Erratum: Gas-induced friction and diffusion of rigid rotors [Phys. Rev. E 97, 052112 (2018)].

This corrects the article DOI: 10.1103/PhysRevE.97.052112.

Macroscopic Quantum Test with Bulk Acoustic Wave Resonators.

Recently, solid-state mechanical resonators have become a platform for demonstrating nonclassical behavior of systems involving a truly macroscopic number of particles. Here, we perform the most macroscopic quantum test in a mechanical resonator to date, which probes the validity of quantum mechanics by ruling out a classical description at the microgram mass scale. This is done by a direct measurement of the Wigner function of a high-overtone bulk acoustic wave resonator mode, monitoring the gradual decay of negativities over tens of microseconds. While the obtained macroscopicity of µ=11.3 is on par with state-of-the-art atom interferometers, future improvements of mode geometry and coherence times could test the quantum superposition principle at unprecedented scales and also place more stringent bounds on spontaneous collapse models.

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, nonthermal state which is susceptible to inhomogeneous force fields and which exhibits entanglement for sufficiently strong interparticle 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.

Tunable light-induced dipole-dipole interaction between optically levitated nanoparticles.

Arrays of optically trapped nanoparticles have emerged as a platform for the study of complex nonequilibrium phenomena. Analogous to atomic many-body systems, one of the crucial ingredients is the ability to precisely control the interactions between particles. However, the optical interactions studied thus far only provide conservative optical binding forces of limited tunability. In this work, we exploit the phase coherence between the optical fields that drive the light-induced dipole-dipole interaction to couple two nanoparticles. In addition, we effectively switch off the optical interaction and observe electrostatic coupling between charged particles. Our results provide a route to developing fully programmable many-body systems of interacting nanoparticles with tunable nonreciprocal interactions, which are instrumental for exploring entanglement and topological phases in arrays of levitated nanoparticles.

Cooling Nanorotors by Elliptic Coherent Scattering.

Simultaneously cooling the rotational and translational motion of nanoscale dielectrics into the quantum regime is an open task of great importance for sensing applications and quantum superposition tests. Here, we show that the six-dimensional ground state can be reached by coherent-scattering cooling with an elliptically polarized and shaped optical tweezer. We determine the cooling rates and steady-state occupations in a realistic setup and discuss applications for mechanical sensing and fundamental experiments.

Bragg Diffraction of Large Organic Molecules.

We demonstrate Bragg diffraction of the antibiotic ciprofloxacin and the dye molecule phthalocyanine at a thick optical grating. The observed patterns show a single dominant diffraction order with the expected dependence on the incidence angle as well as oscillating population transfer between the undiffracted and diffracted beams. We achieve an equal-amplitude splitting of 14ℏk (photon momenta) and maximum momentum transfer of 18ℏk. This paves the way for efficient, large-momentum beam splitters and mirrors for hot and complex molecules.

Conformer Selection by Matter-Wave Interference.

We establish that matter-wave diffraction at near-resonant ultraviolet optical gratings can be used to spatially separate individual conformers of complex molecules. Our calculations show that the conformational purity of the prepared beam can be close to 100% and that all molecules remain in their electronic ground state. The proposed technique is independent of the dipole moment and the spin of the molecule and thus paves the way for structure-sensitive experiments with hydrocarbons and biomolecules, such as neurotransmitters and hormones, which have evaded conformer-pure isolation so far.

Rotational Friction and Diffusion of Quantum Rotors.

We present the Markovian quantum master equation describing rotational decoherence, friction, diffusion, and thermalization of planar, linear, and asymmetric rotors in contact with a thermal environment. It describes how an arbitrary initial rotation state decoheres and evolves toward a Gibbs-like thermal ensemble, as we illustrate numerically for the linear and the planar top, and it yields the expected rotational Fokker-Planck equation of Brownian motion in the semiclassical limit.

Gas-induced friction and diffusion of rigid rotors.

We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift forces and torques. We provide the rotranslational friction and diffusion tensors for specular and diffuse reflection off particles with spherical, cylindrical, and cuboidal shape, and show that the theory describes thermalization, photophoresis, and the inverse Magnus effect in the free molecular regime.

Rotational Alignment Decay and Decoherence of Molecular Superrotors.

We present the quantum master equation describing the coherent and incoherent dynamics of a rapidly rotating molecule in the presence of a thermal background gas. The master equation relates the rate of rotational alignment decay and decoherence to the microscopic scattering amplitudes, which we calculate for anisotropic van der Waals scattering. For large rotational energies, we find quantitative agreement of the resulting alignment decay rate with recent superrotor experiments.

Optically driven ultra-stable nanomechanical rotor.

Nanomechanical devices have attracted the interest of a growing interdisciplinary research community, since they can be used as highly sensitive transducers for various physical quantities. Exquisite control over these systems facilitates experiments on the foundations of physics. Here, we demonstrate that an optically trapped silicon nanorod, set into rotation at MHz frequencies, can be locked to an external clock, transducing the properties of the time standard to the rod's motion with a remarkable frequency stability f r/Δf r of 7.7 × 1011. While the dynamics of this periodically driven rotor generally can be chaotic, we derive and verify that stable limit cycles exist over a surprisingly wide parameter range. This robustness should enable, in principle, measurements of external torques with sensitivities better than 0.25 zNm, even at room temperature. We show that in a dilute gas, real-time phase measurements on the locked nanorod transduce pressure values with a sensitivity of 0.3%.

