We investigate the motional resonances of dual-species Coulomb crystals comprised of $^9$Be$^+$ and $^{24}$Mg$^+$ ions held in a 4-rod linear Paul trap. Our experimental data and simulations show that the secular motion of such mixed crystals has rich dynamics. Their secular spectra can differ significantly from those of pure ion crystals. We propose a simple model based on mechanical coupling with Coulomb interactions between the two different ion species that explains many features of the secular spectrum. Our findings contribute to a more reliable identification of the ion species in mixed crystals.
While it is straightforward to count laser-cooled trapped ions by fluorescence imaging, detecting the number of dark ions embedded and sympathetically cooled in a mixed ion crystal is more challenging. We demonstrate a method to track the number of dark ions in real time with single-particle sensitivity. This is achieved by observing discrete steps in the amount of fluorescence emitted from the coolant ions while exciting secular motional resonances of dark ions. By counting the number of fluorescence steps, we can identify the number of dark ions without calibration and without relying on any…
We report the realization of a heteronuclear two-atom of $^{87}$Rb-$^{85}$Rb in the ground state of an optical tweezer (OT). Starting by trapping two different isotopic single atoms, a $^{87}$Rb and a $^{85}$Rb in two strongly focused and linearly polarized OT with 4 $μ$m apart, we perform simultaneously three dimensional Raman sideband cooling for both atoms and the obtained 3D ground state probabilities of $^{87}$Rb and $^{85}$Rb are 0.91(5) and 0.91(10) respectively. There is no obvious crosstalk observed during the cooling process. We then merge them into one tweezer via a species-dependen…
Transport, separation, and merging of trapped ion crystals are essential operations for most large-scale quantum computing architectures. In this work, we develop a theoretical framework that describes the dynamics of ions in time-varying potentials with a motional squeeze operator, followed by a motional displacement operator. Using this framework, we develop a new, general protocol for trapped ion transport, separation, and merging. We show that motional squeezing can prepare an ion wave packet to enable transfer from the ground state of one trapping potential to another. The framework and p…
We demonstrate the preparation and coherent control of the angular momentum state of a two-ion crystal. The ions are prepared with an average angular momentum of $7780\hbar$ freely rotating at 100~kHz in a circularly symmetric potential, allowing us to address rotational sidebands. By coherently exciting these motional sidebands, we create superpositions of states separated by up to four angular momentum quanta. Ramsey experiments show the expected dephasing of the superposition which is dependent on the number of quanta separating the states. These results demonstrate coherent control of a co…
Quantum theory of electrically levitated nanoparticle-ion systems: Motional dynamics and sympathetic cooling
Institute for Theoretical Physics and Vienna Center for Quantum Science and Technology, Technical University of Vienna（维也纳大学理论物理研究所与维也纳量子科学与技术中心）；Institut für Experimentalphysik, Universität Innsbruck（因斯布鲁克大学实验物理研究所）
Motional ground state cooling and internal state preparation are important elements for quantum logic spectroscopy (QLS), a class of quantum information processing. Since QLS does not require the high gate fidelities usually associated with quantum computation and quantum simulation, it is possible to make simplifying choices in ion species and quantum protocols at the expense of some fidelity. Here, we report sideband cooling and motional state detection protocols for $^{138}$Ba$^+$ of sufficient fidelity for QLS without an extremely narrowband laser or the use of a species with hyperfine str…
Most ions lack the fast, cycling transitions that are necessary for direct laser cooling. In most cases, they can still be cooled sympathetically through their Coulomb interaction with a second, coolable ion species confined in the same potential. If the charge-to-mass ratios of the two ion types are too mismatched, the cooling of certain motional degrees of freedom becomes difficult. This limits both the achievable fidelity of quantum gates and the spectroscopic accuracy. Here we introduce a novel algorithmic cooling protocol for transferring phonons from poorly- to efficiently-cooled modes. …
We use a co-trapped ion ($^{88}\mathrm{Sr}^{+}$) to sympathetically cool and measure the quantum state populations of a memory-qubit ion of a different atomic species ($^{40}\mathrm{Ca}^{+}$) in a cryogenic, surface-electrode ion trap. Due in part to the low motional heating rate demonstrated here, the state populations of the memory ion can be transferred to the auxiliary ion by using the shared motion as a quantum state bus and measured with an average accuracy of 96(1)%. This scheme can be used in quantum information processors to reduce photon-scattering-induced error in unmeasured memory …
