Ramsey Interferences and Spin Echoes from Electron Spins Inside a Levitating Macroscopic Particle

Enhanced Tripartite Interactions in Spin-Magnon-Mechanical Hybrid Systems

Coherent tripartite interactions among degrees of freedom of completely different nature are instrumental for quantum information and simulation technologies, but they are generally difficult to realize and remain largely unexplored. Here, we predict a tripartite coupling mechanism in a hybrid setup comprising a single nitrogen-vacancy (NV) center and a micromagnet. We propose to realize direct and strong tripartite interactions among single NV spins, magnons, and phonons via modulating the relative motion between the NV center and the micromagnet. Specifically, by introducing a parametric drive (two-phonon drive) to modulate the mechanical motion (such as the center-of-mass motion of a NV spin in diamond trapped in an electrical trap or a levitated micromagnet in a magnetic trap), we can obtain a tunable and strong spin-magnon-phonon coupling at the single quantum level, with up to 2 orders of magnitude enhancement for the tripartite coupling strength. This enables, for example, tripartite entanglement among solid-state spins, magnons, and mechanical motions in quantum spin-magnonics-mechanics with realistic experimental parameters. This protocol can be readily implemented with the well-developed techniques in ion traps or magnetic traps and could pave the way for general applications in quantum simulations and information processing based on directly and strongly coupled tripartite systems.

Spin-Controlled Quantum Interference of Levitated Nanorotors

We describe how to prepare an electrically levitated nanodiamond in a superposition of orientations via microwave driving of a single embedded nitrogen-vacancy (NV) center. Suitably aligning the magnetic field with the NV center can serve to reach the regime of ultrastrong coupling between the NV and the diamond rotation, enabling single-spin control of the particle's three-dimensional orientation. We derive the effective spin-oscillator Hamiltonian for small amplitude rotation about the equilibrium configuration and develop a protocol to create and observe quantum superpositions of the particle orientation. We discuss the impact of decoherence and argue that our proposal can be realistically implemented with near-future technology.

Angle Locking of a Levitating Diamond Using Spin Diamagnetism

Nanodiamonds with embedded nitrogen-vacancy (NV) centers have emerged as promising magnetic field sensors, as hyperpolarizing agents in biological environments, as well as efficient tools for spin mechanics with levitating particles. These applications currently suffer from random environmental interactions with the diamond which implies poor control of the N-V direction. Here, we predict and report on a strong diamagnetism of a pure spin origin mediated by a population inversion close to a level crossing in the NV center electronic ground state. We show control of the sign of the magnetic susceptibility as well as angle locking of the crystalline axis of a microdiamond along an external magnetic field, with bright perspectives for these applications.

Levitodynamics: Levitation and control of microscopic objects in vacuum

[Figure: see text].

Spin-Mechanics with Nitrogen-Vacancy Centers and Trapped Particles

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.

Motional Dynamical Decoupling for Interferometry with Macroscopic Particles

We extend the concept of dynamical decoupling from spin to mechanical degrees of freedom of macroscopic objects, for application in interferometry. In this manner, the superposition of matter waves can be made resilient to many important sources of noise when these are driven along suitable paths in space. As a concrete implementation, we present the case of levitated (or free falling) nanodiamonds hosting a color center in a magnetic field gradient. We point out that these interferometers are inherently affected by diamagnetic forces, which restrict the separation of the superposed states to distances that scale with the inverse of the magnetic field gradient. Periodic forcing of the mechanical degree of freedom is shown to overcome this limitation, achieving a linear-in-time growth of the separation distance independent of the magnetic field gradient, while simultaneously protecting the coherence of the superposition from environmental perturbations.

