Cavity cooling of a levitated nanosphere by coherent scattering

We report three-dimensional cooling of a levitated nanoparticle inside an optical cavity. The cooling mechanism is provided by cavity-enhanced coherent scattering off an optical tweezer. The observed 3D dynamics and cooling rates are as theoretically expected from the presence of both linear and quadratic terms in the interaction between the particle motion and the cavity field. By achieving nanometer-level control over the particle location we optimize the position-dependent coupling and demonstrate axial cooling by two orders of magnitude at background pressures as high as $6\times10^{-2}$ mbar. We also estimate a significant ($> 40$ dB) suppression of laser phase noise, and hence of residual heating, which is a specific feature of the coherent scattering scheme. The observed performance implies that quantum ground state cavity cooling of levitated nanoparticles can be achieved for background pressures below $10^{-7}$ mbar

Fluctuation-induced Forces on Nanospheres in External Fields

We analyze the radiative forces between two dielectric nanospheres mediated via the quantum and thermal fluctuations of the electromagnetic field in the presence of an external drive. We generalize the scattering theory description of fluctuation forces to include external quantum fields, allowing them to be in an arbitrary quantum state. The known trapping and optical binding potentials are recovered for an external coherent state. We demonstrate that an external squeezed vacuum state creates similar potentials to a laser, despite its zero average intensity. Moreover, Schr\"odinger cat states of the field can enhance or suppress the optical potential depending on whether they are odd or even. Considering the nanospheres trapped by optical tweezers, we examine the total interparticle potential as a function of various experimentally relevant parameters, such as the field intensity, polarization, and phase of the trapping lasers. We demonstrate that an appropriate set of parameters could produce mutual bound states of the two nanospheres with potential depth as large as $\sim200$ K. Our results are pertinent to ongoing experiments with trapped nanospheres in the macroscopic quantum regime, paving the way for engineering interactions among macroscopic quantum systems

Force-Gradient Sensing and Entanglement via Feedback Cooling of Interacting Nanoparticles

We show theoretically that feedback-cooling of two levitated, interacting nanoparticles enables differential sensing of forces and the observation of stationary entanglement. The feedback drives the two particles into a stationary, non-thermal state which is susceptible to inhomogeneous force fields and which exhibits entanglement for sufficiently strong inter-particle couplings. We predict that force-gradient sensing at the zepto-Newton per micron range is feasible and that entanglement due to the Coulomb interaction between charged particles can be realistically observed in state-of-the-art setups.Comment: 14 pages, 4 figure

Exponentially Enhanced non-Hermitian Cooling

Certain non-Hermitian systems exhibit the skin effect, whereby the wavefunctions become exponentially localized at one edge of the system. Such exponential amplification of wavefunction has received significant attention due to its potential applications in e.g., classical and quantum sensing. However, the opposite edge of the system, featured by the exponentially suppressed wavefunctions, remains largely unexplored. Leveraging this phenomenon, we introduce a non-Hermitian cooling mechanism, which is fundamentally distinct from traditional refrigeration or laser cooling techniques. Notably, non-Hermiticity will not amplify thermal excitations, but rather redistribute them. Hence, thermal excitations can be cooled down at one edge of the system, and the cooling effect can be exponentially enhanced by the number of auxiliary modes, albeit with a lower bound that depends on the dissipative interaction with the environment. Non-Hermitian cooling does not rely on intricate properties such as exceptional points or non-trivial topology, and it can apply to a wide range of Bosonic modes such as photons, phonons, magnons, etc.Comment: 12 pages, 4 figure

Non-Hermitian dynamics and nonreciprocity of optically coupled nanoparticles

Non-Hermitian dynamics, as observed in photonic, atomic, electrical, and optomechanical platforms, holds great potential for sensing applications and signal processing. Recently, fully tunable nonreciprocal optical interaction has been demonstrated between levitated nanoparticles. Here, we use this tunability to investigate the collective non-Hermitian dynamics of two nonreciprocally and nonlinearly interacting nanoparticles. We observe parity-time symmetry breaking and, for sufficiently strong coupling, a collective mechanical lasing transition, where the particles move along stable limit cycles. This work opens up a research avenue of nonequilibrium multi-particle collective effects, tailored by the dynamic control of individual sites in a tweezer array

Cavity cooling of an optically levitated submicron particle

The coupling of a levitated submicron particle and an optical cavity field promises access to a unique parameter regime both for macroscopic quantum experiments and for high-precision force sensing. We report a demonstration of such controlled interactions by cavity cooling the center-of-mass motion of an optically trapped submicron particle. This paves the way for a light–matter interface that can enable room-temperature quantum experiments with mesoscopic mechanical systems

Research campaign : macroscopic quantum resonators (MAQRO)

The objective of the proposed macroscopic quantum resonators (MAQRO) mission is to harness space for achieving long free-fall times, extreme vacuum, nano-gravity, and cryogenic temperatures to test the foundations of physics in macroscopic quantum experiments at the interface with gravity. Developing the necessary technologies, achieving the required sensitivities and providing the necessary isolation of macroscopic quantum systems from their environment will lay the path for developing novel quantum sensors. Earlier studies showed that the proposal is feasible but that several critical challenges remain, and key technologies need to be developed. Recent scientific and technological developments since the original proposal of MAQRO promise the potential for achieving additional science objectives. The proposed research campaign aims to advance the state of the art and to perform the first macroscopic quantum experiments in space. Experiments on the ground, in micro-gravity, and in space will drive the proposed research campaign during the current decade to enable the implementation of MAQRO within the subsequent decade