Quantum information processing and metrology with trapped ions

Wineland, David J.; Leibfried, D.

doi:10.1002/lapl.201010125

Cited by 95 publications

(108 citation statements)

References 221 publications

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“…Two of the primary objectives in quantum information processing and computing, are scaling to large numbers of quantum gates, and achieving fault-tolerant gate operation [1][2]. A promising approach to achieving both objectives is to use trapped ions, in which the quantum information is encoded on internal atomic states [3].…”

Section: Introductionmentioning

confidence: 99%

A 750-mW, continuous-wave, solid-state laser source at 313 nm for cooling and manipulating trapped 9Be+ ions

et al. 2011

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We present a solid-state laser system that generates 750 mW of continuous-wave single-frequency output at 313 nm. Sum-frequency generation with fiber lasers at 1550 nm and 1051 nm produces up to 2 W at 626 nm. This visible light is then converted to UV by cavity-enhanced second-harmonic generation. The laser output can be tuned over a 495 GHz range, which includes the 9 Be + laser cooling and repumping transitions. This is the first report of a narrow-linewidth laser system with sufficient power to perform fault-tolerant quantum-gate operations with trapped 9 Be + ions by use of stimulated Raman transitions. IntroductionTwo of the primary objectives in quantum information processing and computing, are scaling to large numbers of quantum gates, and achieving fault-tolerant gate operation [1][2]. A promising approach to achieving both objectives is to use trapped ions, in which the quantum information is encoded on internal atomic states [3]. Efforts to improve ion-trap scalability have focused on multizone arrays [4][5], with complex surface-electrode geometries that provide multiple trapping zones [6]. These traps include control electrodes that enable the shuttling of ions between zones that are used to perform gate operations, state detection, and information storage. For fault-tolerant two-qubit (quantum bit) gate operations, error-correction protocols have been proposed [7][8], but these require a sufficiently low error per gate (typically assumed to be less that 10 -4 ), and this threshold has not yet been achieved. In one approach, qubits are encoded into ground-state hyperfine states, since these are very well isolated from environmental effects that cause memory error. However, gate operations are usually performed via optical transitions with laser beams, leading to spontaneous emission that dominates gate error. Spontaneous emission is reduced by a large detuning from atomic resonance, but then higher laser powers required to maintain the gate speed. For example, Ozeri et al. calculate that with the commonly trapped ion species of 9 Be + , 25 Mg + , and 43 Ca + , in order to reach the fault-tolerant regime for a two-qubit phase gate, one needs narrow-linewidth, continuous-wave (cw) laser power in the range of 140 mW to 540 mW (and detuning from atomic resonance on the THz scale) [9].The most challenging aspect of developing laser sources for this purpose is that most of the wavelengths are in the UV region. For trapped 43 Ca + ions, the required 729 nm or 397 nm light can be generated directly with semiconductor lasers; but for the shorter wavelengths needed for most other trapped-ion species, the traditional approach has been to frequency-double the visible output from a ring dye laser. While solid-state lasers have replaced gas and dye lasers in many spectral regions, some wavelengths have remained difficult to produce. [11]. Their setup includes a frequencydoubled Nd:YAG laser at 532 nm, a titanium sapphire laser at 760 nm, and sum-frequency generation (SFG) in an enhancement cavity resona...

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Section: Introductionmentioning

confidence: 99%

A 750-mW, continuous-wave, solid-state laser source at 313 nm for cooling and manipulating trapped 9Be+ ions

et al. 2011

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“…Fig. 3(a) shows the evolution of the graph state fidelity P graph (t) = Tr p {ρ(t)|Φ g Φ g |} for ǫ = 0.05 and ǫ = 0.1 (solid lines), where ρ(t) is the density matrix evolved under the full Hamiltonian (9) and Tr p denotes the partial trace over the phonon degrees of freedom. The dashed line shows the evolution calculated from the effective spin Hamiltonian (10).…”

Section: B Generation Of Graph Statesmentioning

confidence: 99%

“…A pioneering role in this context is played by systems of trapped ions [8,9], where effective, phonon-mediated spin-spin interactions can be implemented and controlled by applying state-dependent light forces [10][11][12][13][14][15][16]. Indeed, several proof-of-principle experiments [17][18][19][20] have already demonstrated the possibility to simulate Ising interactions with up to nine spins and with such ion trap quantum simulators it might soon be possible to outperform the best numerical simulations which are achievable on classical computers today.…”

