Continuous outcoupling of ultracold strontium atoms combining three different traps

Continuous generation of ultracold or Bose-condensed ¹⁾ atoms is one of the long-standing targets in laser cooling of atoms, as it significantly benefits precision measurements with atomic clocks ^2,3) and interferometers ^4,5) suffered from the Dick effect ^6,7) caused by the dead-time required to prepare laser-cooled atoms. So far, zero-dead-time operation of atomic clocks has been demonstrated by combining two interleaved clocks, ^8,9) showing the 1/τ improvement of the clock stability instead of $1/\sqrt{\tau }$ of the intermittent clocks with τ, the averaging time. The continuous atomic source is also the key ingredient for the realization of the continuous-wave superradiant lasers ¹⁰⁾ and a longitudinal Ramsey spectroscopy. ¹¹⁾

Laser cooling of atoms to μK temperature requires multiple laser-cooling steps consisting of different laser parameters ¹²⁾ or electronic transitions. ^13,14) For atoms with a degenerate ground state, such as alkaline-metal elements, Doppler and sub-Doppler cooling are applied sequentially by changing the laser parameters. ^15–17) For atoms with the non-degenerate ground state, as in alkaline-earth-metal (like) elements, two-stage cooling is commonly applied, where atoms are quickly laser-cooled to a few mK on the broad ¹S₀−¹P₁ transition and are further cooled to sub μK on the narrow ¹S₀−³P₁ transition. ^14,18) As the laser cooling shares the ¹S₀ ground state, two-stage cooling needs to be conducted sequentially. By properly arranging the two cooling processes in space, continuous generation of ultracold atoms ^19,20) and the Bose–Einstein condensate ¹⁾ have been demonstrated.

Multiple laser cooling stages and outcoupling of atoms can be simultaneously conducted for atoms having metastable states. ²¹⁾ Simultaneous magneto-optical trapping (MOT) of atoms using the broad and narrow transitions starting from the ground and metastable states have been demonstrated for Ca, ²²⁾ where the achieved temperature of 20 μK was limited by the magnetic field that was shared for the broad and narrow MOT transitions. Sequential tuning of the magnetic field allowed achieving 6 μK ²³⁾ and sub-Doppler ²⁴⁾ temperatures for Sr atoms, which are readily used for optical lattice clocks. Direct loading of atoms into a deep optical-dipole trap (ODT) in the ³P₀ metastable state during the first stage cooling ²⁵⁾ and loading of atoms into the ODT after laser cooling in the metastable state ²⁶⁾ have been reported.

In this Letter, we report a continuous cooling and outcoupling of ⁸⁸Sr atoms in the ³P₀ metastable state by a moving lattice. The atomic flux is 10³ atoms s⁻¹ with a temperature of 5 μK. During the first stage MOT on the ¹S₀−¹P₁ transition, laser-cooled atoms relaxed to the ³P₂ state are magnetically trapped and Doppler cooled ²⁷⁾ on the 5s5p ³P₂−5s4d ³D₃ transition, where a highly anisotropic quadrupole field allows the simultaneous operation of the broad-line and narrow-line cooling. The cold fraction of atoms in the 5s5p ³P₂ state are loaded into a moving lattice and optically pumped to the ³P₀ state that is free from the cooling lasers and trapping magnetic field. These two-stage cooling and outcoupling processes are conducted in the same location, allowing a compact design of the system compared to the spatially separated one. ¹⁹⁾

