We assess the most macroscopic matter-wave experiments to date as to the extent to which they probe the quantum-classical boundary by demonstrating interference of heavy molecules and cold atomic ensembles. To this end, we consider a rigorous Bayesian test protocol for a parametrized set of hypothetical modifications of quantum theory, including well-studied spontaneous collapse models, that destroy superpositions and reinstate macrorealism. The range of modification parameters ruled out by the measurement events quantifies the macroscopicity of a quantum experiment, while the shape of the posterior distribution resulting from the Bayesian update reveals how conclusive the data are at testing macrorealism. This protocol may serve as a guide for the design of future matter-wave experiments ever closer to truly macroscopic scales.
Recently there has been much interest in optomechanical devices for the production of macroscopic quantum states. Here we focus on a proposed scheme for achieving macroscopic superpositions via nested interferometry. We consider the effects of finite temperature on the superposition produced. We also investigate in detail the scheme's feasibility for probing various novel decoherence mechanisms.
A method for performing nonlocal interferometry using phase-entangled macroscopic coherent states is described. The required entanglement can be generated using weak nonlinearities while Bell's inequality can be violated using single photons as a probe. The entanglement is relatively robust against photon loss and Bell's inequality can be violated over a relatively large distance in optical fibers despite the fact that a large number of photons are absorbed in the process.
The propagation of macroscopic entangled states over large distances in the presence of loss is of fundamental interest and may have practical applications as well. Here we describe two different techniques in which state discrimination can be used to violate Bell's inequality with macroscopic phase-entangled coherent states. We find that Bell's inequality can be violated by these macroscopic states over a distance of approximately 400 km in commercially-available optical fibers.
We define a quantum witness for high-mass matter-wave interferometers that allows us to test fundamental assumptions of macroscopic realism. We propose an experimental realisation using absorptive laser gratings and show that such systems can strongly violate a macrorealistic quantum-witness equality. The measurement of the witness can therefore provide clear evidence of physics beyond macrorealism for macromolecules and nanoparticles.
We show that the generation of entanglement of two heavily macroscopic mirrors with masses of up to several kilograms are feasible with state of the art techniques of high-precision laser interferometry. The basis of such a demonstration would be a Michelson interferometer with suspended mirrors and simultaneous homodyne detections at both interferometer output ports. We present the connection between the generation of entanglement and the Standard Quantum Limit (SQL) for a free mass. The SQL is a well-known reference limit in operating interferometers for gravitational-wave detection and prov…
Usually, decoherence is generated from the coupling with an outer environment. However, a macroscopic object generically possesses its own environment in itself, namely the complicated dynamics of internal degrees of freedom. We address a question: when and how the internal dynamics decohere interference of the center of mass motion of a macroscopic object. We will also show that weak localization of a macroscopic object in disordered potentials can be destroyed by such decoherence.
We present a scheme for achieving macroscopic quantum superpositions in optomechanical systems by using single photon postselection and detecting them with nested interferometers. This method relieves many of the challenges associated with previous optical schemes for measuring macroscopic superpositions, and only requires the devices to be in the weak coupling regime. It requires only small improvements on currently achievable device parameters, and allows observation of decoherence on a timescale unconstrained by the system's optical decay time. Prospects for observing novel decoherence mech…
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 more than 150 nm. The scheme employs the near-field Talbo…
We establish an objective scheme to determine the macroscopicity of quantum mechanical superposition tests, which is based on the Bayesian hypothesis falsification of macrorealistic modifications of quantum theory. The measure uses the raw data gathered in an experiment, taking into account all measurement uncertainties, and can be used to directly assess any conceivable quantum test. We determine the resulting macroscopicity for three recent tests of quantum physics: double-well interference of Bose-Einstein condensates, Leggett-Garg tests with atomic random walks, and entanglement generation…
We utilise a magneto-mechanical levitated massive resonator in the quantum regime to prepare highly macroscopic quantum superposition states. Using these macroscopic superpositions we present a novel interferometry protocol to perform absolute gravimetry with a sensitivity that exceeds state of the art atom-interferometric and corner-cube gravimeters by a factor of 20. In addition, our scheme allows probing the gravitational field on a length scale eight orders of magnitude smaller than other methods.
