Long-range temperature-controlled transport of ultra-cold atoms with an accelerated lattice

The transport of clouds of cold atoms or Bose–Einstein condensates (BEC) from their production area to other areas of experimental interest has drawn much attention since first implementations in the 90s [1]. Various approaches have been considered, using magnetic or optical fields, depending on the desired specifications. Magnetic traps have proven to be a suitable solution for moving thermal clouds at temperatures above the micro-Kelvin range over long distances of tens of centimeters, but at the cost of heating up the sample [2–7]. On the other hand, trapping the atomic cloud in optical lattices has proven to be a solution of choice for precise displacement of single atoms over distances of the order of the centimeter [8, 9], for adiabatic centimeter-long transport of ultracold atoms [10], or fast transport of cold atoms in the decimeter range using Bessel beams [11]. Other solutions involving the use of a focus-tunable moiré lens [12], other optical systems of tunable-zoom [13] or optical tweezers [14] have also shown their interest to transport atomic cloud either on short distances with reasonably small heating or, on long distances, with more consequent warm-up of the atomic cloud and a weak confinement in the direction of transport.

In the experiment reported here, we aim at performing ultra-sensitive short range forces measurements, with a quantum sensor based on $\mathrm{^{87}Rb}$ atoms trapped in an optical trap, consisting of a vertical shallow lattice $\lambda_\mathrm{Verdi} = 532$ nm overlapped with a transverse confinement potential $\lambda_\mathrm{IR} = 1064$ nm. In such a system, energy differences between adjacent lattice sites can be probed with a Ramsey-Raman interferometer [15] providing us a local measurement of the vertical force exerted on the atoms. The goal is to probe micrometer-range forces occurring between our atomic cloud and the surface of a mirror. Previous attempts at similar measures have shown the importance of preparing the sample away from the surface of the mirror in order to minimize any undesired adsorption of the atoms [16, 17]. Furthermore, the spatial resolution of the measurements is limited by the final size of the cloud in the vertical direction, perpendicular to the surface of the mirror, and by the accuracy of our control of the distance from the cloud to the mirror. We start with a cloud of a few micrometers [15]. To ensure an accurate control of the distance covered by the atoms and their vertical confinement throughout transport, we chose to transport them using a moving lattice [1, 10, 11].

We present here the outcomes of our experimental setup which enables the transportation of up to $25\%$ of a sub-micro-Kelvin atomic cloud on a distance of the order of 30 cm, without inducing excessive heating and while maintaining control over its size and final position. We first provide a general overview of the experimental setup and of the main sources of loss expected, before reporting our results on the transport efficiency and the control of the atoms position.

Figure 1(a) summarizes the main steps of the atom preparation. A two-dimensional magneto-optical-trap (2D-MOT) loads atoms in a three-dimensional magneto-optical trap (3D-MOT), which in turn loads a crossed dipole trap where evaporative cooling is performed down to a temperature of 300 nK and an atomic density of the order of 10¹² atoms cm⁻³. Then, atoms are launched upward and transported over 30 cm, up to the vicinity of the surface of the lattice mirror, where measurements are to be performed.

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The elevator consists of the overlapping of two counterpropagating beams 'Bloch 1' and 'Bloch 2' whose frequency differences and intensities are tuned over time. Atoms are thus loaded in an accelerated or decelerated lattice of adjustable depth.

2.1. Setup

2.2. Atoms in moving lattices

The periodic potential U(z) resulting from the interference of the two counter-propagating beams 'Bloch 1,2' of intensity $I_{1,2}$ is proportional to the local intensity experienced by the atoms $I(z) = 2 I_0 (1 + m \cos 2\,kz)$, where I₀ is the average intensity, m the ratio of the geometric and arithmetic means of the intensities of each beam and k is the modulus of the wavevector of the laser:

$$\begin{align} U(z) = \frac{U_0}{2} (1 + m \cos 2 k z) \end{align} \tag{ 1 }$$

For a detuning Δ of the order of hundreds of GHz with respect to the D2 line of ⁸⁷Rb, the depth is $U_0 \sim \hbar \Gamma^2 I_0 / (3 \Delta I_s)$, where Γ and I_s are the natural linewidth and the saturation intensity of the transition. By imposing a frequency difference $\Delta\omega$ between the two Bloch beams, we then move the lattice potential with a velocity $v_\mathrm{latt} = \Delta\omega/2k$. This allows us to coherently accelerate the atoms through Bloch oscillations [18], each oscillation imparting a $2 \hbar k$ momentum transfer to the atoms.

