Hyperfine and optical barium ion qubits

Dietrich, Matthew R.; Kurz, N.; Noël, Thomas; Shu, Gang; Blinov, B. B.

doi:10.1103/physreva.81.052328

Phys. Rev. A

2010

DOI: 10.1103/physreva.81.052328

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Hyperfine and optical barium ion qubits

Matthew R. Dietrich

N. Kurz

Thomas Noël

et al.

Abstract: State preparation, qubit rotation, and high fidelity readout are demonstrated for two separate 137 Ba + qubit types. First, an optical qubit on the narrow 6S 1/2 to 5D 5/2 transition at 1.76 µm is implemented. Then, leveraging the techniques developed there for readout, a ground state hyperfine qubit using the magnetically insensitive transition at 8 GHz is accomplished.

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Cited by 38 publications

(37 citation statements)

References 35 publications

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“…State detection is performed by monitoring the ion fluorescence at the 493-nm cooling laser transition, which is collected with a microscope objective with a numerical aperture of 0.28 , spatially filtered, and sent to a photomultiplier tube (PMT). With photon counts of approximately 3000/s while fluorescing, we are able to distinguish bright and dark states with over 99% efficiency after 10 ms of observation time [23].…”

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confidence: 92%

“…The laser is frequency stabilized via a Pound-Drever-Hall (PDH) lock to a temperature-stabilized Zerodur TM cavity with a finesse of approximately 1000 and free spectral range of 0.5 GHz placed in high vacuum [22]. Coherence times of approximately 150 µs of Rabi oscillations between the ground state and the excited state indicate a laser linewidth of no greater than 10 kHz [23]. A double-pass acousto-optic modulator (AOM) shifts the frequency of a part of the laser power and introduces the frequency modulation necessary for a locking signal.…”

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confidence: 99%

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Measurement of the Landégfactor of the5D5/2state of Ba ii with a single trapped ion

et al. 2010

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We present a terrestrial measurement of the Landé g factor of the 5D 5/2 state of singly ionized barium. Measurements were performed on single Doppler-cooled 138 Ba + ions in a linear Paul trap. A frequency-stabilized fiber laser with a nominal wavelength of 1.762 µm was scanned across the 6S 1/2 ↔ 5D 5/2 transition to spectroscopically resolve transitions between Zeeman sublevels of the ground and excited states. From the relative positions of the four narrow transitions observed at several different values for the applied magnetic field, we find a value of 1.2020 ± 0.0005 for g 5D 5/2 .

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confidence: 92%

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confidence: 99%

Measurement of the Landégfactor of the5D5/2state of Ba ii with a single trapped ion

et al. 2010

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“…The procedure to measure the hyperfine intervals is similar to that proposed in [4,10] and the relevant level structure is given in Fig. 1.…”

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confidence: 99%

“…By combining high precision radio frequency (rf) spectroscopy with shelving techniques [4,5] on singly trapped ions, we measure the hyperfine intervals of the 5D 3/2 manifold to an accuracy below a few Hz. Together with theoretical calculations, this permits a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants and the first observation of the magnetic octupole moment in 137 Ba + .…”

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confidence: 99%

Spectroscopy on a single trapped ^137Ba^+ ion for nuclear magnetic octupole moment determination

Lewty¹,

Chuah²,

Cazan³

et al. 2012

Opt. Express

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We present precision measurements of the hyperfine intervals in the 5D 3/2 manifold of a single trapped Barium ion, 137 Ba + . Measurements of the hyperfine intervals are made between mF = 0 sublevels over a range of magnetic fields allowing us to interpolate to the zero field values with an accuracy below a few Hz, an improvement on previous measurements by three orders of magnitude. Our results, in conjunction with theoretical calculations, provide a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants. In addition, we obtain the magnetic octupole constant (C) with an accuracy below 0.1 Hz. This gives a subsequent determination of the nuclear magnetic octupole moment, Ω, with an uncertainty of 1% limited almost completely by the accuracy of theoretical calculations. This constitutes the first observation of the octupole moment in 137 Ba + and the most accurately determined octupole moment to date. High precision measurements of the hyperfine structure provides stringent tests for state-of-the-art atomic structure calculations. These calculations play a crucial role in the interpretation of parity nonconservation (PNC) experiments which provide important tests of the standard model at low energy [1]. The accuracy of calculated PNC matrix elements can be assessed by comparing measured hyperfine structure constants with calculated values [2]. In addition, the hyperfine structure provides insight into the nuclear structure of atoms [3].In this paper we present precision measurements of the hyperfine intervals of the 5D 3/2 manifold of 137 Ba + . By combining high precision radio frequency (rf) spectroscopy with shelving techniques [4,5] on singly trapped ions, we measure the hyperfine intervals of the 5D 3/2 manifold to an accuracy below a few Hz. Together with theoretical calculations, this permits a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants and the first observation of the magnetic octupole moment in 137 Ba + . We determine the magnetic octupole moment, Ω, to an accuracy of 1% percent limited almost entirely by uncertainties in the theory. Ba + is an excellent candidate for magnetic octupole determination. Long lived metastable D states permit high precision spectroscopy measurements of the hyperfine levels, and high precision calculations are possible [6]. In [7] it was shown that the hyperfine intervals, δW F = W F − W F +1 , of the 5D 3/2 manifold can be written where C is the magnetic octupole hyperfine constant while η and ζ are the correction terms characterizing the mixing with the upper 5D 5/2 manifold. With measured values of the hyperfine intervals, δW k , and theoretical estimates for the correction terms we can solve the equations for the hyperfine constants. The octupole moment, Ω, can then be extracted from our theoretical result [8]using the CCSD(T) method described in [2,9], where µ N is the Bohr magneton and b is the barn unit of area. The procedure to measure the hyp...

