Abstract

Controlling the motion of macroscopic oscillators in the quantum regime has been the subject of intense research in recent decades. In this direction, opto-mechanical systems, where the motion of micro-objects is strongly coupled with laser light radiation pressure, have had tremendous success. In particular, the motion of levitating objects can be manipulated at the quantum level thanks to their very high isolation from the environment under ultra-low vacuum conditions. To enter the quantum regime, schemes using single long-lived atomic spins, such as the electronic spin of nitrogen-vacancy (NV) centers in diamond, coupled with levitating mechanical oscillators have been proposed. At the single spin level, they offer the formidable prospect of transferring the spins’ inherent quantum nature to the oscillators, with foreseeable far-reaching implications in quantum sensing and tests of quantum mechanics. Adding the spin degrees of freedom to the experimentalists’ toolbox would enable access to a very rich playground at the crossroads between condensed matter and atomic physics. We review recent experimental work in the field of spin-mechanics that employ the interaction between trapped particles and electronic spins in the solid state and discuss the challenges ahead. Our focus is on the theoretical background close to the current experiments, as well as on the experimental limits, that, once overcome, will enable these systems to unleash their full potential.

Highlights

  • The unique control offered by single quantum systems, such as atoms or ions, has enabled an immense boost in the development of quantum technologies

  • We focus on the important results that have been accomplished and the remaining hurdles on the way towards operating in the quantum regime with these platforms

  • In order to evaluate the dynamical back-action from the spins to the mechanical oscillator with retardation, one will include the dissipation of the electronic spin

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Summary

Introduction

The unique control offered by single quantum systems, such as atoms or ions, has enabled an immense boost in the development of quantum technologies. Initial work proposed to coupling levitated silica nano-spheres, and even viruses, to the optical modes of a high finesse cavities [4,5,6] The promises of this schemes have been supported by recent experiments that reported trapped particles cooled to the quantum regime [7,8,9,10]. Ensembles of NV− centers coupled identically to mechanical oscillators can exhibit magnetic phase transitions, paving the way towards nano-scale magnetism with long-lived and controllable spins in a trapped particle [19,20] This growing research field will drive advances in quantum metrology via quantum enhanced gyroscopy and matter-wave interferometry [19,21,22].

Trapping Crystals
Center of Mass Harmonic Motion
Angular Confinement
Trapping Platforms
Coupling to an Ancillary Quantum System
Hamiltonian of the Spin–Mechanical System
Coupling to the Center of Mass
Coupling to the Libration
Force and Torque Sensitivity
Observing NV Static Spin-Dependent Torque and Force
Dynamical Resonant Spin–Mechanical Interaction
Bistability and Spin-Spring Effect
Spin-Bistability
Dynamical Backaction
Spin-Cooling
Equations of Motion
Stationary Solutions
Effective Susceptibility
Dynamical Spin-Rigidity in the Adiabatic Limit
Challenges Ahead for Levitated Spin-Mechanics
Production of Diamond
Control of Diamond Shape and Properties
Internal Temperature of Levitated Diamonds
Findings
Conclusions
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