Quantum Acoustomechanics with a Micromagnet

We show theoretically how to strongly couple the center-of-mass motion of a micromagnet in a harmonic potential to one of its acoustic phononic modes. The coupling is induced by a combination of an oscillating magnetic field gradient and a static homogeneous magnetic field. The former parametrically couples the center-of-mass motion to a magnonic mode while the latter tunes the magnonic mode in resonance with a given acoustic phononic mode. The magnetic fields can be adjusted to either cool the center-of-mass motion to the ground state or to enter into the strong quantum coupling regime. The center of mass can thus be used to probe and manipulate an acoustic mode, thereby opening new possibilities for out-of-equilibrium quantum mesoscopic physics. Our results hold for experimentally feasible parameters and apply to levitated micromagnets as well as micromagnets deposited on a clamped nanomechanical oscillator.

Higher order correlations in a levitated nanoparticle phonon laser

We present theoretical and experimental investigations of higher order correlations of mechanical motion in the recently demonstrated optical tweezer phonon laser, consisting of a silica nanosphere trapped in vacuum by a tightly focused optical beam [R. M. Pettit et al., Nature Photonics 13, 402 (2019)]. The nanoparticle phonon number probability distribution is modeled with the master equation formalism in order to study its evolution across the lasing threshold. Up to fourth-order equal-time correlation functions are then derived from the probability distribution. Subsequently, the master equation is transformed into a nonlinear quantum Langevin equation for the trapped particle's position. This equation yields the non-equal-time correlations, also up to fourth order. Finally, we present experimental measurements of the phononic correlation functions, which are in good agreement with our theoretical predictions. We also compare the experimental data to existing analytical Ginzburg-Landau theory where we find only a partial match.

Optomechanics with levitated particles

Optomechanics is concerned with the use of light to control mechanical objects. As a field, it has been hugely successful in the production of precise and novel sensors, the development of low-dissipation nanomechanical devices, and the manipulation of quantum signals. Micro- and nano-particles levitated in optical fields act as nanoscale oscillators, making them excellent low-dissipation optomechanical objects, with minimal thermal contact to the environment when operating in vacuum. Levitated optomechanics is seen as the most promising route for studying high-mass quantum physics, with the promise of creating macroscopically separated superposition states at masses of 10⁶ amu and above. Optical feedback, both using active monitoring or the passive interaction with an optical cavity, can be used to cool the centre-of-mass of levitated nanoparticles well below 1 mK, paving the way to operation in the quantum regime. In addition, trapped mesoscopic particles are the paradigmatic system for studying nanoscale stochastic processes, and have already demonstrated their utility in state-of-the-art force sensing.

Observation of a Quantum Phase from Classical Rotation of a Single Spin

The theory of angular momentum connects physical rotations and quantum spins together at a fundamental level. Physical rotation of a quantum system will therefore affect fundamental quantum operations, such as spin rotations in projective Hilbert space, but these effects are subtle and experimentally challenging to observe due to the fragility of quantum coherence. We report on a measurement of a single-electron-spin phase shift arising directly from physical rotation, without transduction through magnetic fields or ancillary spins. This phase shift is observed by measuring the phase difference between a microwave driving field and a rotating two-level electron spin system, and it can accumulate nonlinearly in time. We detect the nonlinear phase using spin-echo interferometry of a single nitrogen-vacancy qubit in a diamond rotating at 200 000 rpm. Our measurements demonstrate the fundamental connections between spin, physical rotation, and quantum phase, and they will be applicable in schemes where the rotational degree of freedom of a quantum system is not fixed, such as spin-based rotation sensors and trapped nanoparticles containing spins.

Nonadiabatic dynamics and geometric phase of an ultrafast rotating electron spin

The spin in a rotating frame has attracted a lot of attentions recently, as it deeply relates to both fundamental physics such as pseudo-magnetic field and geometric phase, and applications such as gyroscopic sensors. However, previous studies only focused on adiabatic limit, where the rotating frequency is much smaller than the spin frequency. Here we propose to use a levitated nano-diamond with a built-in nitrogen-vacancy (NV) center to study the dynamics and the geometric phase of a rotating electron spin without adiabatic approximation. We find that the transition between the spin levels appears when the rotating frequency is comparable to the spin frequency at zero magnetic field. Then we use Floquet theory to numerically solve the spin energy spectrum, study the spin dynamics and calculate the geometric phase under a finite magnetic field, where the rotating frequency to induce resonant transition could be greatly reduced.