Trapped-atom interferometer with ultracold Sr atoms

We report on a trapped atom interferometer based on Bragg diffraction and Bloch oscillations with alkaline-earth-metal atoms. We use a Ramsey–Bordé Bragg interferometer with ${}^{88}\mathrm{Sr}$ atoms combined with Bloch oscillations to extend the interferometer time. Thanks to a long coherence time for Bloch oscillations of ${}^{88}\mathrm{Sr}$ atoms, we observed interference up to 1 s evolution time in the lattice. A detailed study of decoherence sources during the Bloch phase is also presented. While still limited in sensitivity by lattice lifetime and beam inhomogeneity this result opens the way to high contrast trapped interferometers with extended interrogation time.

Figure 1

(a) Schematic view of the experimental apparatus. Precooled ${}^{88}\mathrm{Sr}$ atoms trapped in a vertical optical lattice operating at 532 nm (narrow green arrows) are launched upwards. Bragg pulses at 461 nm (thick blue arrows) are then applied to first velocity select the atoms along the vertical direction and subsequently to apply the interferometer sequence. The Bragg beams, with frequency ${\omega }_1$ and ${\omega }_2$ and orthogonal polarizations, are sent from the bottom, rotated by a $\lambda /4$-wave plate and retroreflected by a mirror (M) on top. The lattice beams come from two independent fibers with linear polarizations and are superimposed onto the Bragg beams' center by means of two dichroic mirrors (DM). (b) Atomic trajectories separated by $2n\hslash k_{\mathrm{blue}}$ in the interferometer. In the middle of the interferometric sequence, the atoms are trapped in the green vertical optical lattice (green shaded region) where they undergo Bloch oscillations.

Figure 2

Typical Ramsey–Bordé plus Bloch interferometer fringes for an order of Bragg transition $n=1$, obtained by scanning the frequency chirping $\alpha$. In this particular measurement we choose $T_R=1$ ms and $T^{\prime }=123$ ms, where $T_B=85.2$ ms for $N=49$. The sinusoidal fit gives a visibility of 0.4.

Figure 3

Contrast decay as a function of Bloch evolution time $T_B$. The separation time is $T_R=1$ ms, and $T^{\prime }=37.8\text{ms}+T_B$. The solid line is an exponential decay fit, giving a time constant of 900(10) ms. With this parameter choice the interference is preserved for more than $N=575$ Bloch oscillations. The inset shows the contrast as a function of $T_R$, with different sets of $T_B$ (red circles for $T_B=3.5$ ms, blue squares for $T_B=20.4$ ms, and black triangles for $T_B=59.1$ ms). The solid lines in corresponding colors are exponential decay functions numerically estimated with the model of Eq. (4).

Figure 4

Lattice decay measurements in the presence of Bragg light square pulse. The blue squares correspond to ${150}^{\circ }$ C heat-pipe temperature, and red circles to ${400}^{\circ }$ C. The upper blue and lower red solid lines are exponential decay fits for each respective set of data. The decay time constants according to the fits are 3.07 (13) ms for ${150}^{\circ }$ C and 3.10 (13) ms for ${400}^{\circ }$ C. The two vertical axes are offset with respect to each other to display these two sets of data clearly. The inset plot is Rabi oscillations taken at ${150}^{\circ }$ C and ${400}^{\circ }$ C with the same plot notation.

Figure 5

Contrast measurements for different Bloch oscillation periods $T_B$ (with Ramsey time $T_R=1$ ms) as a function of final pulse delay time $\delta T$. The contrast envelope for a pure Ramsey–Bordé interferometer is also reported as a reference. Offsets were removed for better comparison of the fitted curves. The inset shows the estimated coherence length of the atomic sample given by the Gaussian fit of the contrast measurements.

Figure 6

Bloch oscillations in the recaptured lattice. The top plot is the calibrated TOF signal of $\sim 5$ ms and $\sim 800$ ms evolution time. Correspondingly, the bottom plot is the width of the velocity distribution of the atomic cloud.

Figure 7

Bragg spectroscopy of the atomic cloud before Bloch evolution (black circles), and after 20.6 ms Bloch evolution (red squares). The dashed black line and solid red line are Gaussian amplitude fits of the respective data set.

Figure 8

The black circles are the contrast-loss measurements versus the distance $D$ between the atomic cloud and the top window of the vacuum chamber (the minus sign means the atoms are below the window), the solid line is a numerical estimate with Eq. (4), using a Lorentzian distribution with a width scaling as $D^{-2}$. For this measurement we choose $T_R=1$ ms and $T_B=38.4$ ms. The inset plot is the contrast decay as a function of $T_R$, for a fixed $T_B=20.4$ ms, for two different lattice beam waists. Black diamonds correspond to beam waist of $300\mu \mathrm{m}$, and red squares with $800\mu \mathrm{m}$ (the solid lines are to guide the eye).