A schematic of our experiment is shown in Fig. 1(a). Atoms effused from an atomic oven are decelerated in a Zeeman slower and magneto-optically cooled and trapped on the ¹S₀−¹P₁ transition at λ_B = 461 nm, which we refer to as B-MOT. A bar-magnet and current-carrying coils produce an elongated spherical-quadrupole magnetic field, as shown in Fig. 1(b), which enables the simultaneous operation of multiple cooling and trapping stages. A large magnetic field gradient of ∼10 mT cm⁻¹ in the radial (x–y) direction allows tight confinement of atoms in the B-MOT and magnetic trapping, while the small gradient ∼0.7 mT cm⁻¹ in the z-direction facilitates laser cooling on the narrow 5s5p ³P₂−5s4d ³D₃ transition at λ_IR = 2.92 μm with γ_IR/2π = 57 kHz, which is referred to as IR-cooling. Figure 1(c) shows the relevant energy levels of ⁸⁸Sr. During the B-MOT, a small fraction (≈1/70 000) of atoms in the 5s5p ¹P₁ state are relaxed, via the 5s4d ¹D₂ state, to the 5s5p ³P₂ state, where atoms in the low-field-seeking sublevels m_J > 0 are magnetically trapped. The atoms are trapped along the minima of the magnetic field strength ∣B∣ shown by the dotted line in Fig. 1(b).

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Figure 2(a) shows the Zeeman shift on the ³P₂−³D₃ transition along the dotted line [see Fig. 1(b)], which is given by ν_B(m_J , Δm_J ) ≈ μ_B (−m_J /6 + 4Δm_J /3)∣B∣/h with μ_B /h ≈ 14 MHz mT⁻¹ the Bohr magneton in frequency, and Δm_J = ±1, 0 corresponds to the σ^±, π transitions. In contrast to the Doppler cooling in the magnetic trap on the broad transition, ²⁸⁾ the narrow transition linewidth γ_IR well resolves the Δm_J = ±1, 0 transitions for a small bias magnetic field of tens of μT that is compatible with the B-MOT. A blue-detuned laser, as indicated by the black-dashed line in Fig. 2(a), efficiently pumps the atoms to the m_J = 2 state by exciting the Δm_J = 1 transitions. It would be nice if this optical pumping process coexists with the Doppler cooling.

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We apply the blue-detuned IR-cooling laser downward along the z-axis [see Fig. 1(a)], where the magnetic field gradient β_z = d∣B∣/dz is in the range of 0.5–1.5 mT cm⁻¹ and becomes larger as ∣z∣ increases. This relatively small field gradient facilitates the Doppler cooling on the narrow transition while allowing stable atom trapping against gravity for β_z ≥ mg/(3μ_B) = 0.52 mT cm⁻¹. Figure 2(b) shows the magneto-gravitational potential for the atoms in the m_J = 2 sublevel, which is given by U(x, y, z) = 3μ_B∣B∣ + mgz with mg, the gravity. As the atomic temperature increases, atomic orbit $r=\sqrt{{x}^{2}+{y}^{2}}$ in radial motion becomes larger and β_z is reduced, causing larger gravitational sag.

The Doppler cooling condition is satisfied for the hatched area in Fig. 2(a), where the blue-detuned IR-cooling laser (black-dashed line) is red-detuned in respect to Zeeman shift of magnetically trapped atoms in the m_J = 2 state (blue-solid line). ²⁷⁾ As this cooling laser optically pumps the atoms to the ³P₂(m_J = 2) state, stable magnetic trapping coexists with Doppler cooling. The red line in Fig. 2(c) illustrates the combined force F(z) = F_BG + F_R consisting of the magneto-gravitational force F_BG and the radiation pressure F_R. Here we assume the detuning of the IR cooling laser δ_IR = 2.0 MHz and the intensity $I=35{I}_{0}^{(\mathrm{IR})}$ with ${I}_{0}^{(\mathrm{IR})}=0.3\,\mu {\rm{W}}\,{\mathrm{cm}}^{-2}$ the saturation intensity of the IR transition. The laser-cooled atoms are finally trapped around z₀ given by F(z₀) = 0.

