We realize a spin-1 Dicke model using magnetic sub-levels of the lowest F = 1 hyperfine level of 87 Rb atoms confined to a high finesse cavity. We study this system under conditions of imbalanced driving, which is predicted to have a rich phase diagram of nonequilibrium phases and phase transitions. We observe both super-radiant and oscillatory phases from the cavity output spectra as predicted by theory. Exploring the system over a wide range of parameters, we obtain the boundaries between the normal, super-radiant and the oscillatory phases, and compare with a theoretical model.

The Dicke model is of fundamental importance in quantum mechanics for understanding the collective behaviour of atoms coupled to a single electromagnetic mode. In this paper, we demonstrate a Dicke-model simulation using cavity-assisted Raman transitions in a configuration using counterpropagating laser beams. The observations indicate that motional effects should be included to fully account for the results and these results are contrasted with the experiments using single-beam and co-propagating configurations. A theoretical description is given that accounts for the beam geometries used in the experiments and indicates the potential role of motional effects. In particular a model is given that highlights the influence of Doppler broadening on the observed thresholds. arXiv:1801.07888v1 [quant-ph]

Measurement of the branching ratios for 6P 1/2 decays to 6S 1/2 and 5D 3/2 in 138 Ba + are reported with the decay probability from 6P 1/2 to 5D 3/2 measured to be p = 0.268177 ± (37)stat − (20)sys. This result differs from a recent report by 12σ. A detailed account of systematics is given and the likely source of the discrepancy is identified. The new value of the branching ratio is combined with a previous experimental results to give a new estimate of τ = 7.855(10) ns for the 6P 1/2 lifetime. In addition, ratios of matrix elements calculated from theory are combined with experimental results to provide improved theoretical estimates of the 6P 3/2 lifetime and the associated matrix elements. arXiv:1905.06523v1 [physics.atom-ph]

We propose and experimentally demonstrate a scheme which effects hyperfine averaging during a Ramsey interrogation of a clock transition. The method eliminates the need to average over multiple optical transitions, reduces the sensitivity of the clock to its environment, and reduces inhomogeneous broadening in a multi-ion clock. The method is compatible with auto-balanced Ramsey spectroscopy, which facilitates elimination of residual shifts due to imperfect implementation and ac stark shifts from the optical probe. We demonstrate the scheme using correlation spectroscopy of the 1 S0 ↔ 3 D1 clock transition in a three-ion Lu + clock. From the demonstration we are able to provide a measurement of the 3 D1 quadrupole moment, Θ( 3 D1) = 0.634(9)ea 2 0 .

We demonstrate precision measurement and control of inhomogeneous broadening in a multiion clock consisting of three 176 Lu + ions. Microwave spectroscopy between hyperfine states in the 3 D1 level is used to characterise differential systematic shifts between ions, most notably those associated with the electric quadrupole moment. By appropriate alignment of the magnetic field, we demonstrate suppression of these effects to the ∼ 10 −17 level relative to the 1 S0 ↔ 3 D1 optical transition frequency. Correlation spectroscopy on the optical transition demonstrates the feasibility of a 10 s Ramsey interrogation in the three ion configuration with a corresponding projection noise limited stability of σ(τ ) = 8.2 × 10 −17 / √ τ .With fractional uncertainties near to ∼ 10 −18 , stateof-the-art optical atomic clocks are among the most accurate scientific artefacts [1]. The two most successful realizations are ensembles of neutral atoms stored in optical lattices [2,3] and ions confined in radio-frequency (RF) traps [4,5]. The latter offers strong confinement such that atoms can be reused for subsequent clock interrogation and measurement. The stability of the current generation of trapped-ion optical clocks is limited by single-ion operation. This has limited the instability of ion-based clocks to ∼ 10 −15 / √ τ , for which averaging times τ of several days or even weeks are required to reach 10 −18 resolution. Modest improvements to stability can be expected as laser technology develops to allow longer interrogation times but ideally this would go hand-in-hand with an increase in the number of ions.Within the standard quantum limit (SQL), clock stability improves with the √ N where N is the number of atoms [6]. With an ensemble of ions, frequency resolution could be further enhanced using entangled states [7][8][9][10][11] or cascaded interrogation schemes [12,13]. From a technological standpoint, extension of clock operation to a small ensemble of ions is an immediate application for devices developed for small-scale quantum information processing (QIP). However, characterizing and maintaining exquisite control over various systematic effects in an ion ensemble is a significant challenge.Multi-ion operation is complicated by electric quadrupole (EQ) shifts arising from the Coulomb fields of neighbouring ions, excess-micromotion (EMM) shifts induced by the radio-frequency (rf) trapping field, and inhomogeneous magnetic fields. Efforts and proposals towards high-accuracy multi-ion optical clocks include (i) precision engineering of the ion trap to suppress EMM shifts [14], (ii) employing clock transitions with a negative differential scalar polarisability, ∆α 0 , to eliminate EMM shifts in a large ion crystal [15,16], and (iii) using dynamic decoupling or rf-dressed states to 646 nm 1 S 0 3 D 1 3 D 2 3 P 0 = 8 = 7 = 6 847.7 nm Hyperfine splitting: ~11.2 GHz 10.5 GHz 3 P 1 1 D 2 622 nm 895 nm 350 nm FIG. 1. Relevant energy level diagram of a 176 Lu + ion showing: the 1 S0 ↔ 3 D1 clock transition at 848 nm, the 3 D1 ↔ 3 ...

