Single ion as a shot-noise-limited magnetic-field-gradient probe

Walther, Andreas; Poschinger, Ulrich; Ziesel, Frank; Hettrich, M.; Wiens, A.; Welzel, J.; Schmidt‐Kaler, F.

doi:10.1103/physreva.83.062329

Cited by 7 publications

(6 citation statements)

References 19 publications

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“…Eight additional magnets are placed to compensate for the magnetic field gradient at the ion position. This is done by characterizing the magnetic field homogeneity by measuring the Zeeman splitting at different locations along the trap axis [22], and results in a spatial variation of the Zeeman splitting of less than 2π× 1 kHz in a position range of ± 1 mm around the trapping location. The closest distance of a magnet to a µ-metal wall is about 20 cm, such that no saturation of the µ-metal occurs, which would compromise the shielding.…”

Section: Methodsmentioning

confidence: 99%

“…• Drifts of the trapped ion position in conjunction with the magnetic field inhomogeneity: By performing Ramsey measurements in combination with ion shuttling [22], we observed a gradient of the Zeeman splitting of about 2π× 8·10 6 Hz/m. Thus, positions drifts from uncontrolled charging of the trap or its thermal expansion might also contribute.…”

Section: Decoherence Sourcesmentioning

confidence: 98%

See 1 more Smart Citation

A long-lived Zeeman trapped-ion qubit

Ruster¹,

Schmiegelow²,

Kaufmann³

et al. 2016

Appl. Phys. B

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108

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We demonstrate a coherence time of 2.1(1)~s for electron spin superposition states of a single trapped $^{40}$Ca$^+$ ion. The coherence time, measured with a spin-echo experiment, corresponds to residual rms magnetic field fluctuations $\leq$~2.7$\times$10$^{-12}$~T. The suppression of decoherence induced by fluctuating magnetic fields is achieved by combining a two-layer $\mu$-metal shield, which reduces external magnetic noise by 20 to 30~dB for frequencies of 50~Hz to 100~kHz, with Sm$_2$Co$_{17}$ permanent magnets for generating a quantizing magnetic field of 0.37~mT. Our results extend the coherence time of the simple-to-operate spin qubit to ultralong coherence times which so far have been observed only for magnetic insensitive transitions in atomic qubits with hyperfine structure

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Section: Methodsmentioning

confidence: 99%

Section: Decoherence Sourcesmentioning

confidence: 98%

A long-lived Zeeman trapped-ion qubit

Ruster¹,

Schmiegelow²,

Kaufmann³

et al. 2016

Appl. Phys. B

Self Cite

108

View full text Add to dashboard Cite

show abstract

“…4a is obtained using the carrier transition with and without transport. After a magnetic field gradient compensation has been performed [22], no phase shift between the two data sets is obtained, proving that the Zeeman splitting between the spin energy levels remains constant during the transport. The data in Fig.…”

mentioning

confidence: 97%

Controlling Fast Transport of Cold Trapped Ions

et al. 2012

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We realize fast transport of ions in a segmented micro-structured Paul trap. The ion is shuttled over a distance of more than 10 4 times its groundstate wavefunction size during only 5 motional cycles of the trap (280 µm in 3.6 µs). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10±0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing. . Scalable information processing in a multiplexed ion trap can be accomplished by having fixed processing sites where logic operations are performed, and ion qubits will be moved in and out of these regions by shuttling operations. The duration of such shuttling has to be much faster than the relevant decoherence times [4]. Furthermore, it is desirable to reduce the total time consumption of all relevant operations, where shuttling will contribute a considerable amount [5], and aim for the performance of the naturally fast solid state architectures [6]. So far, ion shuttling in a multiplexed trap has been demonstrated together with additional sympathetic cooling [7], and in the adiabatic regime, where the transient displacement of the ion is smaller than the size of the its wavepacket [8,9]. Transport of neutral atoms have also been performed using magnetic [10] or optical [11] techniques.Because quantum gate operations require ions close to the motional ground state and fast transport inherently creates motional excitation, the challenge is to develop transport protocols that guarantee sufficiency small energy transfer. In this work we demonstrate shuttling operations that are highly non-adiabatic while the final state of the ion is close to the motional groundstate. We also show that quantum information stored in both the motional and the spin degree of freedom is preserved through the shuttling.During a shuttling operation, the ion motion in the harmonic trapping potential is excited when the acceleration is sufficiently strong. This motional excitation is a harmonic oscillation, characterized by a well defined phase, thus allowing it to be canceled out by proper management of the forces involved during or after the transport. We experimentally demonstrate two methods of canceling the acquired motional excitation. One method uses two shuttles, where the transport to the destination generates the same net momentum transfer as the transport back, but is applied 180 • out of phase with respect to the secular oscillation of the ion (Fig. 1b). We refer to this as the pairwise energy-neutral transport. For the second scheme, the self-neutral transport we apply a sharp counter-"kick" to the ion at the end of a single transport operation, stopping its motion (Fig. 1c). This case of single-sided transport allows even faster shuttling and can be sequentially repeated since it is ener...

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“…If one has no a priori knowledge about B 0 one has to average [37] over all possible values of B 0 and one cannot infer the value of G. It is possible to avoid this problem by measuring this expectation value for different positioning {x i } at a fixed probing time t. This strategy has been realized with a single ion moving through a gradient field in Ref. [14]. However, this scheme is definitely a less practical solution as one has to make sure that the initial quantum states are the same, despite the change in the configuration of the chain.…”

Section: B Optimal Measurements For Experimental Realizationsmentioning

confidence: 99%

“…A different problem is the estimation of the gradient of a spatially distributed magnetic field [10][11][12]. Of course, one may just measure the field at different positions [13] or move a single probe through the field [14,15], and then compute the gradient. But these are not necessarily the optimal strategies, especially in cases where one aims to measure small fluctuations of a large offset field.…”

Section: Introductionmentioning

confidence: 99%

Estimation of gradients in quantum metrology

et al. 2017

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We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of $N$ particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Usually gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the off-set field determining the level-splitting of the particles and results in collective dephasing. In this work we use the framework of quantum metrology to assess the maximal accuracy for gradient estimation. For arbitrary positioning of particles, we identify optimal entangled and separable states allowing the estimation of gradients with the maximal accuracy, quantified by the quantum Fisher information. We also analyze the performance of states from the decoherence-free subspace (DFS), which are insensitive to the fluctuations of the magnetic offset field. We find that these states allow to measure a gradient directly, without the necessity of estimating the magnetic offset field. Moreover, we show that DFS states attain a precision for gradient estimation comparable to the optimal entangled states. Finally, for the above classes of states we find simple and feasible measurements saturating the quantum Cram\'er-Rao bound.Comment: 22 pages, 8 figures. See also the related work by I. Apellaniz et al. arXiv: 1703.09056 (2017

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Single ion as a shot-noise-limited magnetic-field-gradient probe

Cited by 7 publications

References 19 publications

A long-lived Zeeman trapped-ion qubit

A long-lived Zeeman trapped-ion qubit

Controlling Fast Transport of Cold Trapped Ions

Estimation of gradients in quantum metrology

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