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Quantum mechanics predicts that massive particles exhibit wave-like behavior. Matterwave interferometry has been able to validate such predictions through ground-breaking experiments involving microscopic systems like atoms and molecules. The wavefunction of such systems coherently extends over a distance much larger than their size, an achievement that is incredibly challenging for massive and more complex objects. Yet, reaching similar level of coherent diffusion will enable tests of fundamental physics at the genuinely macroscopic scale, as well as the development of quantum sensing apparata of great sensitivity. We report on experimentally achieving an unprecedented degree of position diffusion in a massive levitated optomechanical system through frequency modulation of the trapping potential. By starting with a pre-cooled state of motion and employing a train of sudden pulses yet of mild modulation depth, we surpass previously attained values of position diffusion in this class of systems to reach diffusion lengths that exceed the physical dimensions of the trapped nanoparticle., Comment: 5 pages, 3 figures, RevTeX4-2

In 1971, Zel'dovich predicted the amplification of electromagnetic (EM) waves scattered by a rotating metallic cylinder, gaining mechanical rotational energy from the body. Since then, this phenomenon has been believed to be unobservable with electromagnetic fields due to technological difficulties in meeting the condition of amplification, that is, the cylinder must rotate faster than the frequency of the incoming radiation. Here, we show that this key piece of fundamental physics has been hiding in plain sight for the past 60 years in the physics of induction generators. We measure the amplification of an electromagnetic field, generated by a toroid LC-circuit, scattered by an aluminium cylinder spinning in the toroid gap. We show that when the Zel'dovich condition is met, the resistance induced by the cylinder becomes negative implying amplification of the incoming EM waves. These results reveal the connection between the concept of induction generators and the physics of this fundamental effect that was believed to be unobservable, and hence open new prospects towards testing the Zel'dovich mechanism in the quantum regime, as well as related quantum friction effects., Comment: 5 pages and 3 figure plus supplementary file

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 figures

Despite the unquestionable empirical success of quantum theory, witnessed by the recent uprising of quantum technologies, the debate on how to reconcile the theory with the macroscopic classical world is still open. Spontaneous collapse models are one of the few testable solutions so far proposed. In particular, the continuous spontaneous localization (CSL) model has become subject of an intense experimental research. Experiments looking for the universal force noise predicted by CSL in ultrasensitive mechanical resonators have recently set the strongest unambiguous bounds on CSL; further improving these experiments by direct reduction of mechanical noise is technically challenging. Here, we implement a recently proposed alternative strategy, that aims at enhancing the CSL noise by exploiting a multilayer test mass attached on a high quality factor microcantilever. The test mass is specifically designed to enhance the effect of CSL noise at the characteristic length $r_c=10^{-7}$ m. The measurements are in good agreement with pure thermal motion for temperatures down to 100 mK. From the absence of excess noise we infer a new bound on the collapse rate at the characteristic length $r_c=10^{-7}$ m, which improves over previous mechanical experiments by more than one order of magnitude. Our results are explicitly challenging a well-motivated region of the CSL parameter space proposed by Adler., Comment: 9 pages, 7 figures

Levitated nanoparticles and microparticles are excellent candidates for the realization of extremely isolated mechanical systems, with a huge potential impact in sensing applications and in quantum physics. Magnetic levitation based on static fields is a particularly interesting approach, due to the unique property of being completely passive and compatible with low temperatures. Here, we show experimentally that micromagnets levitated above type-I superconductors feature very low damping at low frequency and low temperature. In our experiment, we detect 5 out of 6 rigid-body mechanical modes of a levitated ferromagnetic microsphere, using a dc SQUID (Superconducting Quantum Interference Device) with a single pick-up coil. The measured frequencies are in agreement with a finite element simulation based on ideal Meissner effect. For two specific modes we find further substantial agreement with analytical predictions based on the image method. We measure damping times $\tau$ exceeding $10^4$ s and quality factors $Q$ beyond $10^7$, improving by $2-3$ orders of magnitude over previous experiments based on the same principle. We investigate the possible residual loss mechanisms besides gas collisions, and argue that much longer damping time can be achieved with further effort and optimization. Our results open the way towards the development of ultrasensitive magnetomechanical sensors with potential applications to magnetometry and gravimetry, as well as to fundamental and quantum physics., Comment: 13 pages, 8 figures

We consider a nanoparticle levitated in a Paul trap in ultrahigh cryogenic vacuum, and look for the conditions which allow for a stringent noninterferometric test of spontaneous collapse models. In particular we compare different possible techniques to detect the particle motion. Key conditions which need to be achieved are extremely low residual pressure and the ability to detect the particle at ultralow power. We compare three different detection approaches based respectively on a optical cavity, optical tweezer and a electrical readout, and for each one we assess advantages, drawbacks and technical challenges.

