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arXiv:0801.0078 · Physical Review Letters

Individual Addressing of Trapped Ions and Coupling of Motional and Spin States Using rf Radiation

M. Johanning, A. Braun, Nuala Timoney, Vladimir Elman, Werner Neuhauser, C. Wunderlich

Published Feb 20, 2009• 130 citations
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Abstract

Individual electrodynamically trapped and laser cooled ions are addressed in frequency space using radio-frequency radiation in the presence of a static magnetic field gradient. In addition, an interaction between motional and spin states induced by an rf field is demonstrated employing rf optical double resonance spectroscopy. These are two essential experimental steps towards realizing a novel concept for implementing quantum simulations and quantum computing with trapped ions.

DOI
10.1103/physrevlett.102.073004

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•Nov 1, 2015•2 citations
Individual electrodynamically trapped and laser cooled ions are addressed in frequency space using radio-frequency radiation in the presence of a static magnetic field gradient. In addition, an interaction between motional and spin states induced by an rf field is demonstrated employing rf optical double resonance spectroscopy. These are two essential experimental steps towards realizing a novel concept for implementing quantum simulations and quantum computing with trapped ions.
Recently it has been shown that the simulation of one quantum system by means of observing the dynamics of another suitably tailored quantum system can be experimentally far less demanding than universal quantum computation. A system of pair-wise coupled spins described by a Heisenberg model, or a variant thereof, is particularly useful for quantum simulations that in turn are relevant, for instance, for condensed matter physics. We work on the implementation of a pseudo-spin many-body system that will serve as a well controlled prototype system and will allow for the exploration of quantum simulations: in a particular type of ion trap individual atomic ions interact via an adjustable pseudo-spin-spin coupling and, in addition, each spin is individually accessible, thus providing us with an "ion spin molecule". An important milestone towards realizing such ion spin molecules is the individual addressing of a particular spin employing a spatially varying magnetic field. We demonstrate for the first time individual addressing of ions using radio frequency radiation. Yb+ions are confined in a linear Paul trap and laser cooled such that they form a linear Coulomb crystal. Then, an RF-optical double resonance experiment is performed.
Excess "micromotion" of trapped ions due to the residual radio-frequency (rf) trapping field at their location is often undesirable and is usually carefully minimized. Here, we induce precise amounts of excess micromotion on individual ions by adjusting the local static electric field they experience. Micromotion modulates the coupling of an ion to laser fields, ideally tuning it from its maximum value to zero as the ion is moved away from the trap's rf null. We use tunable micromotion to vary the Rabi frequency of stimulated Raman transitions over two orders of magnitude, and to individually control the rates of resonant fluorescence from three ions under global laser illumination without any changes to the driving light fields. The technique is amenable to situations where addressing individual ions with focused laser beams is challenging, such as tightly packed linear ion strings or two-dimensional ion arrays illuminated from the side.
Novel ion traps that provide either a static or a dynamic magnetic gradient field allow for the use of radio-frequency radiation for coupling internal and motional states of ions, which is essential for conditional quantum logic. We show that the Hamiltonian describing this coupling in the presence of a resonant dynamic gradient, is identical, in a dressed state basis, to the Hamiltonian in the case of a static gradient. The coupling strength is in both cases described by the same effective Lamb-Dicke parameter. This insight can be used to overcome demanding experimental requirements when using a dynamic gradient field for state-of-the-art experiments with trapped ions, for example, in quantum information science. At the same time, this insight opens new experimental perspectives by way of using a single resonant or detuned dynamic gradient field, inducing long-range coupling, for conditional multi-qubit dynamics.
We investigate high frequency motional states of trapped atomic ions. Trapped ions in rf traps are confined by an approximate harmonic potential and exhibit quantum motional states that mediate essential techniques in quantum computing, simulation, networking, and precision measurement. However, motional state decoherence mechanisms, heating and dephasing, are broadly limiting: reduced two-qubit gate fidelities; lower fidelity and lifetime of highly nonclassical bosonic states; long laser cooling times; and large recoil heating rates. These also challenge the scalability of increasingly sophisticated protocols. We propose high motional frequency ion trapping as an operating regime that addresses these challenges and reshapes the design landscape for quantum information experiments and quantum control techniques. We report an experimentally motivated investigation of realizing this high-frequency regime and discuss the consequences for laser cooling, motional state coherence, fidelity and lifetime of nonclassical bosonic states, and scalability of experimental runtimes. We report clear design trajectories for ion traps to reach high motional frequency, a new limiting mechanism for laser cooling at these high frequencies, and more than an order-of-magnitude speedup in experimental duty cycles with larger speed ups possible for quantum error correction protocols. Taken together, high motional frequency ion trapping has broad implications for the future of quantum information experiments.
This thesis describes experimental work in which the spin and motional states of one and two trapped atomic ions are manipulated with long-wavelength radiation in the microwave and radio frequency (RF) regime. This allows single- and two-qubit quantum logic gates to be implemented with long-wavelength radiation, in contrast to laser frequency radiation used in the majority of work to date. The two-qubit gate scheme developed represents a significant advance towards a large scale quantum computing architecture in which laser light is not needed for coherent manipulation. An experimental setup is built in which a macroscopic linear Paul trap is fitted with permanent magnets to create a strong axial magnetic field gradient. This addition allows the spin and motional states of the ions to be coupled using long-wavelength radiation. The coherence time of qubits that are sensitive to the magnetic field gradient is increased by nearly three orders of magnitude with the use of dressed states and the lifetime and coherence time are measured to be T1 = 0.63(4) s and T2 = 0.65(5) s, respectively. Using the dressed-state qubit, sideband cooling of a single ion to the motional ground state is demonstrated, and the final mean phonon number after cooling is measured to be \bar{n} = 0.13(4). Finally, a two-qubit gate is demonstrated using the dressed-state qubits in conjunction with the magnetic field gradient, and a Bell state fidelity of F = 0.985(12) is determined. This is a significant increase in fidelity for a two-qubit gate based on long-wavelength radiation compared to previous work. The errors are analysed and it is shown that with the next generation of microfabricated traps being developed in the group, the gate fidelity using this scheme can be pushed far into the fault tolerant regime. This makes this scheme promising as an integral part of a large scale quantum computing architecture.