We present a scheme to generate an arbitrary two-dimensional quantum state of motion of a trapped ion. This proposal is based on a sequence of laser pulses, which are tuned appropriately to control transitions on the sidebands of two modes of vibration. Not more than $(M+1)(N+1)$ laser pulses are needed to generate a pure state with upper phonon number $M$ and $N$ in the $x$ and $y$ direction respectively.
We propose and demonstrate a scalable scheme for the simultaneous determination of internal and motional states in trapped ions with single-site resolution. The scheme is applied to the study of polaritonic excitations in the Jaynes- Cummings Hubbard model with trapped ions, in which the internal and motional states of the ions are strongly correlated. We observe quantum phase transitions of polaritonic excitations in two ions by directly evaluating their variances per ion site. Our work establishes an essential technological method for large-scale quantum simulations of polaritonic systems.
We present two methods for characterization of motional-mode configurations that are generally applicable to the weak and strong-binding limit of single or multiple trapped atomic ions. Our methods are essential to realize control of the individual as well as the common motional degrees of freedom. In particular, when implementing scalable radio-frequency trap architectures with decreasing ion-electrode distances, local curvatures of electric potentials need to be measured and adjusted precisely, e.g., to tune phonon tunneling and control effective spin-spin interaction. We demonstrate both me…
Non-Gaussian states represent a powerful resource for quantum information protocols in the continuous variables regime. Cat states, in particular, have been produced in the motional degree of freedom of trapped ions by controlled displacements dependent on the ionic internal state. An alternative method harnesses the Kerr nonlinearity naturally existent in this kind of system. We present detailed calculations confirming its feasibility for typical experimental conditions. Additionally, this method permits the generation of complex non-Gaussian states with negative Wigner functions. Especially,…
To achieve high-fidelity operations on a large-scale quantum computer, the parameters of the physical system must be efficiently characterized with high accuracy. For trapped ions, the entanglement between qubits are mediated by the motional modes of the ion chain, and thus characterizing the motional-mode parameters becomes essential. In this paper, we develop and explore physical models that accurately predict both magnitude and sign of the Lamb-Dicke parameters when the modes are probed {\it in parallel}. We further devise an advanced characterization protocol that shortens the characteriza…
Quantum coherence is one of the clearest departures from classical physics, exhibited when a system is in a superposition of different basis states. Here the coherent superposition of three motional Fock states of a single trapped ion is experimentally certified, with a procedure provably robust against imperfect operation. As the motional state cannot be directly interrogated, our scheme uses an interference pattern generated by projective measurement of the coupled qubit state. The minimum number of coherently superposed states is inferred from a series of threshold values based on analysis …
Entangling gates in trapped-ion quantum computing have primarily targeted stationary ions with initial motional distributions that are thermal and close to the ground state. However, future systems will likely incur significant non-thermal excitation due to, e.g., ion transport, longer operational times, and increased spatial extent of the trap array. In this paper, we analyze the impact of such coherent motional excitation on entangling-gate error by performing simulations of Molmer-Sorenson (MS) gates on a pair of trapped-ion qubits with both thermal and coherent excitation present in a shar…
In this paper we propose a scheme to model the phonon analog of optical elements, including a polarizing beam splitter, a half- wave plate, and a quarter- wave plate, as well as an implementation of CNOT and Pauli gates, by using two atoms confined in a 2D plane. The internal states of the atoms are taken to be Rydberg circular states. Using this model we can manipulate the motional state of the atom, with possible applications in optomechanical integrated circuits for quantum information processing and quantum simulation. Towards this aim, we study the interaction of two trapped atoms with tw…
Quantum manipulation of individual phonons could offer new resources for studying fundamental physics and creating an innovative platform in quantum information science. Here, we propose to generate quantum states of strongly correlated phonon bundles associated with the motion of a trapped atom. Our scheme operates in the atom-phonon resonance regime where the energy spectrum exhibits strong anharmonicity such that energy eigenstates with different phonon numbers can be well-resolved in the parameter space. Compared to earlier schemes operating in the far dispersive regime, the bundle states …
Preparation and light-mediated distribution of motional state entanglement
我们描述和分析了（i）纠缠一个或几个谐波捕获原子或离子的正交运动模式的数值方案，以及（ii）通过先前工作中提出的光介导的量子态转移过程将纠缠从这些局域模式之一转移到远处的捕获原子（或原子）。Parkins和H. J. Kimble，J. Opt. B：量子半类。1，496（1999）]。这些方案的可能性包括在相距较远的囚禁原子的位置和动量中产生Einstein-Podolsky-Rosen态以及制备离域介观振动态。