Quantum superposition is central to quantum theory but challenges our concepts of reality and spacetime when applied to macroscopic objects like Schrödinger's cat. For that reason, it has been a long-standing question whether quantum physics remains valid unmodified even for truly macroscopic objects. By now, the predictions of quantum theory have been confirmed via matter-wave interferometry for massive objects up to $10^4\,$ atomic mass units (amu). The rapid development of new technologies promises to soon allow tests of quantum theory for significantly higher test masses by using novel tec…
Matter-wave interferometry with solids is highly susceptible to minute fluctuations of environmental fields, including gravitational effects from distant sources. Hence, experiments require a degree of shielding that is extraordinarily challenging to achieve in realistic terrestrial or even space-based set-ups. Here, we design protocols that exploit the spatial correlations that are inherent in perturbations due to distant sources to reduce significantly their impact on the visibility of interference patterns. We show that interference patterns that are robust to such type of noise can be enco…
Equilibration and the eigenstate thermalization hypothesis as limits to observing macroscopic quantum superpositions
Escola Politécnica de Pernambuco, Universidade de Pernambuco（伯南布哥联邦大学应用理工学院）；Universidade Estadual de Santa Cruz（圣克鲁斯州立大学）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
Certifying Macroscopic Quantum Mechanics via Hypothesis Testing with Finite Data
ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科技研究院）；Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；ICREA – Institucio Catalana de Recerca i Estudis Avançats（加泰罗尼亚研究与高等学院）
Matter-wave interferometry is a direct test of the quantum superposition principle for massive systems, and of collapse models. Here we show that the bounds placed by matter-wave interferometry depend weakly on the details of the collapse mechanism. Specifically, we compute the bounds on the CSL model and its variants, provided by the the KDTL interferometry experiment of Arndt's group [Phys. Chem. Chem. Phys., 2013, 15, 14696-14700], which currently holds the record of largest mass in interferometry. We also show that the CSL family of models emerges naturally by considering a minimal set of …
A three-body quantum correlation is calculated for two particles reflecting from a mirror. Correlated interference, a consequence of conservation of energy and momentum, occurs for states in which the order of reflection is indeterminate. The resulting quantum joint probability density function exhibits interference with diverse characteristics, depending on the coherence lengths of the substates. Marginal probability density functions can contain information about the quantum nature of all three bodies, even if only one particle is measured. Microscopic particles reflecting from a mesoscopic …
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at the Planck scale. If directions in emergent quantum geometry do not commute, new quantum-geometrical degrees of freedom can produce detectable macroscopic deviations from classicality: spatially coherent, transverse position indeterminacy between any pair of world lines, with a displacement amplitude much larger than the Planck length. Positions of separate b…
We discuss modern developments in quantum optics with organic molecules, clusters and nanoparticles -- in particular recent realizations of near-field matter-wave interferometry. A unified theoretical description in phase space allows us to describe quantum interferometry in position space and in the time domain on an equal footing. In order to establish matter-wave interferometers as a universal tool, which can accept and address a variety of nanoparticles, we elaborate on new quantum optical elements, such as diffraction gratings made of matter and light, as well as their absorptive and disp…
We propose a new Wigner inequality suitable for test of the hypothesis of realism. We show that this inequality is not identical neither to the well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form. The obtained inequality is suitable for test of realism not only in quantum mechanical systems, but also in quantum field systems. Also we propose a mathematically consistent derivation of the Leggett--Garg inequality in Wigner form, which was recently presented in the literature, for three and $n$ distinct moments of time. Contrary to these works, our rigor derivation uses…
Heralded generation and manipulation of quantum entanglement between two macroscopic and spatially separated crystals at room temperature is theoretically studied. We show that by combining an x-ray parametric down-conversion source and x-ray interferometry with nuclear resonant scattering techniques, two macroscopic crystals hosting Mössbauer nuclei located each on an interferometer arm can be entangled for few tens of nanoseconds. The coherence time of the entanglement state can be prolonged up to values comparable to the lifetime of a single nuclear excited state, on the order of hundred na…
New quantum degrees of freedom of space-time, originating at the Planck scale, could create a coherent indeterminacy and noise in the transverse position of massive bodies on macroscopic scales. An experiment is under development at Fermilab designed to detect or rule out a transverse position noise with Planck spectral density, using correlated signals from an adjacent pair of Michelson interferometers. A detection would open an experimental window on quantum space-time.