Trapped ions are a promising candidate for large scale quantum computation. Several systems have been built in both academic and industrial settings to implement modestly-sized quantum algorithms. Efficient cooling of the motional degrees of freedom is a key requirement for high-fidelity quantum operations using trapped ions. Here, we present a technique whereby individual ions are used to cool individual motional modes in parallel, reducing the time required to bring an ion chain to its motional ground state. We demonstrate this technique experimentally and develop a model to understand the e…
Spin Dephasing as a Probe of Mode Temperature, Motional State Distributions, and Heating Rates in a 2D Ion Crystal
我们利用自旋相关的光学偶极力来描述二维Wigner晶体的横向质心（COM）运动模式，该晶体由数百个$^9$ Be $^+$组成.通过比较由自旋相关力产生的测量自旋退相与半经典退相模型的预测，我们获得的绝对模温度与多普勒激光冷却极限和先前发表的技术（B. C. Sawyer等人，Phys. Rev. Lett. \textbf{108}，213003（2012））。此外，退相直方图的结构允许在初始热运动状态和相干运动状态之间进行区分。我们还应用这里讨论的技术来测量，第一次，环境加热速率的COM模式的2D库仑晶体在潘宁陷阱。这种测量放置在异常的单离子加热速率的上限，由于电场噪声从陷阱电极表面的$\frac{d\bar{n}}{dt}\sim 5$的$^{-1}$为我们的陷阱在795 kHz的频率，其中$\bar{n}$是平均占用的量化COM运动的轴向谐波井。
We reported the realization of a $^{174}\mathrm{Yb}^+$-$^{113}\mathrm{Cd}^+$ bi-species Coulomb crystal comprising $^{174}\mathrm{Yb}^+$ ions as coolant and verified its potential for application as a $^{113}\mathrm{Cd}^+$ microwave frequency standard employing sympathetic cooling.The two species of massive ions stably trapped in a Paul trap make up this large two-component crystal. The $^{113}\mathrm{Cd}^+$ ions are trapped in the center, which reduces considerably RF heating and excess micromotion to which the $^{113}\mathrm{Cd}^+$ ions are subjected. Under this scheme, the uncertainty due t…
Transport properties of high-energy-density plasmas are influenced by the ion collision rate. Traditionally, this rate involves the Coulomb logarithm, $\lnΛ$. Typical values of $\lnΛ$ are $\approx 10~\mbox{to}~20$ in kinetic theories where transport properties are dominated by weak-scattering events caused by long-range forces. The validity of these theories breaks down for strongly-coupled plasmas, when $\lnΛ$ is of order one. We present measurements and simulations of collision data in strongly-coupled plasmas when $\lnΛ$ is small. Experiments are carried out in the first dual-species ultrac…
In order to realize the full potential of ion trap quantum computers, an improved understanding is required of the motional heating that trapped ions experience. Experimental studies of the temperature-, frequency-, and ion--electrode distance-dependence of the electric field noise responsible for motional heating, as well as the noise before and after ion bombardment cleaning of trap electrodes, suggest that fluctuations of adsorbate dipoles are a likely source of so-called `anomalous heating,' or motional heating of the trapped ions at a rate much higher than the Johnson noise limit. Previou…
We discuss the coupling of the motion of two ion species in separate Penning traps via a common tank circuit. The enhancement of the coupling assisted by the tank circuit is demonstrated by an avoided crossing behavior measurement of the motional modes of two coupled ions. We propose an intermittent laser cooling method for sympathetic cooling and provide a theoretical description. The technique enables tuning of the coupling strength between two ion species in separate traps and thus allows for efficient sympathetic cooling of an arbitrary type of single ion for high-precision Penning-trap ex…
Trapped atomic ions find wide applications ranging from precision measurement to quantum information science and quantum computing. Among the different atomic species employed, beryllium ions are widely used due to its light mass and convenient atomic structure. However, the ion loading process requires a high temperature for sufficient vapor pressure, generating undesirable gas load for the background vacuum and limiting the lifetime of a long ion chain. Here, we demonstrate a simple method to rapidly produce pure linear chains of beryllium ions with pulsed laser ablation, serving as a starti…
The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher dimensional systems. Here, we report on the trappin…
Coulomb crystallization of xenon highly charged ions in a laser-cooled Ca+ matrix
University of Birmingham（伯明翰大学）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）；Humboldt-Universität zu Berlin（柏林洪堡大学）；Deutsches Elektronen-Synchrotron (DESY)（德国电子同步辐射中心）；Physikalisch-Technische Bundesanstalt（德国联邦物理技术研究院）
Ion trap systems are a leading platform for large scale quantum computers. Trapped ion qubit crystals are fully-connected and reconfigurable, owing to their long range Coulomb interaction that can be modulated with external optical forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals, simplifying the scaling of ion trap quantum computers. To this end, we present analytical work tha…
We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 $^{171}$Yb$^+$ ions, we demonstrate that the structural phase boundaries and vibrational mode frequencies of such crystals are well-described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced he…