We have demonstrated transport of Be+ ions through a 2D Paul-trap array that incorporates an X-junction, while maintaining the ions near the motional ground-state of the confining potential well. We expand on the first report of the experiment [1], including a detailed discussion of how the transport potentials were calculated. Two main mechanisms that caused motional excitation during transport are explained, along with the methods used to mitigate such excitation. We reduced the motional excitation below the results in Ref. [1] by a factor of approximately 50. The effect of a mu-metal shield…
Remote Gottesman-Kitaev-Preskill Entanglement Generation between Trapped Ions
School of Mathematical and Physical Sciences, Keio University（庆应义塾大学数理科学学院）；Department of Electronics and Electrical Engineering, Keio University（庆应义塾大学电子电气工程系）；Advanced ICT Research Institute, National Institute of Information and Communications Technology (NICT)（信息通信研究机构高级ICT研究所）
Characterization and cancellation of power-line-induced motional-mode frequency noise in a trapped-ion system
Seoul National University（首尔大学）；Department of Computer Science and Engineering, Seoul National University（首尔大学计算机科学与工程系）；Automation and Systems Research Institute, Seoul National University（首尔大学自动化与系统研究所）；NextQuantum, Seoul National University（首尔大学NextQuantum）
Efficient preparation and detection of the motional state of trapped ions is important in many experiments ranging from quantum computation to precision spectroscopy. We investigate the stimulated Raman adiabatic passage (STIRAP) technique for the manipulation of motional states in a trapped ion system. The presented technique uses a Raman coupling between two hyperfine ground states in $^{25}$Mg$^+$, implemented with delayed pulses, which removes a single phonon independent of the initial motional state. We show that for a thermal state the STIRAP population transfer is more efficient than a …
Trapped atomic ions are a versatile platform for studying interactions between spins and bosons by coupling the internal states of the ions to their motion. Measurement of complex motional states with multiple modes is challenging, because all motional state populations can only be measured indirectly through the spin state of ions. Here we present a general method to determine the Fock state distributions and to reconstruct the density matrix of an arbitrary multi-mode motional state. We experimentally verify the method using different entangled states of multiple radial modes in a 5-ion chai…
We present a new method of spin-motion coupling for trapped ions using microwaves and a magnetic field gradient oscillating close to the ions' motional frequency. We demonstrate and characterize this coupling experimentally using a single ion in a surface-electrode trap that incorporates current-carrying electrodes to generate the microwave field and the oscillating magnetic field gradient. Using this method, we perform resolved-sideband cooling of a single motional mode to its ground state.
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 present a study of the coherence properties of a variety of motional states of a single ion confined in a Penning ion trap. We demonstrate that the motion of the ion has a coherence time of the order of one second, using Ramsey interferometry. We introduce a technique for preparing the ion in an incoherent superposition of highly-excited motional states using a simple modification of optical sideband cooling. Coherent manipulation of these states allow measurements of optical and motional coherence to be carried out. We show that these highly-excited motional state superpositions have long …
Modular mixed-species ion-trap networks are a promising framework for scalable quantum information processing, where one species acts as a memory qubit and another as a communication qubit. This architecture requires high-fidelity mixed-species entangling gates to transfer information from communication to memory qubits through their collective motion. We investigate the character of the motional modes of a mixed-species ion chain for entangling operations and also sympathetic cooling. We find that the laser power required for high-fidelity entangling gates based on transverse modes is at leas…
In this work, we derive analytic formulae that determine the effect of error mechanisms on one- and two-qubit gates in trapped ions and electrons. First, we analyze, and derive expressions for, the effect of driving field inhomogeneities on one-qubit gate fidelities. Second, we derive expressions for two-qubit gate errors, including static motional frequency shifts, trap anharmonicities, field inhomogeneities, heating, and motional dephasing. We show that, for small errors, each of our expressions for infidelity converges to its respective numerical simulation; this shows our formulae are suff…
We implement faster-than-adiabatic two-qubit phase gates using smooth state-dependent forces. The forces are designed to leave no final motional excitation, independently of the initial motional state in the harmonic, small-oscillations limit. They are simple, explicit functions of time and the desired logical phase of the gate, and are based on quadratic invariants of motion and Lewis-Riesenfeld phases of the normal modes.