The zero crossing of the dynamic differential scalar polarizability of the S 1/2 −D 5/2 clock transition in 138 Ba + has been determined to be 459.1614(28) THz. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ( 700 nm). In particular it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.PACS numbers: 06.30.Ft, 06.20.fb Singly-ionized barium has been well studied over the years with a wide range of precision measurements [1][2][3][4][5][6][7][8] that have provided valuable benchmark comparisons for theory [9][10][11][12][13][14]. It was recently proposed that some of these measurements, specifically high accuracy measurements of transition matrix elements and branching ratios, could be used to construct an accurate representation of the dynamic differential scalar polarizability, ∆α 0 (ω) of the S 1/2 −D 5/2 clock transition over a large wavelength range [15]. Crucial to that proposal was a determination of a zero crossing ∆α 0 (ω 0 ) = 0 near 653 nm, which bounds significant contributions to ∆α 0 (ω) from the ultraviolet (uv) spectrum. Here we determine ω 0 with an inaccuracy of a few GHz.To find ω 0 , a linearly polarized laser beam near 653 nm is focussed onto the ion to induce an ac Stark shift of the clock transition and the shift measured as a function of the laser frequency ω. The ac Stark shift, δ s (M J ), induced by the 653-nm laser is given bywhere M J denotes the applicable eigenstate of D 5/2 , α 2 (ω) is the dynamic tensor polarizability of D 5/2 , and θ is angle between the 653-nm laser polarization and the quantization axis. The tensor component can be eliminated by determining the average ac Stark shiftHence, with the laser intensity fixed, δ 0 (ω) is directly proportional to ∆α 0 (ω), which is approximately linear * phybmd@nus.edu.sg in a neighbourhood of ω 0 . Consequently, ω 0 can be determined from a linear fit to measurements of δ 0 (ω) as a function of ω with an accuracy limited by the projection noise of the measurements, and a small nonlinearity in ∆α 0 (ω), which can be estimated from theory. Although the laser power is actively stabilized outside the experiment chamber, etaloning effects and uncalibrated frequency response of the detector can give rise to a frequency dependence of the resulting laser intensity at the ion. In addition, pointing stability of the laser can also degrade the accuracy of the ac Stark shift measured at a single frequency. To compensate these effects, one can make use of the weighted average δ 2 (ω) = 25 42 δ s (5/2) − 1 5 δ s (3/2) − 4 5 δ s (1/2)which is a measure of the tensor polarizability. The ratio δ 0 (ω)/δ 2 (ω) is then independent of slow variations in the intensity but has the same zero crossing. In addition, setting θ ≈ π/2 minimizes the influence of magnetic field pointing stability, which would compromise the stability of δ 2 (ω). Measurements are carr...

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