Helical Bessel Guiding for Multi-Orbit Ultracold-Atom Rotation Sensing

Matter-wave Sagnac interferometry measures rotation by comparing the phases of atomic wave packets travelling along separate paths that enclose an area. A larger enclosed area produces a stronger rotation signal, increases the rotation scale factor, and can improve sensitivity. Cold-atom gyroscopes can already achieve precise measurements, but improving their sensitivity without increasing the size of the instrument remains difficult. Guided interferometers address this challenge by controlling the atomic paths with optical or magnetic potentials which allow a larger sensing area to be created within a compact system.

For a multi-turn interferometer to work well, the two atomic wave packets must follow stable paths, remain coherent, and meet again at the correct points. This becomes harder as more turns are added. In magnetically guided systems, small changes in trap alignment or field strength can shift the atomic paths and reduce the interference signal. Repeated crossings between the wave packets can also lead to losses. A practical multi-turn gyroscope therefore needs a guide that can control the atoms reliably throughout the full measurement.

Programmable optical dipole potentials offer a different route because the atomic trajectory can be written into the spatial structure of the light field. Spatial light modulators can reshape such fields dynamically, while Bessel-like beams provide a narrow central intensity lobe that can be engineered to follow a prescribed three-dimensional path. For a helical guide, however, the field must do more than trace the desired centerline. It must confine the atoms transversely, transport them along the helix, compensate gravity, and retain a sufficiently stable guiding core over the required propagation distance. These requirements have to be met without introducing excessive photon scattering or an optical configuration whose complexity offsets the advantage of programmable guiding.

 In a recently published research paper in Photonics Research Dr. Xin Lv, Professor Zhaoying Wang, and Professor Qiang Lin from Zhejiang University proposed and numerically analysed a theoretical ultracold-atom gyroscope in which a far-detuned, angular-spectrum-engineered Bessel-like beam is designed to guide a Bose–Einstein condensate along programmable helical trajectories. The same optical field encodes the helix geometry, transverse confinement, and an axial intensity gradient that compensates gravity. A synchronized sequence of Bragg pulses and spatial-light-modulator updates is designed to send two matter-wave packets through reciprocal, opposite-handed multi-turn paths before recombination. Its distinct feature is the use of stable three-dimensional optical guiding to increase effective Sagnac area through repeated orbits within a compact spatial footprint.

The researchers designed the helical guide by engineering the beam’s angular spectrum. Its centre follows a programmed spiral path, while the beam’s intensity changes along the direction of travel to counteract gravity. In the simulations, the atoms can move through the helix at a nearly steady speed while remaining confined close to the bright central core of the Bessel-like beam.

The authors created a simulated beam using a limited optical window, so it is described as Bessel-like instead of the ideal Bessel beam. In numerical propagation tests, its guiding region stayed stable as the beam travelled. In a separate numerical test, when the main lobe was blocked, it quickly formed again, suggesting that the guide could recover from a local disturbance. The intensity change used to balance gravity also caused only a very small shift in the simulated atom position. The team then modelled the motion of ultracold rubidium atoms in the optical potential. The simulated atoms closely followed helical paths with different programmed pitches. Under the representative parameters considered, optical confinement was much stronger than the force caused by photon scattering, indicating that scattering should have little influence on the intended trajectory. A single structured beam could therefore provide both three-dimensional guiding and gravity compensation.

For the interferometer, a Bragg pulse divides the condensate into two wave packets moving in opposite directions. They travel along helices of opposite handedness, while later pulses reverse their momenta and updates to the spatial light modulator switch the direction of the guide. A final pulse is designed to bring the packets back together at their starting point.

In the ideal path-symmetric model, the laser-phase contributions cancel within a single measurement. The calculated phase is therefore mainly determined by propagation through the rotating system. Repeated turns increase the total enclosed area and strengthen the Sagnac response. In the representative eight-turn design, the paper reports an effective area of about 72 mm², corresponding to a large calculated rotation scale factor.

The proposed spiral Bessel-beam gyroscope by Zhejiang University scientists could support several important engineering applications that require accurate rotation sensing in a compact system. Its main advantage is the ability to guide ultracold atoms through several turns inside a programmable helical optical path. Each additional turn increases the effective enclosed area and strengthens the Sagnac phase used to measure rotation, without requiring the instrument to become proportionally larger. This makes the design relevant to compact precision gyroscopes, where sensitivity and physical size often compete with one another.

Another possible engineering application is in inertial navigation. Rotation sensors are essential in systems that must determine their orientation when satellite navigation is weak, interrupted, or unavailable. The proposed concept could contribute to future navigation units for aircraft, ships, underwater vehicles, or other platforms that require stable measurements over extended periods. The paper does not demonstrate such a field-ready device, but it provides a practical optical layout and identifies operating conditions needed for experimental development.

The programmable optical guide also offers engineering flexibility. By changing the spatial-light-modulator pattern, the radius, pitch, and handedness of the atomic trajectory can be adjusted without rebuilding the entire apparatus. This may allow one instrument to be configured for different measurement ranges or experimental conditions. The authors also suggest that tilting the helical axis and repeating the measurement could, in principle, recover all three components of the rotation vector.

Another useful feature is the reduced need for repeated wave-packet crossings. The two atomic packets overlap only at selected points in the interferometer sequence, which may help limit losses and preserve coherence during multi-orbit operation. The reciprocal geometry is also expected to suppress common laser-phase noise and slow common-mode disturbances. From an engineering perspective, the study supplies more than a sensing concept. It defines a beam-generation method, an atom-guiding strategy, a Bragg-pulse sequence, and quantitative limits associated with photon scattering, magnetic noise, optical-intensity fluctuations, and condensate phase diffusion. These elements provide a technical basis for building and testing a compact multi-orbit atom gyroscope.