The dominant error sources for state-of-the-art laser-free trapped-ion entangling gates are decoherence of the qubit state and the ion motion. The effect of these decoherence mechanisms can be suppressed with additional control fields, or with techniques that have the disadvantage of reducing gate speed. Here, we propose using a near-motional-frequency magnetic field gradient to implement a laser-free gate that is simultaneously resilient to both types of decoherence, does not require additional control fields, and has a relatively small cost in gate speed.
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 frequen…
A protocol is provided to reconstruct the Wigner function for the motional state of a trapped ion via fluorescence detection on another ion in the same trap. This "sympathetic tomography" of a dark ion without optical transitions suitable for state measurements is based on the mapping of its motional state onto one of the collective modes of the ion pair. The quantum state of this vibrational eigenmode is subsequently measured through sideband excitation of the bright ion. Physical processes to implement the desired state transfer and read-out are derived, and the accomplishment of the scheme …
We show that the motion of a cold trapped ion can be squeezed by modulating the intensity of a phase-stable optical lattice placed inside the trap. As this method is reversible and state selective it effectively implements a controlled-squeeze gate. We show how to use this resource, that can be useful for quantum information processing with continuous variables, in order to prepare coherent superpositions of states which are squeezed along complementary quadratures. We show that these states, which we denote as "${\mathcal X}$-states", exhibit high sensitivity to small displacements along two …
We propose a new scheme for supplying voltages to the electrodes of microfabricated ion traps, enabling access to a regime in which changes to the trapping potential are made on timescales much shorter than the period of the secular oscillation frequencies of the trapped ions. This opens up possibilities for speeding up the transport of ions in segmented ion traps and also provides access to control of multiple ions in a string faster than the Coulomb interaction between them. We perform a theoretical study of ion transport using these methods in a surface-electrode trap, characterizing the pr…
The effect of geometrical perturbations on ion oscillation frequencies in a 3-D quadrupole trap is analyzed by theoretical simulations and compared with the experimental results. Theoretically, the distorted potential within this non-ideal trap caused by the insertion of filament has been simulated. An analytical expression for the potential is then fitted and numerical solution of the equations of trapped ion motion is obtained. Motional frequencies are then calculated from the Fourier transformation of the simulated ion trajectories at any given trapping potential and compared with our exper…
Electric field noise is a major source of motional heating in trapped ion quantum computation. While the influence of trap electrode geometries on electric field noise has been studied in patch potential and surface adsorbate models, only smooth surfaces are accounted for by current theory. The effects of roughness, a ubiquitous feature of surface electrodes, are poorly understood. We investigate its impact on electric field noise by deriving a rough-surface Green's function and evaluating its effects on adsorbate-surface binding energies. At cryogenic temperatures, heating rate contributions …
We study the entangling power of a nanoelectromechanical system (NEMS) simultaneously interacting with two separately trapped ions. To highlight this entangling capability, we consider a special regime where the ion-ion coupling does not generate entanglement in the system, and any resulting entanglement will be the result of the NEMS acting as an entangling device. We study the dynamical behavior of the bipartite NEMS-induced ion-ion entanglement as well as the tripartite entanglement of the whole system (ions+NEMS). We found some quite remarkable phenomena in this hybrid system. For instance…
We theoretically propose and experimentally demonstrate a parallel-electromagnetically-induced transparency (parallel-EIT) cooling technique for ion crystals in the Paul trap. It has less stringent requirements on the cooling resonance condition than the standard electromagnetically-induced transparency (EIT) cooling, thus allowing, in principle, to simultaneously cool the motional mode spectrum with an arbitrary range. A proof-of-principle validation for this cooling scheme is experimentally demonstrated with up to 4 trapped 40Ca+ ions. We observe simultaneous near-ground-state cooling for al…
本文研究了在S_1/2-P_1/2（493 nm）和P_1/2-D_3/2（650 nm）共振附近激光照射下，两个138 Ba ~+离子在电动势阱中集体振动的冷却。离子的运动状态由空间分辨光电倍增管监测。根据失谐量和强度的冷却激光，宏观上不同的运动状态对应于不同的离子温度观察。我们还推导出离子的温度从详细的分析计算的激光冷却考虑到塞曼结构的能级参与。观察到的运动状态与计算的温度完全匹配。在塞曼分裂S_1/2-D_3/2拉曼跃迁的暗共振附近观察到明显的加热。在这里，双光子过程主导激光和离子之间的相互作用。识别出暗示最有效的激光冷却的激光参数状态。