New avenues for matter-wave-enhanced spectroscopy.

We present matter-wave interferometry as a tool to advance spectroscopy for a wide class of nanoparticles, clusters and molecules. The high sensitivity of de Broglie interference fringes to external perturbations enables measurements in the limit of an individual particle absorbing only a single photon on average, or even no photon at all. The method allows one to extract structural and electronic information from the loss of the interference contrast. It is minimally invasive and works even for dilute ensembles.

Cavity-Assisted Manipulation of Freely Rotating Silicon Nanorods in High Vacuum.

Optical control of nanoscale objects has recently developed into a thriving field of research with far-reaching promises for precision measurements, fundamental quantum physics and studies on single-particle thermodynamics. Here, we demonstrate the optical manipulation of silicon nanorods in high vacuum. Initially, we sculpture these particles into a silicon substrate with a tailored geometry to facilitate their launch into high vacuum by laser-induced mechanical cleavage. We manipulate and trace their center-of-mass and rotational motion through the interaction with an intense intracavity field. Our experiments show that the anisotropy of the nanorotors leads to optical forces that are three times stronger than on silicon nanospheres of the same mass. The optical torque experienced by the spinning rods will enable cooling of the rotational motion and torsional optomechanics in a dissipation-free environment.

Near-field interferometry of a free-falling nanoparticle from a point-like source.

Matter-wave interferometry performed with massive objects elucidates their wave nature and thus tests the quantum superposition principle at large scales. Whereas standard quantum theory places no limit on particle size, alternative, yet untested theories--conceived to explain the apparent quantum to classical transition--forbid macroscopic superpositions. Here we propose an interferometer with a levitated, optically cooled and then free-falling silicon nanoparticle in the mass range of one million atomic mass units, delocalized over >150 nm. The scheme employs the near-field Talbot effect with a single standing-wave laser pulse as a phase grating. Our analysis, which accounts for all relevant sources of decoherence, indicates that this is a viable route towards macroscopic high-mass superpositions using available technology.

Incoherent control of the retinal isomerization in rhodopsin.

We propose to control the retinal photoisomerization yield through the backaction dynamics imparted by a nonselective optical measurement of the molecular electronic state. This incoherent effect is easier to implement than comparable coherent pulse shaping techniques, and is also robust to environmental noise. A numerical simulation of the quantum dynamics shows that the isomerization yield of this important biomolecule can be substantially increased above the natural limit.

Optomechanical sensing of spontaneous wave-function collapse.

Quantum experiments with nanomechanical oscillators are regarded as a test bed for hypothetical modifications of the Schrödinger equation, which predict a breakdown of the superposition principle and induce classical behavior at the macroscale. It is generally believed that the sensitivity to these unconventional effects grows with the mass of the mechanical quantum system. Here we show that the opposite is the case for optomechanical systems in the presence of generic noise sources, such as thermal and measurement noise. We determine conditions for distinguishing these decoherence processes from possible collapse-induced decoherence in continuous optomechanical force measurements.

Macroscopicity of mechanical quantum superposition states.

We propose an experimentally accessible, objective measure for the macroscopicity of superposition states in mechanical quantum systems. Based on the observable consequences of a minimal, macrorealist extension of quantum mechanics, it allows one to quantify the degree of macroscopicity achieved in different experiments.

Adaptive resummation of Markovian quantum dynamics.

We introduce a method for obtaining analytic approximations to the evolution of Markovian open quantum systems. It is based on resumming a generalized Dyson series in a way that ensures optimal convergence even in the absence of a small parameter. The power of this approach is demonstrated by two benchmark examples: the spatial detection of a free particle and the Landau-Zener problem in the presence of dephasing. The derived approximations are asymptotically exact and exhibit errors on the per mill level over the entire parameter range.

Effect of molecular rotation on enantioseparation.

Recently, several laser schemes have been proposed to separate racemic mixtures of enantiomers by splitting a molecular beam into subbeams consisting of molecules of definite chirality [Y. Li, C. Bruder, and C. P. Sun, Phys. Rev. Lett. 99, 130403 (2007); X. Li and M. Shapiro, J. Chem. Phys. 132, 194315 (2010)]. These ideas rely on laser-induced effective gauge potentials in an adiabatic basis which lead to a chirality dependent force on the center-of-mass. However, the effect of molecular rotation has been neglected in these studies. Accounting for the full molecular quantum state we find that the potentials from the adiabatic dressed state approach cannot be recovered once the molecular orientation dynamics is included, even in the rotational ground state. This affects substantially the ability to perform enantioseparation in the above mentioned setups.

Detecting entanglement in spatial interference.

We discuss an experimentally amenable class of two-particle states of motion giving rise to nonlocal spatial interference under position measurements. Using the concept of modular variables, we derive a separability criterion which is violated by these non-Gaussian states. While we focus on the free motion of material particles, the presented results are valid for any pair of canonically conjugate continuous variable observables and should apply to a variety of bipartite interference phenomena.