Along with the development of the magneto-optical trap (MOT) technique, many species of atoms have been successfully trapped and greatly isolated from the external environment^[1–3]. It makes them promising for the realizations of quantum repeater and quantum networks^[4–6]. In order to realize the control and manipulation for atomic states, the trapped atoms need to efficiently interface with resonant probe light via atom–light interaction^[7–11]. In this respect, a tapered optical nanofiber provides an ideal platform. The strong confinement evanescent field near the nanofiber improves atom–light coupling and allows atomic trapping near the nanofiber surface^[12–14]. In recent years, two-color trappings including a state-insensitive nanofiber trap for atoms have been realized^[15–17]. The atoms are trapped in a one-dimensional optical lattice near the nanofiber surface. Due to the collisional blockade effect^[18,19], at most, one atom can be located for each optical lattice site. The strong coupling between the trapped atomic array and fiber-guided mode contributes to the study of chiral quantum optics^[20], collective excitation^[21], and correlating photons under nonlinear response^[22]. Using electromagnetically induced transparency, slow light and the storage of optical pulses are also realized in the nanofiber optical lattice^[23,24]. In the nanofiber trapping regime, the optical depth (OD) can reach a few percent per atom, which enables the large OD with a trapped atomic array and confirms it as a viable platform for studying atom–light interactions.

In this Letter, we focus on the optical nanofiber trapping scheme. By applying dark MOT (DMOT) technique, the trapped cesium atoms are transferred to the lower hyperfine ground state (dark state). The minimized atomic collisions and radiation pressure allow the higher atomic density and lower atomic temperature, which are the critical elements to the loading efficiency of the nanofiber optical lattice. With the application of DMOT, the bright–dark state transfer efficiency of nanofiber trapped atoms reaches 98%, providing the essential requirements for developing the quantum repeater with a fiber-based hybrid system^[21].

As shown in Fig. 1(a), the diameter of the nanofiber is 500 nm over a length of 5 mm fabricated from a single mode fiber (Fibercore, SM800-5.6-125) by flame brushing^[25–28]. The designed diameter guarantees the quasi-fundamental mode ${\mathrm{HE}}_{11}$ along the nanofiber, and the designed taper angle (2 mrad) guarantees the adiabatical transformations for fiber-guided modes from both sides. Owing to the high transmission (99.5%), the nanofiber can tolerate power of input light over 30 mW in a vacuum. Figure 1(b) shows the schematic of the experimental setup. A couple of counter-propagating red-detuned lights (935 nm, 0.35 mW for each beam) create the attractive potential. Another couple of parallel polarized blue-detuned lights (686.1 nm, 686.5 nm, 5 mW for each beam) create repulsive potential. Overlapping the van der Waals potential from the nanofiber surface, the evanescent field of trapping lights constructs the nanofiber optical lattice. The application of the magic wavelength for trapping lights strongly immunizes the AC Stark shifts of cesium energy levels. The polarization of fiber-guided lights is calibrated by the Rayleigh scattering induced by the imperfection of nanofibers. With theoretical calculation, the center of the optical lattice trap is located 173 nm away from the nanofiber surface. The trapping frequencies are about 352 kHz radially, 77 kHz azimuthally, and 500 kHz along the nanofiber. The probe light is coupled into the nanofiber from one side and detected with the single photon counter module (SPCM), filtering via volume Bragg gratings (VBGs, OptiGrate, SPC-852) and interference filter (Semrock, LL01-852-12.5). Figure 1(c) shows the hyperfine energy level of cesium atoms used in our experiment. The trapping frequency is red-detuned 12 MHz from the $6S_{1/2},F=4\to 6P_{3/2},F^{\prime }=5$ transition, and the repumping light is resonant on $6S_{1/2},F=3\to 6P_{3/2},F^{\prime }=4$. Here, the center region of the repumping beam is dumped and substituted by the depumping light, for which the diameter is 3 mm, overlapping the trapped atomic ensemble. The corresponding intensity of the depumping light is about $0.3\mathrm{mW}/{\mathrm{cm}}^2$, and the frequency is resonant on the $6S_{1/2},F=4\to 6P_{3/2},F^{\prime }=4$ transition.

To increase the loading efficiency for the nanofiber optical lattice, we optimized the polarization gradient cooling progress and measured the corresponding atomic temperature from DMOT. The trapping power of each beam is fixed at $4.7\mathrm{mW}/{\mathrm{cm}}^2$. After 1.5 s, the loaded atomic number from normal MOT becomes saturated. In the polarization gradient cooling stage, the trapping frequency is detuned from $-12\mathrm{MHz}$ to $-60\mathrm{MHz}$ within 5 ms. The powers of trapping light and repumping light are reduced to zero. Meanwhile, the depumping light is always turned on.