A recent experiment [K. C. Lee et al., Science 334, 1253 (2011)] succeeded in detecting entanglement between two macroscopic specks of diamonds, separated by a macroscopic distance, at room temperature. This impressive results is a further confirmation of the validity of quantum theory in (at least parts of) the mesoscopic and macroscopic domain, and poses a challenge to collapse models, which predict a violation of the quantum superposition principle, which is the bigger the larger the system. We analyze the experiment in the light of such models. We will show that the bounds placed by experi…
Experimental observation of the decoherence of macroscopic objects is of fundamental importance to the study of quantum collapse models and the quantum to classical transition. Optomechanics is a promising field for the study of such models because of its fine control and readout of mechanical motion. Nevertheless, it is challenging to monitor a mechanical superposition state for long enough to investigate this transition. We present a scheme for entangling two mechanical resonators in spatial superposition states such that all quantum information is stored in the mechanical resonators. The sc…
We theoretically study macroscopic entanglement between a magnetically trapped Bose-Einstein condensate and a superconducting loop. We treat the superconducting loop in a quantum superposition of two different flux states coupling with the magnetic trap to generate macroscopic entanglement. The scheme also provides a platform to investigate interferometry with an entangled Bose Einstein condensate and to explore physics at the quantum-classical interface.
Hybrid spin-mechanical systems have great potentials in sensing, macroscopic quantum mechanics, and quantum information science. In order to induce strong coupling between an electron spin and the center-of-mass motion of a mechanical oscillator, a large magnetic gradient is usually required, which is difficult to achieve. Here we show that strong coupling between the electron spin of a nitrogen-vacancy (NV) center and the torsional vibration of an optically levitated nanodiamond can be achieved in a uniform magnetic field. Thanks to the uniform magnetic field, multiple spins can strongly coup…
We study how macroscopic superpositions of coherent states produced by the nondissipative dynamics of binary mixtures of ultracold atoms are affected by atom losses. We identify different decoherence scenarios for symmetric or asymmetric loss rates and interaction energies in the two modes. In the symmetric case the quantum coherence in the superposition is lost after a single loss event. By tuning appropriately the energies we show that the superposition can be protected, leading to quantum correlations useful for atom interferometry even after many loss events.
Interferometers operating at or close to quantum limits of precision have found wide application in tabletop searches for physics beyond the standard model, the study of fundamental forces and symmetries of nature and foundational tests of quantum mechanics. The limits imposed by quantum fluctuations and measurement backaction on conventional interferometers ($δϕ\sim 1/\sqrt{N}$) have spurred the development of schemes to circumvent these limits through quantum interference, multiparticle interactions and entanglement. A prominent example of such schemes, the so-called $SU(1,1)$ interferometer…
We present a minimal model for the quantum evolution of matter under the influence of classical gravity in the Newtonian limit. Based on a continuous measurement-feedback channel that acts simultaneously on all constituent masses of a given quantum system, the model scales and applies consistently to arbitrary mass densities, and it recovers the classical Newton force between macroscopic masses. The concomitant loss of coherence is set by a model parameter, does not depend on mass, and can thus be confined to unobservable time scales for micro- and macroscopic systems alike. The model can be p…
In quantum interferometry, it is vital to control and utilize nonlinear interactions for achieving high-precision measurements. Attribute to their long coherent time and high controllability, ultracold atoms including Bose condensed atoms have been widely used for implementing quantum interferometry. Here, we review the recent progresses in theoretical studies of quantum interferometry with Bose condensed atoms. In particular, we focus on the nonlinear phenomena induced by the atom-atom interaction and how to control and utilize these nonlinear phenomena. Under the mean-field description, due …
We investigate the influence of Unruh radiation on matter-wave interferometry experiments using neutral objects modeled as dielectric spheres. The Unruh effect leads to a loss of coherence through momentum diffusion. This is a fundamental source of decoherence that affects all objects having electromagnetic interactions. However, the effect is not large enough to prevent the observation of interference for objects of any size, even when the path separation is larger than the size of the object. When the acceleration in the interferometer arms is large, inertial tidal forces will disrupt the ma…
Nano- and micromechanical solid-state quantum devices have become a focus of attention. Reliably generating nonclassical states of their motion is of interest both for addressing fundamental questions about macroscopic quantum phenomena and for developing quantum technologies in the domains of sensing and transduction. We used quantum optical control techniques to conditionally generate single-phonon Fock states of a nanomechanical resonator. We performed a Hanbury Brown and Twiss-type experiment that verified the nonclassical nature of the phonon state without requiring full state reconstruct…
We analyze methods to go beyond the standard quantum limit for a class of atomic interferometers, where the quantity of interest is the difference of phase shifts obtained by two independent atomic ensembles. An example is given by an atomic Sagnac interferometer, where for two ensembles propagating in opposite directions in the interferometer this phase difference encodes the angular velocity of the experimental setup. We discuss methods of squeezing separately or jointly observables of the two atomic ensembles, and compare in detail advantages and drawbacks of such schemes. In particular we …
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 …
The possibility to test quantum measurement theories is discussed in the more phenomenological framework of the quantum nondemolition theory. A simple test of the hypothesis of the state vector collapse is proposed by looking for deviations from the Boltzmann distribution of the energy associated to only one complex amplitude of a macroscopic harmonic oscillator.
