Optical spectral imaging of a single layer of a quantum gas with an ultranarrow optical transition

We demonstrated high-sensitivity optical spectral imaging of a single layer of a quantum gas of ytterbium atoms in a two-dimensional optical lattice using the ultranarrow ${}^1{S}_0$-${}^3{P}_2$ transition. We successfully obtained a set of excitation-frequency-dependent fluorescence images with an excitation laser of the linewidth of 1 kHz (FWHM), and the overall features were well explained by considering the inhomogeneous light shift originating from the Gaussian beam shape of the optical lattice potential which provided the steepest potential gradient of 3.6 kHz/$\mu$m. This result is also the successful demonstration of the tunable local atom addressing along the equipotential contour depending on the excitation laser frequency with the frequency resolution of 8 kHz and the spatial resolution of approximately 2 $\mu$m. The demonstrated technique will be useful for many purposes including the measurement of interaction shift in the study of a quantum gas and quantum information processing.

Figure 1

Principle of spectral imaging. (a) Schematic of the experimental situation. Due to the inhomo-geneous shift in the ${}^1{S}_0$-${}^3{P}_2$ transition in space, a different region is excited for a different excitation frequency. Because the atom cloud is elliptic, the excited region is like a curved line. Note that the cloud center is displaced from the potential center (discussed later). The bottom panel shows the dependence of the excited region alomg the $X$ axis on the excitation frequency $f$. Here $f_1<f_2<f_3$. (b) Relevant energy levels of an Yb atom. $\lambda$ and $\Gamma /2\pi$ denote the wavelength and the natural linewidth of the transition, respectively. The ${}^1{S}_0$-${}^3{P}_2$ transition is the ultranarrow $M2$ transition providing high-spectral resolution. The ${}^1{S}_0$-${}^1{P}_1$ transition is the strong $E1$ transition with $\lambda =$ 399 nm and is exploited for high-spatial-resolution imaging. The ${}^3{S}_1$ state is used for repumping.

Figure 2

Schematic experimental setup and time sequence. (a) After we prepare a 3D BEC by evaporative cooling in a crossed optical trap in a thin glass cell, we load the BEC into a single layer of a vertical lattice with a period of 5 $\mu$m and the vertical trap frequency of ${\omega }_z=2\pi \times 2.8$ kHz, which is formed by two horizontally polarized 532 nm beams with a beam waist of 14 $\mu$m intersecting with each other at an angle of $\alpha$ = 5${}^{\circ }$ in the $X$-$z$ plane. Then we loaded atoms to horizontal ($x$ and $y$) lattices. The atom cloud after the loading was elliptical due to the radial confinement by the vertical lattice beams along the $Y$ axis. Note that the $X$ and $Y$ axes are rotated by 45${}^{\circ }$ in the horizontal plane from the $x$ and $y$ axes, respectively. A bias magnetic field was applied along the $z$ axis to define the quantization axis. The configuration of the excitation beam and the magnetic field only allows $\Delta m=\pm 1$ transitions, where $m$ denotes the magnetic quantum number. (b) Experimental timing sequence. After we ramp up the horizontal lattice depths to $V_x=V_y=5E_r$, we rapidly increase the horizontal and vertical lattice depths to freeze-out the atom distribution. Then we apply a 556 nm beam for photoassociation to remove atom pairs in lattice sites. After that, we further increase horizontal lattice depths and excite the atoms to the ${}^3{P}_2$ state. Then we blast the nonexcited atoms by a 399 nm beam and repumping the excited atoms back to the ground ${}^1{S}_0$ state via the ${}^3{S}_1$ state and the ${}^3{P}_1$ state using a 770 nm beam resonant to the ${}^3{P}_2$-${}^3{S}_1$ transition. We finally perform in situ fluorescence imaging of atoms using high-intensity molasses beams with 399 nm.

Figure 3

Spectral imaging data set. (a) The data set consists of fluorescence images with different excitation laser frequencies. Two images at different frequencies of $f=-412$ kHz and $+188$ kHz are also shown. (b) Reconstructed $X$-$f$ 2D image corresponding to the data in the $Y=0$ (red) plane in (a). (c) Reconstructed $Y$-$f$ 2D image corresponding to the data in the $X=0$ (blue) plane in (a).

Figure 4

Position dependence of the spectrum peak frequencies. The green closed circles, red rectangular squares, and open blue circles are the peak frequencies at the positions on the $X$ axis obtained from the experimental data averaged over the adjacent three pixels (corresponding to $\sim 2$ $\mu$m in the object plane). The green solid, red dotted, and blue dotted and solid lines are the fits to the corresponding peak frequencies based on the position dependence of the carrier, first blue sideband and second blue sideband transitions, respectively.

Figure 5

Spatial structure of the excited region. The left panels (a)–(g) show the average of the observed fluorescence images for the excitation frequencies of 156, 148, 140, 132, 108, 100, and 92 kHz, respectively. The center panels (h)–(n) show the calculated fluorescence images corresponding to (a)–(g), respectively. The right panels (o)–(u) show the line-cut profile on the $X$ axis of the experimental data (black cross) and the calculated profiles (the red solid line).