Bloch oscillations occur when atoms are held in an optical lattice potential, in the presence of an accelerating force pointing along the lattice direction. The force causes the atoms to tunnel through the lattice barriers, so the atoms accelerate much as they would in free space. However, when the velocity of the atoms reaches the Bragg velocity of the lattice, the atoms are coherently reflected and their momentum is reversed. The accelerating force continues to act and the momentum increases again, with the cycle repeating as long as the atoms can be retained. Bloch oscillations are an interesting physical phenomenon with many applications. For example, by measuring the period of the oscillation, the strength of the acceleration can be determined with high precision [1]. [Ed. Note: See References.]

In terrestrial experiments, the acceleration is typically due to gravity and the amplitude of the oscillation is on the order of micrometers, since the atoms do not fall very far before reaching the Bragg velocity of order 1 cm/s. In microgravity, the oscillation amplitude is much larger, reaching the mm scale at milli-g accelerations. A few terrestrial experiments have investigated Bloch oscillations at low accelerations using horizontal optical lattices. However, these efforts are hampered by the need to support the atoms against gravity. This requires a combination of a relatively tight optical trap and magnetic levitation. The tight trap leads to high atomic density and thus complicating effects from interactions. Magnetic levitation cannot easily be made uniform, leading to spatial variations in the accelerating force. For instance, the experiments by Geiger et al. [2] observed oscillation amplitudes of about 150 um, but required a Feshbach resonance to nullify interactions and were limited by inhomogeneity. The sensitivity to accelerations increases with the amplitude of oscillation, so larger amplitudes are desirable.

The microgravity environment on CAL offers a clear opportunity for improvement. The existing Bragg laser can be used to provide the optical lattice, where a depth of about one recoil energy is needed. A tunable acceleration can be obtained using the magnetic gradient control provided in the new upgrade. A gradient of 15 mG/cm gives a suitable acceleration of 1 cm/s^2. The period of the oscillation would be about 0.5 s, which is within the vacuum limits of the system.

Although Bloch oscillations can be described using classical language, they are in fact a quantum phenomenon; classical particles would not "Bragg reflect" from a lattice. The amplitude of the oscillation is set by the spatial extent of the Wannier-Stark wavefunctions of the lattice, and the atomic waves are coherent across this length scale. Large Bloch oscillations are thus comparable to atom interferometry, but Bloch oscillations can be more robust to technical imperfections. For instance, they do not require a well-defined initial atom velocity, and they can tolerate a range of lattice depths. Our group is well-situated to carry out ground studies to support the flight operations. We have an existing apparatus that provides weakly-confined atoms in a highly uniform horizontal magnetic guide. We propose to use this system to test the approach and technical requirements, so that the flight experiments can be more quickly achieved and optimized.

References

[1] Nal?cz I, Masi L, Ferioli G, Petrucciani T, Fattori M, Chwedenczuk J. Sensitivity bounds of a spatial Bloch-oscillation atom interferometer. Physical Review A. 2020 Sep;102(3):033318. https://doi.org/10.1103/PhysRevA.102.033318

[2] Geiger ZA, Fujiwara KM, Singh K, Senaratne R, Rajagopal SV, Lipatov M, Shimasaki T, Driben R, Konotop VV, Meier T, Weld DM. Observation and uses of position-space Bloch oscillations in an ultracold gas. Physical review letters. 2018 May 25;120(21):213201. https://doi.org/10.1103/PhysRevLett.120.213201