Quantum displacement sensing and cooling in 3D levitated cavity optomechanics

Ultra-high sensitivity detection of quantum-scale displacements in cavity optomechanics optimises the combined errors from measurement back-action and imprecisions from incoming quantum noises. This sets the well-known Standard Quantum Limit (SQL). Normal quantum cavity optomechanics allows cooling and detection of a single degree of freedom, along the cavity axis. However, a recent breakthrough that allows quantum ground-state cooling of levitated nanoparticles [Delic et al, arxiv:1911.04406], is uniquely 3D in character, with coupling along the $x$, $y$ and $z$ axes. We investigate current experiments and show that the underlying behaviour is far from the addition of independent 1D components and that ground-state cooling and sensing analysis must consider- to date neglected- 3D hybridisation effects. We characterise the additional 3D spectral contributions and find direct and indirect hybridising pathways can destructively interfere suppressing of 3D effects at certain parameters in order to approach, and possibly surpass, the SQL. We identify a sympathetic cooling mechanism that can enhance cooling of weaker coupled modes, arising from optomechanically induced correlations.Comment: added 3D analysis of new quantum-cooled experiments in arxiv:1911.04406 including hybridisation effect

Creating atom-nanoparticle quantum superpositions

A nanoscale object evidenced in a nonclassical state of its center of mass will hugely extend the boundaries of quantum mechanics. To obtain a practical scheme for the same, we exploit a hitherto unexplored coupled system: an atom and a nanoparticle coupled by an optical field. We show how to control the center of mass of a large ∼500-nm nanoparticle using the internal state of the atom so as to create, as well as detect, nonclassical motional states of the nanoparticle. Specifically, we consider a setup based on a silica nanoparticle coupled to a cesium atom and discuss a protocol for preparing and verifying a Schrödinger-cat state of the nanoparticle that does not require cooling to the motional ground state. We show that the existence of the superposition can be revealed using the Earth's gravitational field using a method that is insensitive to the most common sources of decoherence and works for any initial state of the nanoparticle

Quantum gravitational sensor for space debris

Matter-wave interferometers have fundamental applications for gravity experiments such as testing the equivalence principle and the quantum nature of gravity. In addition, matter-wave interferometers can be used as quantum sensors to measure the local gravitational acceleration caused by external massive moving objects, thus lending itself for technological applications. In this paper, we will establish a three-dimensional model to describe the gravity gradient signal from an external moving object, and theoretically investigate the achievable sensitivities using the matter-wave interferometer based on the Stern-Gerlach setup. As an application we will consider the mesoscopic interference for metric and curvature and gravitational-wave detection scheme [R. J. Marshman, Mesoscopic interference for metric and curvature (MIMAC) & gravitational wave detection, New J. Phys. 22, 083012 (2020)NJOPFM1367-263010.1088/1367-2630/ab9f6c] and quantify its sensitivity to gravity gradients using frequency-space analysis. We will consider objects near Earth-based experiments and space debris in proximity of satellites and estimate the minimum detectable mass of the object as a function of their distance, velocity, and orientation

Gravitational optomechanics: Photon-matter entanglement via graviton exchange

The deflection of light in the gravitational field of the Sun is one of the most fundamental consequences for general relativity as well as one of its classical tests first performed by Eddington a century ago. However, despite its center stage role in modern physics, no experiment has tested it in an ostensibly quantum regime where both matter and light exhibit nonclassical features. This paper shows that the interaction which gives rise to the light-bending also induces photon-matter entanglement as long as gravity and matter are treated at par with quantum mechanics. The quantum light-bending interaction within the framework of perturbative quantum gravity highlights this point by showing that the entangled states can be generated already with coherent states of light and matter exploiting the nonlinear coupling induced by graviton exchange. Furthermore, the quantum light-bending interaction is capable of discerning between the spin-2 and spin-0 gravitons thus also providing a test for alternative theories of gravity at short distances and at the quantum level. We will conclude by estimating the order of magnitude of the entanglement generated by employing the linear entropy. In particular, we find that a half-ring cavity of radius 0.25 m placed around a 10 kg mechanical oscillator operating at 150 Hz, could be used to generate linear entropy of order unity using a petawatt laser source at optical wavelengths. While the proposed scheme is beyond the current experimental realities it nonetheless initiates the discussion about testing the spin of the gravitational interaction at the quantum level

An ultra-narrow line width levitated nano-oscillator for testing dissipative wavefunction collapse