Section: Introductionmentioning

confidence: 99%

Long-range and frustrated spin-spin interactions in crystals of cold polar molecules

2011

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We describe a simple scheme for the implementation and control of effective spin-spin interactions in selfassembled crystals of cold polar molecules. In our scheme spin states are encoded in two long-lived rotational states of the molecules and coupled via state dependent dipole-dipole forces to the lattice vibrations. We show that by choosing an appropriate time dependent modulation of the induced dipole moments the resulting phononmediated interactions compete with the direct dipole-dipole coupling and lead to long-range and tunable spinspin interaction patterns. We illustrate how this technique can be used for the generation of multi-particle entangled spin states and the implementation of spin models with longe-range and frustrated interactions which exhibit non-trivial phases of magnetic ordering.

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“…Our scheme is applicable for providing Raman beams across other ion species and neutral atoms where coherent optical manipulation is required. c 2013 Optical Society of America OCIS codes: 000.0000, 999.9999.Ions held in rf traps are a standard system for quantum information processing experiments [1]. One of the key challenges is to realize coherent operations with fidelities high enough to allow the implementation of quantum error correction protocols [2].…”

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Injection locking of two frequency-doubled lasers with 32 GHz offset for driving Raman transitions with low photon scattering in Ca43^+

2013

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We describe the injection locking of two infrared (794 nm) laser diodes which are each part of a frequencydoubled laser system. An acousto-optic modulator (AOM) in the injection path gives an offset of 1.6 GHz between the lasers for driving Raman transitions between states in the hyperfine split (by 3.2 GHz) ground level of 43 Ca + . The offset can be disabled for use in 40 Ca + . We measure the relative linewidth of the frequency-doubled beams to be 42 mHz in an optical heterodyne measurement. The use of both injection locking and frequency doubling combines spectral purity with high optical power. Our scheme is applicable for providing Raman beams across other ion species and neutral atoms where coherent optical manipulation is required. c 2013 Optical Society of America OCIS codes: 000.0000, 999.9999.Ions held in rf traps are a standard system for quantum information processing experiments [1]. One of the key challenges is to realize coherent operations with fidelities high enough to allow the implementation of quantum error correction protocols [2]. The sub-states of the ground level of alkali earth ions are commonly used as the qubit states [3,4]. In 43 Ca + with its nuclear spin (I = 7/2) a pair of Zeeman states from the F = 3 and F = 4 hyperfine manifolds can be chosen [5, 6]. At specific magnetic field strengths pairs of magnetic-field insensitive clockstates are available that have recently been shown to have extremely long coherence times [7] making 43 Ca + a promising species for quantum information. Coherent transitions between the qubit states may either be driven by rf/microwave radiation [8] or by a pair of Raman laser beams near the 4S 1/2 to 4P 1/2 transition at 397 nm [4]. Their strong coupling to the motion makes Raman beams particularly attractive for sideband cooling and motional entangling gates.With Raman lasers the choice of detuning ∆ from the 4S 1/2 to 4P 1/2 transition is a compromise between higher speed at small detuning (scaling ∼ 1/∆) and lower offresonant photon scattering (which introduces qubit errors) at large detuning (scaling ∼ 1/∆ 2 ). Typical detunings are in the range of 10−1000GHz. For a desired gate speed, the fidelity of qubit operations depends on the available Raman beam power. Typically, powers around 1 mW have been used. For common experimental parameters and a desired two-qubit gate error probability of 10 −4 in a gate time of 10 µs, beam powers of around 100 mW are required [9,10].The two-photon Raman process only depends on the difference frequency between the two beams and its detuning from the qubit resonance which is why there are no stringent requirements for absolute frequency stability. Instead, relative interferometric stability between the beams is needed. (TAs) are not yet commercially available at 397 nm. Another alternative is injection locking, where only a low intensity seed beam needs to be frequency shifted. This has recently been reported with violet diode lasers [13]. While this approach is currently limited to ∼ 20 mW of output power, it shows ...

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Quantum information processing and metrology with trapped ions

Cited by 95 publications

References 221 publications

A 750-mW, continuous-wave, solid-state laser source at 313 nm for cooling and manipulating trapped 9Be+ ions

A 750-mW, continuous-wave, solid-state laser source at 313 nm for cooling and manipulating trapped 9Be+ ions

Long-range and frustrated spin-spin interactions in crystals of cold polar molecules

Injection locking of two frequency-doubled lasers with 32 GHz offset for driving Raman transitions with low photon scattering in Ca43^+

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