Our experimental setup is similar to the one described elsewhere ²⁴⁾ except for the anisotropic quadrupole magnetic field produced by 2 cm diameter coils and a 5 cm long neodymium magnet with a 2 mm-square cross-section and a surface magnetic flux density of 290 mT [see Fig. 1(a)]. The IR cooling laser at 2.92 μm is generated by the difference frequency of 779 nm and 1.062 μm lasers stabilized to a frequency-comb and an optical cavity, respectively. ²⁹⁾ Figure 3(a) shows the atoms in the B-MOT, having an elongated shape with 4 mm × 0.3 mm in the vertical direction. About 10⁵ atoms are trapped in a few hundred ms. The magnetically trapped atoms in the ³P₂ state during the B-MOT is shown in Fig. 3(b), which is probed by a laser resonant to the 5s5p ³P₂−5s5d ³D₃ transition at 496 nm. The radial temperature of the atoms is estimated to be 0.5 mK by the spatial distribution in the magnetic trap. Applying the IR cooling laser gathers atoms around z₀ ≈ −3 mm as shown in Fig. 3(c).

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Figure 3(d) shows the atomic distribution in the magnetic trap after applying the IR-cooling for t_C with the detuning δ_IR = 2.0 MHz. In the beginning, two peaks are observed, corresponding to the oscillatory motion of magnetically trapped atoms released from the B-MOT at z ≈ 0 mm and turning at z ≈ −6 mm. Applying the IR-cooling laser for t_C, the atoms are gradually gathered to the equilibrium position around z₀ ≈ −3 mm that satisfies F(z₀) = 0. The cooling time, which takes up to a second, depends on the cooling laser intensity I. The number of trapped atoms decreases for a larger intensity I by exciting the Δm_J = 0 transitions that optically pump the atoms into the non-trapped m_J ≤ 0 magnetic sublevels. Similarly, small laser detuning δ_IR excites the Δm_J = 0 transitions to reduce the number of atoms. We therefore operate the IR-cooling laser with δ_IR = 2.0 MHz and $I\approx 35{I}_{0}^{\left({\rm{IR}}\right)}$.

The position of the laser-cooled atoms depends on the intensity and detuning of the IR-cooling laser as shown in Fig. 4(a). Atoms are pushed downward by increasing the intensity I and detuning δ_IR of the cooling laser. The red-shaded area shows the equilibrium position F(z₀) = 0 calculated for δ_IR = 2.0 MHz assuming the uncertainties of the magnetic field 5% and the IR-cooling laser intensity 20%.

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After applying IR-cooling for t_C = 2.5 s, we measure the atomic temperature by the time-of-flight by optically pumping the atoms to the ¹S₀ state to be free from the magnetic trap. For cooling conditions as indicated in Fig. 3(d) with t_C = 2.5 s and $I=38{I}_{0}^{(\mathrm{IR})}$, we observe bimodal velocity distribution and apply double Gaussian fit to extract low-temperature component. The atomic temperature T_z in the z-direction increases as the laser intensity I, as shown by the red circles in Fig. 4(b). For $I=38{I}_{0}^{(\mathrm{IR})}$, the atomic temperature was measured to be T_z = 24(5) μK in agreement with the theory ^18,27) that predicts ${T}_{z}=2{T}_{{\rm{D}}}/3\times s/(2{f}_{0}\sqrt{s/{f}_{0}-1-s})$ with f₀ = − (3μ_B β₀ + mg)/(ℏ k γ_IR/2) the ratio between the magneto-gravitational force F_BG and the maximum of the radiation pressure F_R. Here, β₀ is the magnetic field gradient at the trapped position z₀, T_D = ℏ γ_IR/(2k_B) = 1.4 μK the Doppler temperature, and $s=I/{I}_{0}^{(\mathrm{IR})}$ the saturation parameter. Whereas the cooling laser is introduced in the z-direction, the atomic motion in the y-direction decreases, responsible for the anharmonicity of the magnetic trap that couples the z-motion to that of x and y. The radial cooling is more pronounced for larger laser intensity, as shown by black circles in Fig. 4(b).

