on a cryogenic 3D translation stage that is able to scan and image the complete surface of an ion trap. The light can be detected on a photomultiplier tube or spatially resolved on an EMCCD camera. Our trap features a meander structure for driving gates and can trap up to 5 ions of which we, so far, did not lose any due to background gas collisions. This hints at a vacuum pressure of 1e-12 mbar or lower. The demonstrated system could hold a cryogenic QCCD chip with a few 10 qubits
We describe the design, commissioning, and operation of an ultra-low-vibration closed-cycle cryogenic ion trap apparatus. One hundred lines for low-frequency signals and eight microwave/radio frequency coaxial feed-lines offer the possibility of implementing a small-scale ion-trap quantum processor or simulator. With all supply cables attached, more than 1.3 W of cooling power at 5 K is still available for absorbing energy from electrical pulses introduced to control ions. The trap itself is isolated from vibrations induced by the cold head using a helium exchange gas interface. The performance of the vibration isolation system has been characterized using a Michelson interferometer, finding residual vibration amplitudes on the order of 10 nm rms. Trapping of 9Be+ ions has been demonstrated using a combination of laser ablation and photoionization.
While quantum information processing offers a tantalizing possibility of a significant speedup in execution of certain algorithms, as well as enabling previously unmanageable simulations of large quantum systems, it remains extremely difficult to realize experimentally. Recently, fundamental building blocks of a quantum computer, including one and two qubit gates, teleportation and error correction, were demonstrated using trapped atomic ions. Scaling to a larger number of qubits requires miniaturization of the ion traps, currently limited by the sharply increasing motional state decoherence at sub-100 μm ion-electrode distances. This thesis explores the source and suppression of this decoherence at cryogenic temperatures, and demonstrates fundamental logic gates in a surface electrode ion trap.
Construction of the apparatus requires the development of a number of experimental techniques. Design, numerical simulation and implementation of a surface electrode ion trap is presented. Cryogenic cooling of the trap to near 4 K is accomplished by contact with a bath cryostat. Ions are loaded by ablation or photoionization, both of which are characterized in terms of generated stray fields and heat load.
The bulk of new experimental results deals with measurements of electric field noise at the ion's position. Upon cooling to 6 K, the measured rates are suppressed by up to 7 orders of magnitude, more than two orders of magnitude below previously published data for similarly sized traps operated at room temperature. The observed noise depends strongly on fabrication process, which suggests further improvements are possible. The measured dependence of the electric field noise on temperature is inconsistent with published models, and can be explained using a continuous spectrum of activated fluctuators.
The fabricated surface electrode traps are used to demonstrate coherent operations and the classical control required for trapped ion quantum computation. The necessary spectral properties of coherent light sources are achieved with a novel design using optical feedback to a triangular, medium finesse, cavity, followed by electronic feedback to an ultra-high finesse reference cavity. Single and two qubit operations on a single ion are demonstrated with classical fidelity in excess of 95%. Magnetic field gradient coils built into the trap allow for individual addressing of ions, a prerequisite to scaling to multiple qubits. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
Cold, trapped atomic ions have enabled the investigation of fundamental physics and generated a rich field of applications. Foremost among these is quantum computation which has recently driven the development of the sophisticated, scalable surface-electrode trap. Despite the many advantages of surface-electrode traps, the typically smaller ion-electrode distance, d, in these traps results in an increased ion heating rate that is proportional to d^(-4) and a decreased trap well-depth that is proportional to d^(-2). These shortcomings can be simultaneously addressed by installing the trap into a cryogenic environment. With this in mind, a closed-cycle, cryogenic ion trapping apparatus that maintains excellent vacuum, is highly modular, has increased optical access, and uses a simple vibration isolation system has been developed. \n \nSingle ions are trapped and used to characterize system properties such as the motion of the vibration isolation stage. In order to compare this system to a similar room temperature apparatus, the ion trapping lifetime and heating rate are determined. A single ion also serves as a sensitive electric field probe that is used to measure and compensate stray electric fields across the trap. \n \nDue to the long dark ion lifetimes in this system, it is well-suited to probing the stability of small, linear ion crystals. Linear ion crystals of arbitrary length are built in an automated fashion using transport waveforms and the scaling of dark lifetime with ion number for N <= 6 is investigated. These data are then used to consider the relevance of various loss channels.
There has been a great deal of effort and progress made towards building a fully scalable quantum computer but there are still significant engineering challenges to overcome. Trapped ions currently represent the best fundamental technology towards achieving this goal and so they form the basis for the work in this thesis. In this thesis I describe the work towards creating a closed cycle cryogenic vacuum system driven by a Gifford McMahon cryogenic cooler. I will show the equipment required to trap a Ytterbium 174/171 ion on a cryogenic surface ion trap. The primary goal is to create a fast turn-around system for ion trap research. Room temperature systems suffer from long baking times and as such ion traps are rarely changed, this means that there is little room for testing and comparing of trap designs and predicting optimum trapping parameters as each trap is usually not changed unless there is a fault. In the cryogenic system, every effort is made to make the system generic enough to allow for any trap design to be tested and to be replaced within 24 hours. To create reliable trapping parameters we require a toolkit that can numerically simulate the required RF and DC voltages used to trap the ions above the surface of the ion trap. There are many numerical methods that can be used (FEM, FVM, BEM, FTDI, etc) and in this thesis I describe multiple methods and what their relative benefits are. Since we want to create a full toolkit to allow for chip design and optimisation, most commercial programs suffer from inadequate API interfaces or they dictate which programming languages you can interface with. This would limit our abilities to develop and optimise trapping parameters, especially in a cryogenic system where the goal is rapid deployment. To this end I created a new toolkit based on the Scuff BEM solver engine that allows us to go from AutoCAD layout to field solver and gives us accurate field potentials that match micromotion compensated voltages to within 1%. I describe a novel cryogenic resonator built out of superconducting wire based on an auto-transformer topology, I compare its strengths and weaknesses compared to other technologies already in use for trapped ion research. I also describe a novel DSUB design with integrated modular filtering which allows for 50 connections per DSUB. This DSUB is used to connect two sets of 50 wires to a PCB for wirebonding to the surface trap. This allows me to save space within the 4k shield where other PCB designs would not fit. Also it is modular in design which allows for different cutoff frequencies to be swapped out as desired. I also describe different chip mounting technologies including epoxy based, physical clamping and indium foil based. After extensive testing the indium foil diebonded approach is deemed as being the most reliable and fastest non-destructive method. I also describe a novel cryogenic coil design for generating 12T m-1 field gradients for microwave based ion gates with Ytterbium 171. I then describe the creation of a combined RF and microwave antenna for delivering coherent RF and 12.6GHz microwave radiation inside the cryogenic environment. This design is much smaller than typical waveguide typologies used. I finish by showing the first trapped ions in a cryogenic surface ion trap in the UK and heating rate tests performed on two different linear surface traps. The first trap was a sapphire based, 150µm ion height linear trap with a measured heating rate of Se(1MHz) = 5.93(10) * 10-14(V /m)2. The second ion trap is a 50k Silicon based, 100µm ion height linear trap with a measured heating rate of Se(1MHz) = 2.45(10)*10-13(V /m)2