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Physical Review Applied

Rotation Sensing of a Trapped Nanoparticle Assisted by Magnetic Field Gradient

Lv‐Yun Wang, J.-F. Wei, Kaifeng Cui, Shi‐Lei Su, Mang Feng, L.-L. Yan, G. Chen, Huazhong Guo, Chongxin Shan

Published Sep 27, 2023• 2 citations

Abstract

We propose a rotation sensing scheme based on the Sagnac interferometer for a single trapped particle system. In this scheme, the spin and vibrational states of the particle, prepared in a coherent state, are translated into a Schr\"odinger cat state by applying a strong magnetic field gradient to create the spin-dependent force. By reflecting the phase related to the rotational rate accumulated by the two arms of the interferometer to the spin state, we can obtain the rotational rate of the apparatus by performing spin measurement. The scheme can also be applied to the situation with the vibration state in the thermal state. The sensing sensitivity can reach $S=4.47\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\phantom{\rule{0.2em}{0ex}}\mathrm{rad}/\mathrm{s}\phantom{\rule{0.2em}{0ex}}\sqrt{\mathrm{Hz}}$ for a suspended diamond nanoparticle and $S=5.65\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.2em}{0ex}}\mathrm{rad}/\mathrm{s}\phantom{\rule{0.2em}{0ex}}\sqrt{\mathrm{Hz}}$ for a trapped ${}^{40}{\mathrm{Ca}}^{+}$. Combining with the experimental parameters, our scheme is applied to realize the gyroscope in a trapped single nanoparticle and atomic ion.

DOI: 10.1103/physrevapplied.20.034063

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We propose a rotation sensing scheme based on the Sagnac interferometer for a single trapped particle system. In this scheme, the spin and vibrational states of the particle, prepared in a coherent state, are translated into a Schr"odinger cat state by applying a strong magnetic field gradient to create the spin-dependent force. By reflecting the phase related to the rotational rate accumulated by the two arms of the interferometer to the spin state, we can obtain the rotational rate of the apparatus by performing spin measurement. The scheme can also be applied to the situation with the vibration state in the thermal state. The sensing sensitivity can reach

S=4.47\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\phantom{\rule{0.2em}{0ex}}\mathrm{rad}/\mathrm{s}\phantom{\rule{0.2em}{0ex}}\sqrt{\mathrm{Hz}}

for a suspended diamond nanoparticle and

S=5.65\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.2em}{0ex}}\mathrm{rad}/\mathrm{s}\phantom{\rule{0.2em}{0ex}}\sqrt{\mathrm{Hz}}

for a trapped

{}^{40}{\mathrm{Ca}}^{+}

. Combining with the experimental parameters, our scheme is applied to realize the gyroscope in a trapped single nanoparticle and atomic ion.

Abstract We present a protocol for rotation measurement via matter-wave Sagnac interferometry using trapped ions. The ion trap based interferometer encloses a large area in a compact apparatus through repeated round-trips in a Sagnac geometry. We show how a uniform magnetic field can be used to close the interferometer over a large dynamic range in rotation speed and measurement bandwidth without contrast loss. Since this technique does not require the ions to be confined in the Lamb–Dicke regime, Doppler laser cooling should be sufficient to reach a sensitivity of  = 1.4 × 10 − 6 rad s − 1 H z − 1 / 2 .

We propose a motional dynamical decoupling technique by utilizing a sequence of

π

-phase shifts, instead of the conventional

π

-pulses for spin flipping, to implement the quantum enhanced rotation sensing with a 1+2 dimensional hybrid atomic Sagnic interferometor. By fully disentangling the spin from the two-dimensional vibrational modes of the particle under rotation, the spin coherence time and thus the phase accumulation can be significantly increased. Consequently, both the achievable sensitivity and dynamic range of the rotation sensing can be significantly enhanced and extended simultaneously, compared to the previous schemes where the spin and motions of the particle were not completely decoupled. The experimental feasibility for the unambiguous estimation of the rotation parameters is also discussed. Hopefully, this technique holds promise for overcoming certain challenges existing in the usual matter-wave Sagnac interferometers with trapped particles, particularly for the practical inertial navigation that demands both high sensitivity and large dynamic range.

We discuss a scheme to implement a gyroscopic atom sensor with magnetically trapped ultra-cold atoms. Unlike standard light or matter wave Sagnac interferometers no free wave propagation is used. Interferometer operation is controlled only with static, radio-frequency and microwave magnetic fields, which removes the need for interferometric stability of optical laser beams. Due to the confinement of atoms, the scheme may allow the construction of small scale portable sensors. We discuss the main elements of the scheme and report on recent results and efforts towards its experimental realization.

Cooling a solid-state nanoparticle, as a significant prerequisite of the mesoscale quantum sensing, is experimentally challenging. Here we propose an efficient cooling scheme assisted by a strong magnetic-field gradient to cool a nanoparticle down to the ground state of the vibrational degrees of freedom. By combining the Zeeman effect with quantum interference effect, the scheme can accomplish the precooling of the nanoparticle from room temperature to the Doppler cooling limit in several seconds, and can then further cool the precooled nanoparticle to the vibrational ground state within milliseconds. We specify the scheme by exemplifying the nanocrystal of diamond nitrogen-vacancy center suspended in an electromagnetic potential, indicating that this cooling scheme can accomplish the ground-state cooling from room temperature within a few seconds under the condition of currently available techniques. Our work lays a foundation for further three-dimensional cooling of suspended nanoparticles and also for realizing quantum sensing using mesoscopic particles in the future.

We describe a Sagnac interferometer suitable for rotation sensing, implemented using an atomic Bose-Einstein condensate confined in a harmonic magnetic trap. The atom wave packets are split and recombined by standing-wave Bragg lasers, and the trapping potential steers the packets along circular trajectories with a radius of 0.2 mm. Two conjugate interferometers are implemented simultaneously to provide common-mode rejection of noise and to isolate the rotation signal. With interference visibilities of about 50%, we achieve a rotation sensitivity comparable to Earth's rate in about 10 min of operation. Gyroscope operation was demonstrated by rotating the optical table on which the experiment was performed.

The Sagnac interferometry has widely been used to measure rotation frequency. Beyond the conventional single-particle scheme, we propose a multiparticle scheme via Bose condensed atoms. In our scheme, an ensemble of entangled two-state Bose atoms are moved in a ring via a state-dependent rotating potential, and then the atoms are recombined for interference via Ramsey pulses. The phase accumulation time is determined by the state-dependent rotating potential. The ultimate rotation sensitivity can be improved to the Heisenberg limit if the initial internal degrees of freedom are entangled. By implementing parity measurement, the ultimate measurement precision can be saturated, and the achieved measurement precisions approach the Heisenberg limit. Our results provide a promising way to exploit many-body quantum entanglement in precision rotation sensing.