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arXiv:2407.01215 · Physical Review Research

Decoherence of dielectric particles by thermal emission

Jonas Schäfer, Benjamin A. Stickler, Klaus Hornberger

Published Dec 23, 2024• 6 citations
arXivHTMLPDF

Abstract

Levitated nanoparticles are a promising platform for sensing applications and for macroscopic quantum experiments. While the nanoparticles' motional temperatures can be reduced to near absolute zero, their uncontrolled internal degrees of freedom remain much hotter, inevitably leading to the emission of heat radiation. The decoherence and motional heating caused by this thermal emission process is still poorly understood beyond the case of the center-of-mass motion of point particles. Here, we present the master equation describing the impact of heat radiation on the motional quantum state of arbitrarily sized and shaped dielectric rigid rotors. It predicts the localization of spatio-orientational superpositions only based on the bulk material properties and the particle geometry. A counterintuitive and experimentally relevant implication of the presented theory is that orientational superpositions of optically isotropic bodies are not protected by their symmetry, even in the small-particle limit.

DOI
10.1103/physrevresearch.6.043307

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Levitated nanoparticles are a promising platform for sensing applications and for macroscopic quantum experiments. While the nanoparticles' motional temperatures can be reduced to near absolute zero, their uncontrolled internal degrees of freedom remain much hotter, inevitably leading to the emission of heat radiation. The decoherence and motional heating caused by this thermal emission process is still poorly understood beyond the case of the center-of-mass motion of point particles. Here, we present the master equation describing the impact of heat radiation on the motional quantum state of arbitrarily sized and shaped dielectric rigid rotors. It predicts the localization of spatio-orientational superpositions only based on the bulk material properties and the particle geometry. A counterintuitive and experimentally relevant implication of the presented theory is that orientational superpositions of optically isotropic bodies are not protected by their symmetry, even in the small-particle limit.
Optically levitated nanoparticles are ideal experimental testbeds for investigating macroscopic superpositions and microscopic thermodynamics. Integrating such levitated nanoparticles with photonic structures can enable strong coupling between their center-of-mass motion and guided photonic modes, facilitating enhanced control and probing of their motion. When coupling a particle to a photonic structure, such as a waveguide, the effects of fluctuations become prominent at nanoscales. In this work, we analyze the classical and quantized center-of-mass motion of a polarizable particle interacting with the fluctuations of the electromagnetic field in the presence of a medium. We derive a position localization master equation for the particle's quantized center of mass, and examine its classical center-of-mass momentum diffusion, elucidating correspondences between classical and quantum Brownian motion of polarizable particles near media. We study the decoherence rate of the particle in the presence of a planar surface as a function of temperature and distance from the surface, comparing it to common sources of decoherence. Our results are pertinent to experiments aimed at preparing levitated nanospheres in macroscopic quantum states and investigating their Brownian dynamics.
Abstract Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence [1-4]. Quantum control of mechanical motion has been achieved by engineering the radiation pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator [5-8]. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states [9]. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects [10,11], since their trapping potential is fully controllable. In this work, we optically levitate a femto-gram dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its center-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 43%. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales [12,13].
The interaction of an object with its surrounding bath can lead to a coupling between the object's internal degrees of freedom and its center-of-mass motion. This coupling is especially important for nanomechanical oscillators, which are among the most promising systems for preparing macroscopic objects in quantum mechanical states. Here we exploit this coupling to derive the internal temperature of a levitated nanoparticle from measurements of its center-of-mass dynamics. For a laser-trapped silica particle in high vacuum, we find an internal temperature of 1000(60)K1000(60)\phantom{\rule{0.16em}{0ex}}\mathrm{K}1000(60)K. The measurement and control of the internal temperature of nanomechanical oscillators is of fundamental importance because black-body emission sets limits to the coherence of macroscopic quantum states.
We develop the theory describing the quantum coupled dynamics of the center-of-mass motion of a nanoparticle and an ensemble of ions co-trapped in a dual-frequency linear Paul trap. We first derive analytical expressions for the motional frequencies and classical trajectories of both nanoparticle and ions. We then derive a quantum master equation for the ion-nanoparticle system and quantify the sympathetic cooling of the nanoparticle motion enabled by its Coulomb coupling to a continuously Doppler-cooled ion. We predict that motional cooling down to sub-kelvin temperatures is achievable in state-of-the-art experiments even in the absence of motional feedback and in the presence of micromotion. We then extend our analysis to an ensemble of NNN ions, predicting a linear increase of the cooling rate as a function of NNN and motional cooling of the nanoparticle down to tenths of millikelvin in current experimental platforms. Our work establishes the theoretical toolbox needed to explore the ion-assisted preparation of non-Gaussian motional states of levitated nanoparticles.
Abstract Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence1–3. Quantum control of mechanical motion has been achieved by engineering the radiation–pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator4–7. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states8. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects9, 10, since their trapping potential is fully controllable. Here we optically levitate a femtogram (10−15 grams) dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its centre-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 0.43. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales11.
We show how to describe the diffusion of the quantized angular momentum vector of an arbitrarily shaped rigid rotor as induced by its collisional interaction with an environment.We present the general form of the Lindblad-type master equation and relate it to the orientational decoherence of an asymmetric nanoparticle in the limit of small anisotropies.The corresponding diffusion coefficients are derived for gas particles scattering off large molecules and for ambient photons scattering off dielectric particles, using the elastic scattering amplitudes.