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 wavepacket 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 delocalised 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 $100$ 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 localisation., Comment: 7 pages, 3 figures

What gravitational field is generated by a massive quantum system in a spatial superposition? This is one of the most important questions in modern physics, and after decades of intensive theoretical and experimental research, we still do not know the answer. On the experimental side, the difficulty lies in the fact that gravity is weak and requires large masses to be detectable. But for large masses, it becomes increasingly difficult to generate spatial quantum superpositions, which live sufficiently long to be detected. A delicate balance between opposite quantum and gravitational demands is needed. Here we show that this can be achieved in an optomechanics scenario. We propose an experimental setup, which allows to decide whether the gravitational field generated by a quantum system in a spatial superposition is the superposition of the two alternatives, or not. We estimate the magnitude of the effect and show that it offers good perspectives for observability. Performing the experiment will mark a breakthrough in our understanding of the relationship between gravity and quantum theory., Comment: 5 pages; 4 figures; RevTeX4

The test of modifications to quantum mechanics aimed at identifying the fundamental reasons behind the un-observability of quantum mechanical superpositions at the macro-scale is a crucial goal of modern quantum mechanics. Within the context of collapse models, current proposals based on interferometric techniques for their falsification are far from the experimental state-of-the-art. Here we discuss an alternative approach to the testing of quantum collapse models that, by bypassing the need for the preparation of quantum superposition states might help us addressing non-linear stochastic mechanisms such as the one at the basis of the continuous spontaneous localisation model., Comment: 6 pages, accepted for publication in Phys. Rev. Lett.!

We present a proof-of-principle study of superconducting single photon detectors (SSPD) for the detection of individual neutral molecules/nanoparticles at low energies. The new detector is applied to characterize a laser desorption source for biomolecules and it allows to retrieve the arrival time distribution of a pulsed molecular beam containing the amino acid tryptophan, the polypeptide gramicidin as well as insulin, myoglobin and hemoglobin. We discuss the experimental evidence that the detector is actually sensitive to isolated neutral particles., Comment: 6 pages, 6 figures

The generation of organic particle beams is studied in combination with photoionization using uv radiation at 266 nm and vuv light at 157 nm. Single-photon ionization with pulsed vuv light turns out to be sensitive enough to detect various large neutral biomolecular complexes ranging from metal-amino acid complexes to nucleotide clusters and aggregates of polypeptides. Different biomolecular clusters are shown to exhibit rather specific binding characteristics with regard to the various metals that are co-desorbed in the source. We also find that the ion signal of gramicidin can be increased by a factor of fifteen when the photon energy is increased from 4.66 eV to 7.9 eV., Comment: 6 pages, 8 figures

The basic strategy underlying models of spontaneous wave function collapse (collapse models) is to modify the Schroedinger equation by including nonlinear stochastic terms, which tend to localize wave functions in space in a dynamical manner. These terms have negligible effects on microscopic systems-therefore their quantum behaviour is practically preserved. On the other end, since the strength of these new terms scales with the mass of the system, they become dominant at the macroscopic level, making sure that wave functions of macro-objects are always well-localized in space. We will review these basic features. By changing the dynamics of quantum systems, collapse models make predictions, which are different from standard quantum mechanical predictions. Although they are difficult to detect, we discuss the most relevant scenarios, where such deviations can be observed, Comment: 10 Pages. Invited Talk at the Heinz von Foerster Centenary International Conference on Self-Organization and Emergence: Emergent Quantum Mechanics (EmerQuM11). Nov. 10-13, 2011, Vienna, Austria. Proceedings to appear in J. Phys. (Conf. Series)

We report on the theoretical investigation of Wigner distribution function (WDF) reconstruction of the motional quantum state of large molecules in de Broglie interference. De Broglie interference of fullerenes and as the like already proves the wavelike behaviour of these heavy particles, while we aim to extract more quantitative information about the superposition quantum state in motion. We simulate the reconstruction of the WDF numerically based on an analytic probability distribution and investigate its properties by variation of parameters, which are relevant for the experiment. Even though the WDF described in the near-field experiment cannot be reconstructed completely, we observe negativity even in the partially reconstructed WDF. We further consider incoherent factors to simulate the experimental situation such as a finite number of slits, collimation, and particle-slit van der Waals interaction. From this we find experimental conditions to reconstruct the WDF from Talbot interference fringes in molecule Talbot-Lau interferometry., Comment: 16 pages, 9 figures, accepted at New Journal of Physics