Spin-resolved single-atom imaging of ${}^6\mathrm{Li}$ in free space

We present a versatile imaging scheme for fermionic ${}^6\mathrm{Li}$ atoms with single-particle sensitivity. Our method works for freely propagating particles and completely eliminates the need for confining potentials during the imaging process. We illuminate individual atoms in free space with resonant light and collect their fluorescence on an electron-multiplying CCD camera using a high-numerical-aperture imaging system. We detect approximately 20 photons per atom during an exposure of $20\mu \mathrm{s}$ and identify individual atoms with a fidelity of $(99.4\pm 0.3)\%$. By addressing different optical transitions during two exposures in rapid succession, we additionally resolve the hyperfine spin state of each particle. The position uncertainty of the imaging scheme is $4.0\mu \mathrm{m}$, given by the diffusive motion of the particles during the imaging pulse. The absence of confining potentials enables readout procedures such as the measurement of single-particle momenta in time of flight, which we demonstrate here. Our imaging scheme is technically simple and easily adapted to other atomic species.

Figure 1

Single-atom imaging setup for ${}^6\mathrm{Li}$. (a) We deterministically prepare a single atom in an optical tweezer and excite it resonantly with two counterpropagating laser beams. With a high-resolution objective (NA = 0.55) we collect about 20 fluorescence photons and image them onto an EMCCD camera. (b) Typical raw signal in analog-to-digital units (ADU) of a single atom imaged with the EMCCD in electron-multiplication mode. (c) By applying a binarization threshold, we identify pixels where photons impinged. (d) The mean photon signal from a single atom is governed by the random walk of the atom during the photon scattering process and has a width of $w_{\mathrm{sig}}=(10.1\pm 1.4)\mu \mathrm{m}$. The red arrows indicate the orientation of the probe beams.

Figure 2

Performance of the single-atom imaging. (a) To identify and locate single atoms, we use the EMCCD camera in photon counting mode, apply a low-pass filter to the binarized images, and discern single atoms from noise based on the amplitudes of the local maxima in the filtered image. The blue dots correspond to the positions of identified atoms. (b) A histogram of amplitudes shows a bimodal distribution where the peak at lower (higher) amplitude originates from the camera noise (photon clusters). The dashed line depicts the chosen identification threshold for the data taken for a typical image size of $400\times 100\mu \mathrm{m}$ corresponding to $5200{\mathrm{px}}^2$. (b, inset) The detection fidelity depends on the size of the analyzed images and can reach up to $(99.4\pm 0.3)\%$. (c) The position distribution for many realizations of a single atom prepared at a fixed position has an uncertainty of ${\sigma }_{\text{pos}}=(4.0\pm 0.4)\mu \mathrm{m}$, which is much smaller than the filter size (gray line). (d) Single image of multiple atoms. The minimal distance at which we can discern individual atoms with above $90\%$ probability is around $12\mathrm{px}\left(32.4\mu \mathrm{m}\right)$.

Figure 3

Spin-resolved imaging of ${}^6\mathrm{Li}$. (a) At a nonzero magnetic field, we drive the ${\sigma }_{-}$ transition from the $m_j=-1/2$ to $-3/2$ manifold and the ${\sigma }_{+}$-transition from the $m_j=+1/2$ to $+3/2$ manifold which all contain $m_I=\pm 1,0$ sublevels. (b) As the optical frequencies differ by $80\mathrm{MHz}$, we can excite the three lowest hyperfine states $|1\rangle$, $|2\rangle$, and $|3\rangle$ selectively to the three lowest hyperfine states of the excited manifold $|3^{\prime }\rangle$, $|2^{\prime }\rangle$, and $|1^{\prime }\rangle$. With more than $99\%$ probability, the atoms then decay back to their initial state. To compensate for the small probability that atoms in $|2^{\prime }\rangle$ and $|3^{\prime }\rangle$ can decay to $|4\rangle$ and $|5\rangle$, respectively, we additionally drive the ${\sigma }_{+}$ transition. (c) Distribution of the integrated signal from a single atom in state $|3\rangle$ probed with a closed optical transition (left panel) and in state $|1\rangle$ (right panel) at $568\mathrm{G}$ without (purple) and with (blue) the additional ${\sigma }_{+}$ probe beam. The gray bars show the signal with no atom present, solely caused by CICs. We model the distribution (solid line) with a mean photon number of 24.7 and 21.0 for state $|3\rangle$ and $|1\rangle$, respectively. (d) We achieve spin-resolved imaging of two atoms in different hyperfine states by subsequently addressing their resonant transition and using the kinetics mode of the camera.

Figure 4

Momentum imaging of single atoms. (a) The double-well potential formed by two overlapping optical tweezers is centered at the optical dipole trap elongated along the x axis. The latter provides a harmonic potential for the expansion of the quantum state. (b) After an expansion for a quarter trap period along the $x$ axis, $t=T_x/4$, the initial momentum wave function is mapped to real space and the average distribution of the atom corresponds to the momentum distribution of the state, shown here for a single atom prepared in the ground state of the double-well potential. (c) We detect its position distribution after the expansion and observe a probability distribution as expected from a double-slit experiment with constructive interference at the center. (d) Preparing the antisymmetric superposition of $|L\rangle$ and $|R\rangle$ results in destructive interference at the center.

Figure 5

Logarithmic histogram of secondary electrons on a dark image. With the EMCCD camera stochastic amplification of few photoelectrons is possible to overcome the read noise. The distribution of secondary electrons is shown (inset) for one (solid line), two (dashed line), and three (dotted line) primary electrons. We extract the histogram of secondary electrons on a bias-corrected image with a closed camera shutter (blue dots). From this, we extract the read noise ${\sigma }_{\text{read}}$ by fitting a Gaussian function (green solid line) to the peak around zero. The exponential tail at higher values of secondary electrons is caused by clock-induced charges (CICs) from the shifting processes in the EMCCD, where parallel CICs (red region) and serial CICs (blue region) can be distinguished. We fit the pCICs by a simple exponential function (red solid line) and extract the average gain $g$. Due to a significant fraction of sCICs, we choose a binarization threshold of $8{\sigma }_{\text{read}}$ (gray dotted line) to discern a photon signal from read noise.

Figure 6

(a) Average photon distribution after an exposure time of $20\mu \mathrm{s}$. $x$ and $y$ profiles are extracted along the dashed lines. (b) $y$ profile of the photon distribution (blue points), fitted with $\tilde{\rho }(0,y_i,\tau )$ (blue curve) and with a Gaussian distribution (green curve). (c) Width $w=\sqrt{s}$ as extracted from the fitted model vs exposure time, for free expansion (blue points) and with a pinning potential with a depth of $290E_{\mathrm{R}}$ (yellow squares). Inset: Double-logarithmic plot of the width, showing the scaling behavior of the expansion (lines are guides to the eye). (d) Average photon distribution after an exposure time of $20\mu \mathrm{s}$ with a pinning potential with a depth of $290E_{\mathrm{R}}$.