We introduce a moving optical lattice consisting of counter-propagating lasers at λ_L = 813 nm with each power of 250 mW along the z-axis [see Fig. 1(a)]. The lattice lasers are focused to the waist radius w₀ = 30 μm with the Rayleigh range z_R = 3.5 mm, giving the trap depth U_L/k_B = 50 μK. The lattice-trapped atoms move with the velocity v_L = λ_LΔν_L/2, which is set by the frequency difference Δν_L of the lattice lasers.

The lattice-trapped atoms in the ³P₂ state are outcoupled to the ³P₀ state by applying optical pumping lasers resonant to the ³P₂−³S₁ and ³P₁−³S₁ transitions at λ = 707 nm and 688 nm, respectively [see Fig. 1(c)]. These optical pumping lasers are superimposed on one of the lattice lasers and focused on the lattice-trapped atoms with intensities $5\times {10}^{-3}{I}_{0}^{(707)}$ and $2\times {10}^{3}{I}_{0}^{(688)}$, where ${I}_{0}^{(\lambda )}$ is the saturation intensities 2.5 mW cm⁻² and 1.7 mW cm⁻² for the respective transitions. As the pumping laser at 707 nm may affect the atoms not trapped in the moving lattice, the excess laser intensity causes the loss of the magnetically trapped atoms. The intensity of the 707 nm laser is chosen so that the interaction time τ of atoms with the pumping laser satisfies R τ ≈ 1 ²⁶⁾ with R the scattering rate, which we find optimal for R = 1300 s⁻¹.

The light shift given by the moving lattice is estimated to Δ_LS ∼ 1 MHz on the ³P₂(m_J = 2) − ³D₃(m_J = 3) transition. An optimal cooling and lattice-loading position can be shifted by 1 mm [see Fig. 3(c) and Fig. 5(a)] due to the position-dependent Zeeman shift μ_B/h × 0.7 mT cm⁻¹ ≈ 1 MHz mm⁻¹ in the z-direction. The temperature of the lattice-trapped atoms near the loading position is measured to be 5(2) μK, which is roughly one-tenth of the lattice depth U_L/k_B ≈ 50 μK and is determined by the truncation of the lattice depth.

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Finally, we demonstrate the continuous outcoupling of Sr atoms in the ³P₀ state by the moving optical lattice. The IR-cooling laser, moving lattice lasers, and optical pumping lasers at 707 and 688 nm are on all the time. We outcoupled the atoms by the moving lattice with v_L = −2 mm s⁻¹ for the transport time t_T = 1 − 4 s by turning on the B-MOT laser. Then we turn off the B-MOT laser and apply two lasers resonant to the ³P₀−³S₁ transition at 679 nm and the ³P₂−³S₁ transition at 707 nm to optically pump the atoms to the ¹S₀ state. We measure atomic distribution by exciting the ¹S₀−¹P₁ transition as shown in Fig. 5(a).

Figure 5(b) shows the spatial distribution of atoms along the z-axis obtained by integrating the fluorescence image in the y-direction. The right axis shows the corresponding elapsed time calculated as t = (z − z₀)/v_L with z₀ = −4.2 mm the lattice-loading position. Multiplying the atomic density by v_L gives the atomic flux of ϕ = 10³ atoms s⁻¹ at z = z₀. The number of atoms decreases exponentially with a lifetime of τ = 1.2 s during the transport, consistent with the background-gas-collision limited lifetime at 1.0 × 10⁻⁷ Pa. Further improvement of the vacuum pressure to 10⁻⁸ Pa will extend the transport time over 10 s.

In summary, we have demonstrated continuous laser-cooling and outcoupling of ultracold ⁸⁸Sr atoms by combining the magneto-optical trap, the magnetic trapping, and the moving optical lattice conducted in the ground state and the two metastable states. By further extracting atoms outside the B-MOT region of a few cm, outcoupled atoms can be used for clocks and superradiant lasers utilizing the ¹S₀ state. Moreover, by bending the atomic trajectory by a crossed moving lattice, the clock transition can be interrogated without being affected by the fluorescent photons coming from the B-MOT. The developed cooling scheme provides a vital technique for continuously manipulating ultracold atoms.

Acknowledgments