For the measurements presented here, the detuning Δ is set to −250 GHz. For maximum powers around 50 mW in the two beams, with identical waists of 400 µm, we calculate a maximum depth around $150~E_r$, with $E_r = \frac{\hbar^2 k^2}{2m_{Rb}}$ the recoil energy. This is in reasonable agreement with a determination of the depth based on Raman–Nath diffraction, where from the measurement of the populations in the diffracted orders as a function of duration of a square pulse performed before the transport, we deduced a maximum depth of about $110~E_r$.

Figure 2 illustrates the typical sequence of transport. The atoms are first adiabatically loaded into the lattice, by increasing the depth from 0 to $U_\mathrm{acc}$ in 600 µs while ramping the frequency difference between the two beams by 25 MHz s⁻¹. This corresponds to accelerating the lattice by g.

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Then, the lattice is accelerated upwards over 6 ms at a fixed lattice depth $U_\mathrm{acc}$. The chirp of the frequency difference between the beams corresponds to $N_\mathrm{acc}$ Bloch oscillations. After a certain transport time at constant velocity, where the lattice potential may be reduced, the atoms are decelerated at a depth $U_\mathrm{dec}$ with $N_\mathrm{dec}$ Bloch oscillations. The atoms are then adiabatically released by reducing the lattice potential down to zero in 600 µs. They are then trapped in the mixed trap illustrated in figure 1, where force measurements are to be performed. This mixed trap consists of the superposition of a green lattice, which we turn on 400 µs before the end of the adiabatic release, and an IR transverse confinement beam, which we keep at full power of 2 W during the transport and the recapture in the mixed trap.

Between the acceleration and deceleration, we keep the transport lattice at a depth $U_\mathrm{ff}$ in order to keep the atoms vertically and transversally confined. Additional transverse confinement is also provided by the IR laser at 1064 nm. Its waist, of the order of 200 µm is placed at the target position of the atoms, near the surface of the lattice mirror.

2.3. Sources of loss

2.4. Detection

To optimize the launch efficiency of the atoms, we start by imaging in the bottom chamber their position 3 ms after their acceleration. Figure 1(α) left displays an absorption imaging picture featuring three different groups of atoms: ③ launched, ② trapped in a parasitic lattice due to reflection of the 'Bloch 1' beam on the Raman mirror, and ① untrapped and in free fall. By adjusting the polarization of the 'Bloch 1' beam, we eliminate the loss of atoms in both groups ① and ②, which results in a single group of atoms as displayed at the right. We then increase the number of Bloch oscillations until the atoms can reach the top chamber, where we obtain a first signal (similar to the one in figure 1(β)). We next optimize the durations of the different transport phases, keeping the transport distance constant. This initial optimization results in durations of 6 ms for both acceleration and deceleration phases, with 250 Bloch oscillations at the acceleration as displayed in figure 2. We optimize afterwards the other parameters, such as the power of the 'Bloch' beams or the temperature of the atoms before the transport. We finally vary back the duration and number of Bloch oscillations without much improvement.

We illustrate in figure 3 the influence of the initial temperature of the atoms both on the number and the temperature of the atoms after their transport over the 30 cm distance and after their trapping in the mixed trap described above. We find that the efficiency of both processes reduces when increasing the initial temperature. We attribute this for one to the velocity selectivity of the acceleration process, that works best for atoms moving at subrecoil velocities in the frame of the lattice, and for the other to the shallow depth of the mixed trap. Note that the efficiency is not the only relevant parameter when it comes to selecting the most appropriate parameters for our transport system. It can be of interest for instance to work either with high initial temperatures, which, despite the lower efficiency, leads indeed to larger number of transported atoms, or with lower initial temperature, which leads to smaller sizes at the end. These relevant parameters actually depend on the details of the evaporative cooling stage, where temperature, number of atoms and initial size are correlated.