By applying time of flight, we measured the temperature of nanofiber trapped atoms loading from DMOT, which is compared with normal MOT, as shown in Fig. 2. The changes of the Gaussian diameter of the atomic ensemble obey $${\sigma }_{x,y}=\sqrt{{\sigma }_{x,y}^2(0)+\frac{k_B{T}_{x,y}}{m}{t}^2},$$(1)where $m$ is the atomic mass, $T_{x,y}$ is the temperature of the atomic ensemble considering the weighting coefficients in the $x$ and $y$ directions, $k_B$ is the Boltzmann constant, and $t$ is the atomic flying time. In the imaging progress, the duration of the probe pulse is 1 ms, which is resonant on $6S_{1/2},F=3\to 6P_{3/2},F^{\prime }=2$ for DMOT atoms ($6S_{1/2},F=4\to 6P_{3/2},F^{\prime }=5$ for normal MOT atoms). An imaging size calibrated camera records the corresponding atomic ensemble with different atomic flying times. According to Eq. (1) and the measured atomic size from Fig. 2, the calculated atomic temperatures for normal MOT and DMOT are separately 65.8 µK and 44.8 µK, proving the lower atomic temperature for DMOT.

Figure 3 shows the absorption spectra of nanofiber trapped atoms loading from DMOT and normal MOT. After the polarization gradient cooling progress, a frequency fixed probe pulse duration of 1 ms is input into the nanofiber, interacting with the nanofiber trapped atoms by the evanescent field of the fiber-guided mode. The probe power is set to be 1 pW to avoid the recoil heating effect^[29]. For resonant transmission spectra, the OD can be derived from a simple model: $$T(w)=\exp [-\mathrm{OD}\frac{1}{1+4(w-w_0{)}^2/{\mathrm{\Gamma }}^2}],$$(2)where $w_0$ is the resonant frequency, and $\mathrm{\Gamma }$ is the full width at half-maximum (FWHM) of the spectra. Figures 3(a) and 3(b) show the absorption spectra of nanofiber trapped atoms loading from normal MOT. According to Eq. (2), the fitted OD is separately $0.02\pm 0.002$ and $14.4\pm 0.2$, corresponding to the transmission $6S_{1/2},F=3\to 6P_{3/2},F^{\prime }=2$ and $6S_{1/2},F=4\to 6P_{3/2},F^{\prime }=5$. The large OD of the bright state indicates that nearly all trapped atoms are populated into the higher hyperfine level $6S_{1/2},F=4$ for the normal MOT. Figures 3(c) and 3(d) show the absorption spectra of trapped atoms loading from DMOT. The fitted OD is $9.3\pm 0.2$ and $0.55\pm 0.02$, corresponding to the same transmissions as in Figs. 3(a) and 3(b). The increased OD for the $6S_{1/2},F=3\to 6P_{3/2},F^{\prime }=2$ transition interprets that most trapped bright atoms have been transferred to the dark state with DMOT. For fitting consequences of trapped atoms with normal MOT (red line) and DMOT (blue line), the frequency shifts are $0.33\pm 0.07\mathrm{MHz}$ and $1.24\pm 0.08\mathrm{MHz}$, benefitting from the application of cesium magic-wavelength lights for trapping potential. The AC Stark shift effect and inhomogeneous Zeeman broadening are strongly eliminated. Compared with Figs. 3(a) and 3(d), the larger frequency shifts of Figs. 3(b) and 3(c) are induced by the perturbations from atom-atom interactions in the optical lattice. These coherent dipole-dipole couplings are related to the lattice geometries and OD of trapped atoms^[30], which could be ignored when the OD is very small.

To quantify the trapped atomic numbers and bright–dark state transfer efficiency, we measured the absorption power for nanofiber trapped atoms loading from DMOT, as shown in Fig. 4. The black and red lines are fitted based on the generalized Beer’s law. In the limit of large input power and saturated absorption, we can conclude that $$N\approx \frac{P_{\mathrm{abs}}}{P_{\mathrm{sat}}},$$(3)where $P_{\mathrm{sat}}=3.8\mathrm{pW}$ is the radiated power of a single saturated cesium atom^[16]. Based on Eq. (3) and saturated power fitted from the generalized Beer’s law, we can infer that the trapped atomic numbers populated into states $F=3$ and $F=4$ are $232\pm 26$ and $4.2\pm 0.8$. It indicates that approximately 98% of nanofiber trapped atoms have been transferred to dark state $F=3$. The OD per atom is 4%, as concluded from the confirmed atomic number and OD.

The lifetime of trapped atoms in the nanofiber optical lattice is also measured, as shown in the inset of Fig. 4(a). The input power is fixed at a saturation level (8 nW) to meet the premise of Eq. (3). For lifetime measurement of the inset of Fig. 4(a), the atomic number is calculated and scaled. For nanofiber trapped atoms with a dark state, the ultimate exponential fitted lifetime is $3.9\pm 0.2\mathrm{ms}$ (blue line). A further temperature cooling for the trapped atoms is needed to increase the lifetime in future work.

In conclusion, we have realized dark state atomic trapping in a nanofiber optical lattice by applying the DMOT. The bright–dark state transfer efficiency of trapped atoms reaches about 98%, confirmed by the saturation measurement of power absorption. The AC Stark shift is also strongly suppressed by using the cesium magic-wavelength trapping potential (blue-detuned traveling wave and red-detuned standing wave). This work contributes to the realization of a fiber-based quantum repeater and hybrid quantum network construction.