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 4150 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.

Levitated optomechanics, a new experimental physics platform, holds promise for fundamental science and quantum technological sensing applications. We demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force. We demonstrate rapid parametric feedback cooling of all three motional degrees of freedom from room temperature to a few mK. A single laser at 1550nm, and a single photodiode, are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26nm to 160nm are trapped without feedback to 10 −5 mbar and with feedback-engaged the pressure is reduced to 10 −6 mbar. Modifications to the harmonic motion in the presence of noise and feedback are studied, and an experimental mechanical quality factor in excess of 4×10 7 is evaluated. This particle manipulation is key to build a nanoparticle matter-wave interferometer in order to test the quantum superposition principle in the macroscopic domain.

We propose an interferometric scheme based on an untrapped nano-object subjected to gravity. The motion of the center of mass (c.m.) of the free object is coupled to its internal spin system magnetically, and a free flight scheme is developed based on coherent spin control. The wave packet of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during our scheme. We find a remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling), and also a dynamical decoupling nature of the scheme itself. Together they secure a high visibility of the resulting Ramsey fringes. The mass independence of our scheme makes it viable for a nano-object selected from an ensemble with a high mass variability. Given these advantages, a quantum superposition with a 100 nm spatial separation for a massive object of 10^{9}  amu is achievable experimentally, providing a route to test postulated modifications of quantum theory such as continuous spontaneous localization.

run), and the combination of low pressure ( < ∼ 10 −13 Pa) and low temperature ( < ∼ 20 K) while having full optical access. These conditions cannot be fulfilled with ground-based experiments. E. Technological heritage for MAQROMAQRO benefits from recent developments in space technology. In particular, MAQRO relies on technological heritage from LISA Pathfinder (LPF) [18], the LISA technology package (LTP) [19], GAIA[20], GOCE[21,22], Microscope [23,24] and the James Webb Space Telescope (JWST) [25]. The spacecraft, launcher, ground segment and orbit (L1/L2) are identical to LPF.The most apparent modifications to the LPF design are an external, passively cooled optical instrument thermally shielded from the spacecraft, and the use of two capacitive inertial sensors from ONERA technology. In addition, the propulsion system will be mounted differently to achieve the required low vacuum level at the external subsystem, and to achieve low thruster noise in one spatial direction. The additional optical instruments and the external platform will reach TRL 5 at the start of the BCD phases. For all other elements, the TRL is 6-9 because of the technological heritage from LPF and other missions.

We experimentally squeeze the thermal motional state of an optically levitated nanosphere, by fast switching between two trapping frequencies. The measured phase space distribution of the center-of-mass of our particle shows the typical shape of a squeezed thermal state, from which we infer up to 2.7 dB of squeezing along one motional direction. In these experiments the average thermal occupancy is high and even after squeezing the motional state remains in the remit of classical statistical mechanics. Nevertheless, we argue that the manipulation scheme described here could be used to achieve squeezing in the quantum regime, if preceded by cooling of the levitated mechanical oscillator. Additionally, a higher degree of squeezing could in principle be achieved by repeating the frequency-switching protocol multiple times.While squeezing a quantum state of light [1] has a long history of experiments, the squeezing of a massive mechanical harmonic oscillator has so far not seen many experimental realisations. The first demonstration of squeezing in a classical mechanical oscillator was by Rugar et.al [2]. Squeezing of classical motional states in electromechanical devices by parametric amplification and weak measurements has been subsequently proposed [3], and experimentally demonstrated in an optomechanical system [4]. Schemes relying on sinusoidal modulation of the spring constant have also been proposed and discussed by numerous authors [5][6][7][8]. In optomechanical cavities Genoni et al. suggested that squeezing below the ground-state fluctuations (quantum squeezing for brevity) may be attainable via continuous measurements and feedback [9]. Quantum squeezing of a high-frequency mechanical oscillator has only been experimentally demonstrated very recently, in a microwave optomechanical device [10,11]. Also only very recently a hybrid photonic-phononic waveguide device has shown the correlation properties of optomechanical two-mode squeezing [12]. Another interesting method of generating squeezing, of relevance to this Letter, relies on non-adiabatic shifts of the mechanical frequency. Such method was initially discussed in relation to light fields [13,14]. Similar ideas, utilising impulse kicks on a mechanical oscillator, have been discussed [15,16]. In this Letter we report the first experimental demonstration of mechanical squeezing via non-adiabatic frequency shifts, thus realising a useful tool to manipulate the state of a levitated optomechanical system.Theory-In what follows we shall present a quantum mechanical treatment of our squeezing protocol, in anticipation of future experiments that may achieve quantum squeezing. Due to linearity of the Heisenberg equations of our system, it should be pointed out that formally identical results may be obtained through classical statistical mechanics [17]. We consider a nanosphere of mass m trapped in a harmonic potential. Along the z axis, we can manipulate the system by switching between two HamiltoniansĤ 1 ,Ĥ 2 , whereĤ j =p 2 2m + 1 2 mω 2 jẑ 2 ,ẑ,p denote the...