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“…State readout employs the fact that the 5D 5/2 level is long-lived (τ = 35 s) and disjoint from the cooling cycle. Thus if we address the ion with the cooling lasers we will quickly be able to distinguish between the dark 5D 5/2 level and the bright ground state [14]. With standard refractive optics outside the vacuum chamber we can collect thousands of fluorescence photons per second from an ion in the cooling cycle, whereas the signal from laser scatter and photomultiplier tube (PMT) dark counts is less than one hundred counts per second.…”

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confidence: 99%

Adiabatic passage in the presence of noise

et al. 2012

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We report on an experimental investigation of rapid adiabatic passage (RAP) in a trapped barium ion system. RAP is implemented on the transition from the 6S 1/2 ground state to the metastable 5D 5/2 level by applying a laser at 1.76 µm. We focus on the interplay of laser frequency noise and laser power in shaping the effectiveness of RAP, which is commonly assumed to be a robust tool for high efficiency population transfer. However, we note that reaching high state transfer fidelity requires a combination of small laser linewidth and large Rabi frequency.PACS numbers: 32.80. Xx, 32.80.Qk, 37.10.Ty Adiabatic passage has been used for coherent population transfer in many fields [1][2][3][4]. Nuclear magnetic resonance (NMR) was the first system in which adiabatic passage was implemented [1]. In an NMR system, slowly varying the magnetic field frequency or direction can transfer population between nuclear spin states. The technique has since been applied to infrared and optical transitions in atomic and molecular systems [2,3]. In such systems the frequency of a laser is swept across a transition, effecting population transfer between the ground state and an excited state. More recently, adiabatic passage has been applied in trapped singly ionized alkali earth element systems similar to ours. This has enabled high fidelity (≥ 0.99) readout of ionic qubit states [5,6]. Using adiabatic passage for state detection has several important advantages over a simple π-pulse of resonant light. First, small drifts in laser frequency do not cause a dramatic change in transfer fidelity. Similarly, adiabatic passage is mostly insensitive to frequency shifts caused by magnetic field fluctuations. Additionally, adiabatic passage efficiency is not strongly dependent on laser power, and so obviates the need for laser intensity stabilization. On the other hand, adiabatic passage is necessarily slower than a π-pulse and still requires optical coherence of a sufficient degree that Rabi oscillations can be observed. Previous experiments on RAP were done with sufficiently high Rabi frequency and low driving field noise that the role of noise processes was not investigated. There is considerable interest in the role that noise plays in adiabatic processes for applications in adiabatic quantum computing [7][8][9]. Here we present a detailed study of the dependence of adiabatic passage efficiency on laser noise and other relevant parameters.The theory behind adiabatic passage has been described in several papers and books [5,[10][11][12][13], so we will only sketch the idea in broad strokes. Consider a Hamiltonian H, which describes two states whose energies cross as a function of a parameter ∆. Now add to this Hamiltonian a term which couples the two states, yielding a new Hamiltonian H ′ . The eigenstates of H ′ will exhibit an avoided crossing as a function of ∆. Consider such a coupled system initially in an eigenstate of H with ∆ set such that the energy splitting between the states is much larger than the coupling energy. If ∆ is n...

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Hyperfine and optical barium ion qubits

Cited by 38 publications

References 35 publications

Measurement of the Landégfactor of the5D5/2state of Ba ii with a single trapped ion

Measurement of the Landégfactor of the5D5/2state of Ba ii with a single trapped ion

Spectroscopy on a single trapped ^137Ba^+ ion for nuclear magnetic octupole moment determination

Adiabatic passage in the presence of noise

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