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Physical Review A

Rapid ground-state cooling of a solid-state nanoparticle assisted by a magnetic-field gradient

Lv‐Yun Wang, F.-Q. Guo, Shi‐Lei Su, Chongxin Shan, Mang Feng, Erjun Liang, L.-L. Yan

Published May 31, 2022• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.105.053124

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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 propose an efficient optical electromagnetically induced transparency (EIT) cooling scheme for a cantilever with a nitrogen-vacancy center attached in a non-uniform magnetic field using dynamical Zeeman effect. In our scheme, the Zeeman effect combined with the quantum interference effect enhances the desired cooling transition and suppresses the undesired heating transitions. As a result, the cantilever can be cooled down to nearly the vibrational ground state under realistic experimental conditions within a short time. This efficient optical EIT cooling scheme can be reduced to the typical EIT cooling scheme under special conditions.
The efficient cooling of nanomechanical resonators is essential to exploration of quantum properties of the macroscopic or mesoscopic systems. We propose such a laser-cooling scheme for a nanomechanical cantilever, which works even for the low-frequency mechanical mode and under weak cooling lasers. The cantilever is coupled by a diamond nitrogen-vacancy center under a strong magnetic field gradient and the cooling is assisted by a dynamical Stark-shift gate. Our scheme can effectively enhance the desired cooling efficiency by avoiding the off-resonant and undesired carrier transitions, and thereby cool the cantilever down to the vicinity of the vibrational ground state in a fast fashion.
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 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+. Combining with the experimental parameters, our scheme is applied to realize the gyroscope in a trapped single nanoparticle and atomic ion.
The ground-state cooling and quantum control of levitated nanoparticles have become attainable, which makes the enhanced quantum sensing based on the large mass advantage of mesoscopic quantum systems accessible. Here, we propose an enhanced gravity-sensing protocol for a nanodiamond levitated in a linear ion trap, which improves the sensing sensitivity and further reduces device size. By introducing gravitational acceleration into the vibrational state through transient free fall, we achieve a square-accelerated relative phase accumulation, yielding higher sensitivity than the linear accumulation process. The sensitivity reaches the standard quantum limit for a nanodiamond containing multiple nitrogen-vacancy (N-V) centers. Besides, by using phonon-mediated one-axis twisting dynamics induced by magnetic field gradient to squeeze the initial spin state, the sensitivity can further surpass the standard quantum limit as a scaling law of N^{-5/6}. To fully assess the protocol performance, we further analyze the effects of decoherence and control errors, which are negligible under experimentally achievable conditions. Specifically, the sensitivity reaches ∼18 μGal/sqrt[Hz] for the nanodiamond containing only one N-V center over a free-fall distance of ∼20 μm, while exceeds 0.4 μGal/sqrt[Hz] for 100 N-V centers. Our results will further facilitate research on compact and high-sensitivity gravimeters.
We optically trap a single nanoparticle in high vacuum and cool its three spatial degrees of freedom by means of active parametric feedback. Using a single laser beam for both trapping and cooling we demonstrate a temperature compression ratio of four orders of magnitude. The absence of a clamping mechanism provides robust decoupling from the heat bath and eliminates the requirement of cryogenic precooling. The small size and mass of the nanoparticle yield high resonance frequencies and high quality factors along with low recoil heating, which are essential conditions for ground state cooling and for low decoherence. The trapping and cooling scheme presented here opens new routes for testing quantum mechanics with mesoscopic objects and for ultrasensitive metrology and sensing.
Many-body dynamics constitutes a promising approach for creating correlations between quantum particles which can be used for applications in sensing and metrology. However, utilizing this potential for substantial gains in practical settings is a challenging task with only a very few applications realized to date. Here, we demonstrate an approach to nanoscale magnetic sensing enabled by strongly interacting electronic spins in a room temperature solid. By coherently controlling collective many-body dynamics of a dipolar ensemble of ∼104\sim 10^4∼104 nitrogen-vacancy (NV) centres in diamond with pulsed magnetic field gradients, we demonstrate practical metrological gain up to 7.9(2) dB7.9(2)\,\mathrm{dB}7.9(2)dB for magnetic signal detection and 8.8(3) dB8.8(3)\,\mathrm{dB}8.8(3)dB for magnetic noise sensing, fully accounting for experimental overheads. Finally, we combine these methods to demonstrate a momentum-space-resolved sensing modality that enables detection of spatially correlated magnetic noise at continuously tunable length scales down to 50 nanometers. These observations open the door toward practical applications of interaction-enhanced quantum sensors for nanoscale biological imaging and material characterization.