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The influence of the powers in the Bloch beams during the transport is illustrated in figure 4(a). The larger the powers, the higher the depth, and the more efficient is the transport. However, for an efficient subsequent loading in the mixed trap, the power in the 'Bloch 1' beam needs to be reduced, as shown in figure 4(c), which displays the number of atoms in the mixed trap after a trapping time of 1 s. We attribute this feature to the presence of residual parasitic static lattices, related to the reflection of the 'Bloch 1' beam on the Raman and green lattice mirrors.

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Other parameters have also been varied without much improvement. We can for instance mention the influence of the depth used during the transport ($U_\mathrm{ff}$). While decreasing the depth at this stage reduces in principle losses due to spontaneous emission, it comes at the price of a large decrease in the number of transported atoms, which we attribute to the reduction in the transverse confinement. Therefore this depth is kept constant, as high as during the acceleration and deceleration phases, for all the measurements presented here.

The position stability of the cloud after the transport is a key objective for our experimental setup. To check its evolution over time, we alternate absorption imaging measurements of the cloud before and after the transport. The corresponding Allan standard deviations of those two signals and of their difference are plotted in figure 5.

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A larger measurement noise is observed for the position before the launch in the bottom chamber, which we attribute to the larger size of the cloud, whose center position has been measured after a 6 ms thermal expansion in free fall, and to the larger readout noise of the bottom camera compared to the top one.

On both positions of the cloud, we observe a bump on the Allan deviation, occurring around 200 s. This perturbation is correlated with the temperature cycles of our air conditioning system and is actually eliminated when calculating the difference of the two signals, since the Allan deviation of this difference averages down to about 100 nm at 1000 s. This confirms that the travel distance is not affected by these thermal fluctuations, which are dominated by the fluctuations of the starting position of the atomic cloud, before the transport.

This correlation between the top and bottom positions decreases over longer time scales, of hours or days, as can already be observed in figure 5 for timescales of a few thousand seconds. This could actually be due to deformations in the mechanical structure supporting our two imaging systems, rather than variations in the actual travel distance.

Finally, the final vertical size of the cloud will determine the spatial resolution of our force sensor. But, given the current resolution of our imaging system of about 9 µm, we are actually not able to precisely determine this size, nor its fluctuations. Nevertheless, since the atoms remain trapped at all times, we expect the size of the atomic cloud to be identical to the size at the end of the evaporation (ie of order of a few micrometers in rms width).

We have investigated the efficiency of using Bloch oscillations to transport a cloud of ultracold atoms over a long-range distance of 30 cm, with a precise control of their final position, size and temperature, and with the prerequisites of keeping them trapped at all times. We obtain a maximum efficiency of 25$\%$ for their transport, and in the end, we recapture about 10$\%$ of the initial number of atoms in the final trap, which combines a blue-detuned static lattice and a red-detuned progressive wave for transverse confinement. Spontaneous emission induces in our setup significant losses and heating, which could be reduced by operating at larger detunings, and thus intensities.

Both the number of atoms and the micrometric spatial resolution of the cloud obtained at the end of our transport process with an optical moving lattice are sufficient for us to move on to measurements of short-range forces between the atoms and the dielectric mirror that retroreflects the lattice beam. In order to integrate these measurements over long periods of time, the stability of the transport is also a prerequisite, which our method fulfills.

This research has been carried out in the frame of the QuantERA project TAIOL, funded by the European Union's Horizon 2020 Research and Innovation Programme and the Agence Nationale de la Recherche (ANR-18-QUAN-0015-01).

The data that support the findings of this study are available upon reasonable request from the authors.