The aim of this note is to attract attention of the quantum foundational community to the fact that in Bell's arguments one can not distinguish two hypotheses: a) quantum mechanics is {\it nonlocal}, b) quantum mechanics is {\it nonergodic.} Therefore experimental violations of Bell's inequality can be as well interpreted as supporting the hypothesis that stochastic processes induced by quantum measurements are nonergodic. The latter hypothesis was discussed actively by Buonomano since 1980th. However, in contrast to Bell's hypothesis on nonlocality it did not attract so much attention. The on…
We derive the projection hypothesis in projective quantum measurement by restricting the set of observables. This projection hypothesis accompanies a bipartite system with the von Neumann-type interaction, which consists of a quantum mechanical system, with a meter variable to be measured, and a quantum field theoretically macroscopic extended object, that is, a spatiotemporally inhomogeneous Bose-Einstein condensate in quantum field theory with the quantum coordinate, that is, the zero-energy Goldstone mode(s) of the spontaneously broken global spatial translational symmetry. The key steps in…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory referred to as the "measurement problem", actually has a computational character: It implies that there is a generic algorithm, which guarantees exact solutions to the Schrodinger equation for every physical system in a reasonable amount of time regardless of how many constituent microscopic particles it comprises. From the point of view of computational complexity…
Atom interferometry tests of universality of free fall based on the differential measurement of two different atomic species provide a useful complement to those based on macroscopic masses. However, when striving for the highest possible sensitivities, gravity gradients pose a serious challenge. Indeed, the relative initial position and velocity for the two species need to be controlled with extremely high accuracy, which can be rather demanding in practice and whose verification may require rather long integration times. Furthermore, in highly sensitive configurations gravity gradients lead …
Do the laws of quantum physics still hold for macroscopic objects - this is at the heart of Schrödinger's cat paradox - or do gravitation or yet unknown effects set a limit for massive particles? What is the fundamental relation between quantum physics and gravity? Ground-based experiments addressing these questions may soon face limitations due to limited free-fall times and the quality of vacuum and microgravity. The proposed mission MAQRO may overcome these limitations and allow addressing those fundamental questions. MAQRO harnesses recent developments in quantum optomechanics, high-mass m…
We present a scheme to establish non-classical correlations in the motion of two macroscopically separated massive particles without resorting to entanglement in their internal degrees of freedom. It is based on the dissociation of a diatomic molecule with two temporally separated Feshbach pulses generating a motional state of two counter-propagating atoms that is capable of violating a Bell inequality by means of correlated single particle interferometry. We evaluate the influence of dispersion on the Bell correlation, showing it to be important but manageable in a proposed experimental setup…
A field, which mediates entanglement between two quantum systems, must be of quantum nature. Attempts to witness this way quantumlike features of the gravitational field with tabletop experiments are actively studied recently, in particular by considering to look at two masses in a superposition in two locations, each in one interferometer. Entanglement intervention is probed when the interferometers are put side by side. If the masses interact only via Newtonian attraction, and still some degree of entanglement is found, than the gravitational field must be quantum like, or at least non-class…
Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Due to their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this paper we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far-field of a double-slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in ord…
Using very general and well established ideas of the statistical physics of macroscopic bodies, that is, of those composed of many degrees of freedom, we show how classical behavior of the center of mass motion arises from a fully quantum mechanical description of the dynamics of the whole body. We do not attempt to provide a rigorous proof of the latter statement, but rather, we show or, at least, indicate the hypotheses needed to obtain the purported result. Moreover, we neither attempt to deal with the "most general" physical situation and, instead, we concentrate on a stylized model of a s…
Quantum mechanics marks a radical departure from the classical understanding of Nature, fostering an inherent randomness which forbids a deterministic description; yet the most fundamental departure arises from something different. As shown by Bell [1] and Kochen-Specker [2], quantum mechanics portrays a picture of the world in which reality loses its objectivity and is in fact created by observation. Quantum mechanics predicts phenomena which cannot be explained by any theory with objective realism, although our everyday experience supports the hypothesis that macroscopic objects, despite bei…
Based on the view that thermal equilibrium should be characterized through macroscopic observations, we develop a general theory about typicality of thermal equilibrium and the approach to thermal equilibrium in macroscopic quantum systems. We first formulate the notion that a pure state in an isolated quantum system represents thermal equilibrium. Then by assuming, or proving in certain classes of nontrivial models (including that of two bodies in thermal contact), large-deviation type bounds (which we call thermodynamic bounds) for the microcanonical ensemble, we prove that to represent ther…