Levitated nano-oscillators are seen as promising platforms for testing fundamental physics and testing quantum mechanics in a new high mass regime. Levitation allows extreme isolation from the environment, reducing the decoherence processes that are crucial for these sensitive experiments. A fundamental property of any oscillator is its line width and mechanical quality factor, Q. Narrow line widths in the microHertz regime and mechanical Q's as high as $10^{12}$ have been predicted for levitated systems, but to date, the poor stability of these oscillators over long periods have prevented direct measurement in high vacuum. Here we report on the measurement of an ultra-narrow line width levitated nano-oscillator, whose line width of $81\pm\,23\,\mu$Hz is only limited by residual gas pressure at high vacuum. This narrow line width allows us to put new experimental bounds on dissipative models of wavefunction collapse including continuous spontaneous localisation and Di\'{o}si-Penrose and illustrates its utility for future precision experiments that aim to test the macroscopic limits of quantum mechanics

Testing Dissipative Collapse Models with a Levitated Micromagnet

We present experimental tests of dissipative extensions of spontaneous wave function collapse models based on a levitated micromagnet with ultralow dissipation. The spherical micromagnet, with radius $R=27$ $\mu$m, is levitated by Meissner effect in a lead trap at $4.2$ K and its motion is detected by a SQUID. We perform accurate ringdown measurements on the vertical translational mode with frequency $57$ Hz, and infer the residual damping at vanishing pressure $\gamma/2\pi<9$ $\mu$Hz. From this upper limit we derive improved bounds on the dissipative versions of the CSL (continuous spontaneous localization) and the DP (Di\'{o}si-Penrose) models with proper choices of the reference mass. In particular, dissipative models give rise to an intrinsic damping of an isolated system with the effect parameterized by a temperature constant; the dissipative CSL model with temperatures below 1 nK is ruled out, while the dissipative DP model is excluded for temperatures below $10^{-13}$ K. Furthermore, we present the first bounds on dissipative effects in a more recent model, which relates the wave function collapse to fluctuations of a generalized complex-valued spacetime metric.Comment: 10 pages, 7 figure

Relative Acceleration Noise Mitigation for Nanocrystal Matter-wave Interferometry: Application to Entangling Masses via Quantum Gravity

Matter wave interferometers with large momentum transfers, irrespective of specific implementations, will face a universal dephasing due to relative accelerations between the interferometric mass and the associated apparatus. Here we propose a solution that works even without actively tracking the relative accelerations: putting both the interfering mass and its associated apparatus in a freely falling capsule, so that the strongest inertial noise components vanish due to the equivalence principle. In this setting, we investigate two of the most important remaining noise sources: (a) the non-inertial jitter of the experimental setup and (b) the gravity-gradient noise. We show that the former can be reduced below desired values by appropriate pressures and temperatures, while the latter can be fully mitigated in a controlled environment. We finally apply the analysis to a recent proposal for testing the quantum nature of gravity [S. Bose et. al. Phys. Rev. Lett 119, 240401 (2017)] through the entanglement of two masses undergoing interferometry. We show that the relevant entanglement witnessing is feasible with achievable levels of relative acceleration noise

Dynamical model selection for quantum optomechanical systems

This paper considers the problem of distinguishing between different dynamical models using continuous weak measurements; that is, whether the evolution is quantum mechanical or given by a classical stochastic differential equation. We examine the conditions that optimize quantum hypothesis testing, maximizing one's ability to discriminate between classical and quantum models. We set upper limits on the temperature and lower limits on the measurement efficiencies required to explore these differences, using experiments in levitated optomechanical systems as an example

Mechanical rotation modifies the manifestation of photon entanglement

Mechanical rotation plays a central role in fundamental physics theories and has profound connections with the theory of general relativity. However, very few experiments have so far aimed to explore the interplay of mechanical rotation with entangled photon states. By adding Sagnac interferometers into the arms of a Hong-Ou-Mandel (HOM) interferometer that is placed on a mechanically rotating platform, we experimentally observe the modification of the symmetry of an entangled biphoton state due to noninertial motion. As the platform rotation speed is increased, we observe that HOM interference dips transform into HOM interference peaks. This indicates that the photons pass from perfectly indistinguishable (bosonic behavior), to perfectly distinguishable (fermionic behavior). This demonstration is of relevance to global satellite quantum communications and paves the way for further fundamental research that can test the influence of curved space on quantum entanglement