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We present a measurement of the branching ratios from the 6P 3/2 state of BaII into all dipoleallowed decay channels (6S 1/2 , 5D 3/2 and 5D 5/2 ). Measurements were performed on single 138 Ba + ions in a linear Paul trap with a frequency-doubled mode-locked Ti:Sapphire laser resonant with the 6S 1/2 → 6P 3/2 transition at 455 nm by detection of electron shelving into the dark 5D 5/2 state. By driving a π Rabi rotation with a single femtosecond pulse, an absolute measurement of the branching ratio to 5D 5/2 state was performed. Combined with a measurement of the relative decay rates into 5D 3/2 and 5D 5/2 states performed with long trains of highly attenuated 455 nm pulses, it allowed the extraction of the absolute ratios of the other two decays. Relative strengths normalized to unity are found to be 0. Single trapped ions are a valuable physical system for many applications including quantum computation [1,2], frequency standards, optical metrology [3], precision searches for drifts in fundamental constants [4] and tests of exotic physical theories [5]. Among the advantages over alternatives are their long trapping lifetimes and the relative ease of confining single ions to a small volume in a trap, thereby reducing the systematic effects and negating the need for quantum statistics. The barium ion, particularly the odd 137 isotope with nuclear spin 3/2, has been proposed for use in quantum computation schemes with the hyperfine levels of the 6S 1/2 ground state for the qubit, as an optical frequency standard with a 2051 nm clock transition from 6S 1/2 , F = 2, m F = 0 to 5D 3/2 , F = 0, and as a test of parity-nonconservation with a small dipole coupling between the otherwise dipole-forbidden 6S 1/2 → 5D 3/2 transition [5,6,7].Accurate models of atomic wave functions which include many-body interactions are necessary to calculate dipole and quadrupole matrix elements that appear in the calculations of transition rates, energy level shifts and line widths in the experiments mentioned above. Measurements of branching ratios represent a better quantity from which to verify such values than, for example, precise measurements of the lifetimes of metastable states. They are less prone to systematic uncertainties such as background gas quenching and stray fields to which the long waiting times (tens of seconds) required to accurately measure lifetimes are sensitive. Here we present a single-ion measurement of the branching ratios from the 6P 3/2 state of 138 Ba + to the three states allowed via dipole transitions, 6S 1/2 , 5D 3/2 and 5D 5/2 .A schematic of the optical and electronic arrangement of the experimental apparatus can be found in Fig. 1. The ion trap itself is a linear Paul trap with radiofrequency quadrupole confining potential and DC voltage end caps in ultra high vacuum with operating pressures of about 10 −11 torr. The trap dimensions are ∼ 0.5 mm radially and ∼ 3.3 mm axially. At ∼ 0.5 W of inductivelycoupled RF power at ∼ 32 MHz and 100 V end cap potential, the trap secular frequencies are measured to...

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.

Trapped, laser-cooled ions produce intense fluorescence. Detecting this fluorescence enables efficient measurement of quantum state of qubits based on trapped atoms. It is desirable to collect a large fraction of the photons to make the detection faster and more reliable. Additionally, efficient fluorescence collection can improve speed and fidelity of remote ion entanglement and quantum gates. Here we show a novel ion trap design that incorporates metallic spherical mirror as the integral part of the trap itself, being its RF electrode. The mirror geometry enables up to 35% solid angle collection of trapped ion fluorescence; we measure a 25% effective solid angle, likely limited by imperfections of the mirror surface. We also study properties of the images of single ions formed by the mirror and apply aberration correction. Owing to the simplicity of its design, this trap structure can be adapted for micro-fabrication and integration into more complex trap architectures.

Efficient collection of fluorescence from trapped ions is crucial for quantum optics and quantum computing applications, specifically, for qubit state detection and in generating single photons for ion-photon and remote ion entanglement. In a typical setup, only a few per cent of ion fluorescence is intercepted by the aperture of the imaging optics. We employ a simple metallic spherical mirror integrated with a linear Paul ion trap to achieve photon collection efficiency of at least 10% from a single Ba + ion. An aspheric corrector is used to reduce the aberrations caused by the mirror and achieve high image quality.With their long coherence time and the straightforward manipulation of internal and external states to store and process quantum information, trapped ions are among the most promising candidates for practical quantum computation [1][2][3]. Coupling of ionic qubits to single photons through spontaneous emission offers an attractive alternative [4] to the more traditional ion trap quantum computing architectures [5,6]. Reliable interconversion between quantum states of single ions and single photons thus becomes one of the most crucial tasks. A robust ion-photon coupling scheme is indispensable for implementing remote quantum gates between ions [7,8] and quantum repeaters [9]. Multi-element refractive optical systems are most widely used for ion and atom fluorescence collection and imaging [10][11][12][13][14][15][16]. Recently, such custom-designed, in-vacuum lenses capable of collecting about 4% of the photons from an ion were used to achieve 0.2% fiber coupling efficiency for 397 nm photons from Ca + [17]. High-finesse optical cavities have also been used [18][19][20] but their full potential has yet to be attained with ions where close proximity of the dielectric cavity mirrors is detrimental to the trapping itself.Simple reflective optics offer an attractive alternative and have been previously implemented in non-imaging fluorescence detectors such as [21]. Compared to their complex refractive counterparts, reflective optics can make large deflection of light propagation with considerably fewer elements and simpler surfaces. Because no transparency is necessary, metallic optical surfaces can be used, which can be placed in close proximity to the ion without affecting the trap performance. Much higher numerical apertures (N.A.) can thus be achieved with comparatively small size optics. Though placing an ion in the focus of a parabolic mirror may be the best scenario [22], and traps designed for such implementation have been successfully demonstrated [23], a high-N.A. parabola is a complicated surface to fabricate, especially in a smallscale device, which would be required for a scalable trapped-ion quantum information processor. Spherical mirrors are much simpler and can be fabricated using standard microelectromechanical systems (MEMS) technology [24]. The intrinsic large image aberrations caused * shugang@u.washington.edu by the spherical mirror can be compensated with optics located outside the ...

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...

Abstract. Efficient collection and analysis of trapped ion qubit fluorescence is essential for robust qubit state detection in trapped ion quantum computing schemes. We discuss simple techniques of improving photon collection efficiency using high numerical aperture (N.A.) reflective optics. To test these techniques we placed a spherical mirror with an effective N.A. of about 0.9 inside a vacuum chamber in the vicinity of a linear Paul trap. We demonstrate stable and reliable trapping of single barium ions, in excellent agreement with our simulations of the electric field in this setup. While a large N.A. spherical mirror introduces significant spherical aberration, the ion image quality can be greatly improved by a specially designed aspheric corrector lens located outside the vacuum system. Our simulations show that the spherical mirror/corrector design is an easy and cost-effective way to achieve high photon collection rates when compared to a more sophisticated parabolic mirror setup.

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