[Paper Review] Cooling a Mechanical Resonator with a Nitrogen-Vacancy Center Ensemble Using a Room Temperature Excited State Spin-Strain Interaction

E. R. MacQuarrie, Matthew Otten+2 more|arXiv (Cornell University)|May 23, 2016

Mechanical and Optical Resonators4 citations

TL;DR

This paper proposes a dissipative cooling protocol that uses a room-temperature nitrogen-vacancy (NV) center ensemble to cool a mechanical resonator via a previously uncharacterized excited-state spin-strain interaction. The authors experimentally measure this interaction to be 13.5±0.5 times stronger than the ground-state coupling and theoretically demonstrate that a dense NV ensemble can cool a high-Q resonator from room temperature to sub-thermal phonon occupancy, enabling quantum control at ambient conditions.

ABSTRACT

We propose a protocol to dissipatively cool a room temperature mechanical resonator using a nitrogen-vacancy (NV) center ensemble. The spin ensemble is coupled to the resonator through its orbitally-averaged excited state, which has a spin-strain interaction that has not been previously characterized. We experimentally demonstrate that the spin-strain coupling in the excited state is $13.5\pm0.5$ times stronger than the ground state spin-strain coupling. We then theoretically show that this interaction combined with a high-density spin ensemble enables the cooling of a mechanical resonator from room temperature to a fraction of its thermal phonon occupancy.

Motivation & Objective

• To develop a method for cooling mechanical resonators to sub-thermal phonon occupancy at room temperature using collective spin interactions.
• To characterize the previously unmeasured spin-strain coupling in the NV center excited state (ES) and compare it to the ground state (GS) coupling.
• To demonstrate that the ES spin-strain interaction enables collective enhancement in dense NV ensembles without coherence degradation.
• To propose and analyze a dissipative cooling protocol that does not require long spin coherence times.
• To show that high-Q mechanical resonators can be cooled from room temperature to a fraction of their thermal phonon occupancy using this mechanism.

Proposed method

• The authors measure the spin-strain coupling strength in the NV center excited state using magnetic spectroscopy, finding it to be 13.5±0.5 times stronger than in the ground state.
• They model the hybrid system using a Hamiltonian that includes the NV spin interaction with strain, magnetic fields, and optical excitation, with the key coupling being $ d_{\perp}^e $ in the excited state.
• The effective coupling between the mechanical resonator and the NV ensemble is derived as $ \lambda_{\text{eff}} = G_0 \sqrt{t}/l $, where $ G_0 = d_{\perp}^e \sqrt{\hbar \kappa_0 \alpha \rho / E} $, accounting for strain distribution and ensemble density.
• A dissipative cooling protocol is proposed using a static magnetic bias field to tune resonance, a GHz-frequency magnetic field $ \Omega_{\text{mag}} $ to drive spin transitions, and continuous optical pumping $ \Gamma_{\text{opt}} $ to reset the system.
• The protocol relies on population transfer to the $ |g,-1\rangle $ state, which couples to the mechanical mode via the spin-strain interaction, enabling energy extraction through dissipative processes.
• Theoretical analysis shows that with $ \Omega_{\text{mag}}/2\pi = 60 $ MHz and $ \Gamma_{\text{opt}} = 130 $ MHz, the fraction of the ensemble involved in cooling saturates at $ \alpha \sim 0.017 $, enabling effective cooling.

Experimental results

Research questions

• RQ1 Is the spin-strain coupling in the NV center excited state stronger than in the ground state, and can it be experimentally quantified at room temperature?
• RQ2 Can a dense ensemble of NV centers in the excited state maintain sufficient coherence for collective coupling to a mechanical resonator?
• RQ3 Can a dissipative cooling protocol using the excited-state spin-strain interaction cool a room-temperature mechanical resonator to sub-thermal phonon occupancy without requiring cryogenic conditions?
• RQ4 What are the optimal control fields (magnetic and optical) needed to maximize the cooling rate while minimizing decoherence effects?
• RQ5 How does the mechanical mode frequency and resonator geometry affect the achievable coupling strength and cooling efficiency?

Key findings

• The spin-strain coupling in the NV center excited state is experimentally measured to be $ 13.5 \pm 0.5 $ times stronger than in the ground state, confirming a significant enhancement for cooling applications.
• The excited-state spin-strain interaction is robust against NV center density, as its coherence time is limited by motional narrowing rather than ensemble inhomogeneity, enabling collective enhancement.
• The effective coupling strength between the resonator and the NV ensemble is $ \lambda_{\text{eff}} = G_0 \sqrt{t}/l $, with $ G_0 $ dependent on material parameters and strain distribution.
• With $ \Omega_{\text{mag}}/2\pi = 60 $ MHz and $ \Gamma_{\text{opt}} = 130 $ MHz, the fraction of the ensemble involved in cooling reaches $ \alpha \sim 0.017 $, saturating at high field strengths.
• Theoretical analysis confirms that a high-Q mechanical resonator at room temperature can be cooled to a fraction of its thermal phonon occupancy using this protocol.
• The spectral isolation between the fundamental mode and higher-order modes is sufficient, with a linewidth of ~170 MHz, ensuring minimal crosstalk.