Spin-selective coherent light scattering from ion crystals

Abstract

We study coherent light scattering from linear crystals with up to twelve $^{40}\text{Ca}^+$ ions, acting as single photon emitters. Light-scattering is induced by two-photon laser excitation, starting from the S$_{1/2}\rightarrow$ D$_{5/2}$ quadrupole transition at 729~nm followed by the D$_{5/2}\rightarrow$ P$_{3/2}$ dipole transition at 854~nm, from where the ions decay back to the S$_{1/2}$ ground state via emission of a photon near 393~nm. We realize spin-selective excitation from the Zeeman-split ground states S$_{1/2}$, m$= \pm 1/2$, of the $\text{Ca}^+$ ions and observe in the far field spin-dependent interference patterns displaying the spin textures of the ion crystals. We investigate their dynamics by measuring the temporal evolution of the spatial Fourier frequencies of the observed patterns.

Figures (4)

• Figure 1: i) Sketch of the experimental setup: A linear crystal of $^{40}$Ca$^+$ ions is exposed to laser fields (729nm/854nm/866nm) with beam waist sizes of (25 m/80 m/80 m), respectively. Scattered photons near 393nm are collected by an NA$\,=\,$0.3 objective (Sill, S6ASS2241) and focused at a distance of 127cm on a slit of width 1.4mm (not shown in Fig. 1(i)) to filter out background photons. A multi-channel plate detector (LINCam from Photonscore Inc.) positioned 170cm downstream records the photons in the far field. For single ion addressing, a beam near 729nm is reflected off a dichroic beam splitter and focused by the objective to a waist size of 2 m. ii) Levels and transitions in $^{40}$Ca$^+$; S$_{1/2}$ Zeeman levels m$\,=\,\pm$1/2 serve as spin up/spin down state, respectively. iii) Pulse sequence for spin-dependent detection: After Doppler cooling (397nm/866nm), spins are initialized by the addressing beam (729nm); spin-dependent scattering is recorded under illumination by the global beams (729nm/854nm) while repumping residual population with 866nm from D$_{3/2}$ via the short-lived P$_{1/2}$ level to S$_{1/2}$.
• Figure 2: (i) LINCam image (diameter 17 mm) with interference pattern from a $N=6$ ion linear crystal. Integrating over the y-axis leads to interference fringes displayed for linear crystals with (ii) $N=6$ and (iii) $N=12$ ions; data acquisition time is 240s. The model function (red) takes into account the independently determined ion positions, the laser beam profiles and a quadratic phase shift due to optical aberration, see text for details. (iv) Model function evaluated for the $N=12$ ion crystal, but excluding the quadratic phase shift.
• Figure 3: (i) Fractional width of the $0^\mathrm{th}$ diffraction order, measured for crystals with 4 $\leq N \leq$ 12 ions trapped in a 0.58 MHz axial potential. The expected $1/N$ dependence is plotted (red), no free parameters. (ii) Photon counts integrated over the central peak showing a linear increase with $N$ (red). (iii) Contrast of the interference fringes versus the number of ions $N$. The dependence on $N$ is described by a fit function, see text for details.
• Figure 4: Left side: Interference patterns observed from spin-initialized three-ion crystals with data acquisition time 1ms, repeated for 150,000 times; the three plots show the number of detected photons in each bin position (x-axis) vs. the scattering time t$_{scatt}$ (y-axis) for spin configuration initialization (i): $\{\downarrow,\downarrow,\downarrow\}$, (ii): $\{\downarrow,\uparrow,\downarrow\}$, and (iii): $\{\uparrow,\uparrow,\uparrow\}$. Right side: The three plots display over time the intensity of the different spatial frequencies of the three-ion crystals, corresponding to different inter-ion distances with ions in state $\downarrow$; error bars are within the size of the dots. (iv): For the initial configuration $\{\downarrow,\downarrow,\downarrow\}$, we observe two spatial frequencies which decay as a function of time; (v): In the case of $\{\downarrow,\uparrow,\downarrow\}$, one Fourier frequency is present at the beginning and then decays, while the other one is barely visible throughout the observation time; (vi): Initializing the ion crystal to $\{\uparrow,\uparrow,\uparrow\}$, no spatial frequencies are observed initially, nonetheless they appear over time due a small leakage in the fluorescence cycle.