Collisional decoherence observed in matter wave interferometry

Thermalization and Dephasing in Collisional Reservoirs

We introduce a wide class of quantum maps that arise in collisional reservoirs and are able to thermalize a system if they operate in conjunction with an additional dephasing mechanism. These maps describe the effect of collisions and induce transitions between populations that obey detailed balance, but also create coherences that prevent the system from thermalizing. We combine these maps with a unitary evolution acting during random Poissonian times between collisions and causing dephasing. We find that, at a low collision rate, the nontrivial combination of these two effects causes thermalization in the system. This scenario is suitable for modeling collisional reservoirs at equilibrium. We justify this claim by identifying the conditions for such maps to arise within a scattering theory approach and provide a thorough characterization of the resulting thermalization process.

Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons

Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that-when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate)-these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate. This approach shares with the Relative State Interpretation of Everett the view that collapse of the wavepacket reflects perception of the state of the rest of the Universe relative to the state of observer's records. However, our "let quantum be quantum" approach poses questions absent in Bohr's Copenhagen Interpretation that relied on the preexisting classical domain. Thus, one is now forced to seek preferred, predictable, hence effectively classical but ultimately quantum states that allow observers keep reliable records. Without such (i) preferred basis relative states are simply "too relative", and the ensuing basis ambiguity makes it difficult to identify events (e.g., measurement outcomes). Moreover, universal validity of quantum theory raises the issue of (ii) the origin of Born's rule, pk=|ψk|2, relating probabilities and amplitudes (that is simply postulated in textbooks). Last not least, even preferred pointer states (defined by einselection-environment-induced superselection)-are still quantum. Therefore, unlike classical states that exist objectively, quantum states of an individual system cannot be found out by an initially ignorant observer through direct measurement without being disrupted. So, to complete the 'quantum theory of the classical' one must identify (iii) quantum origin of objective existence and explain how the information about objectively existing states can appear to be essentially inconsequential for them (as it does for states in Newtonian physics) and yet matter in other settings (e.g., thermodynamics). I show how the mathematical structure of quantum theory supplemented by the only uncontroversial measurement postulate (that demands immediate repeatability-hence, predictability) leads to preferred states. These (i) pointer states correspond to measurement outcomes. Their stability is a prerequisite for objective existence of effectively classical states and for events such as quantum jumps. Events at hand, one can now enquire about their probability-the probability of a pointer state (or of a measurement record). I show that the symmetry of entangled states-(ii) entanglement-assisted invariance or envariance-implies Born's rule. Envariance also accounts for the loss of phase coherence between pointer states. Thus, decoherence can be traced to symmetries of entanglement and understood without its usual tool-reduced density matrices. A simple and manifestly noncircular derivation of pk=|ψk|2 follows. Monitoring of the system by its environment in course of decoherence typically leaves behind multiple copies of its pointer states in the environment. Only pointer states can survive decoherence and can spawn such plentiful information-theoretic progeny. This (iii) quantum Darwinism allows observers to use environment as a witness-to find out pointer states indirectly, leaving systems of interest untouched. Quantum Darwinism shows how epistemic and ontic (coexisting in epiontic quantum state) separate into robust objective existence of pointer states and detached information about them, giving rise to extantons-composite objects with system of interest in the core and multiple records of its pointer states in the halo comprising of environment subsystems (e.g., photons) which disseminates that information throughout the Universe.

Nanoscale Magnetism Probed in a Matter-Wave Interferometer

We explore a wide range of fundamental magnetic phenomena by measuring the dephasing of matter-wave interference fringes upon application of a variable magnetic gradient. The versatility of our interferometric Stern-Gerlach technique enables us to study the magnetic properties of alkali atoms, organic radicals, and fullerenes in the same device, with magnetic moments ranging from a Bohr magneton to less than a nuclear magneton. We find evidence for magnetization of a supersonic beam of organic radicals and, most notably, observe a strong magnetic response of a thermal C_{60} beam consistent with high-temperature atomlike deflection of rotational magnetic moments.

Timelessness Strictly inside the Quantum Realm

Time is one of the undisputed foundations of our life in the real world. Here it is argued that inside small isolated quantum systems, time does not pass as we are used to, and it is primarily in this sense that quantum objects enjoy only limited reality. Quantum systems, which we know, are embedded in the everyday classical world. Their preparation as well as their measurement-phases leave durable records and traces in the entropy of the environment. The Landauer Principle then gives a quantitative threshold for irreversibility. With double slit experiments and tunneling as paradigmatic examples, it is proposed that a label of timelessness offers clues for rendering a Copenhagen-type interpretation of quantum physics more "realistic" and acceptable by providing a coarse but viable link from the fundamental quantum realm to the classical world which humans directly experience.

Blind Witnesses Quench Quantum Interference without Transfer of Which-Path Information

Quantum computation is often limited by environmentally-induced decoherence. We examine the loss of coherence for a two-branch quantum interference device in the presence of multiple witnesses, representing an idealized environment. Interference oscillations are visible in the output as the magnetic flux through the branches is varied. Quantum double-dot witnesses are field-coupled and symmetrically attached to each branch. The global system—device and witnesses—undergoes unitary time evolution with no increase in entropy. Witness states entangle with the device state, but for these blind witnesses, which-path information is not able to be transferred to the quantum state of witnesses—they cannot “see” or make a record of which branch is traversed. The system which-path information leaves no imprint on the environment. Yet, the presence of a multiplicity of witnesses rapidly quenches quantum interference.

Quantum-assisted diamagnetic deflection of molecules

We measure the diamagnetic deflection of anthracene and adamantane in a long-baseline matter-wave interferometer.

Entanglement, holonomic constraints, and the quantization of fundamental interactions

We provide a proof for the necessity of quantizing fundamental interactions demonstrating that a quantum version is needed for any non trivial conservative interaction whose strength depends on the relative distance between two objects. Our proof is based on a consistency argument that in the presence of a classical field two interacting objects in a separable state could not develop entanglement. This requirement can be cast in the form of a holonomic constraint that cannot be satisfied by generic interparticle potentials. Extending this picture of local holonomic constraints, we design a protocol that allows to measure the terms of a multipole expansion of the interaction of two composite bodies. The results presented in this work can pave the way for a study of fundamental interactions based on the analysis of entanglement properties.

Additive manufacturing of magnetic shielding and ultra-high vacuum flange for cold atom sensors

Recent advances in the understanding and control of quantum technologies, such as those based on cold atoms, have resulted in devices with extraordinary metrological performance. To realise this potential outside of a lab environment the size, weight and power consumption need to be reduced. Here we demonstrate the use of laser powder bed fusion, an additive manufacturing technique, as a production technique relevant to the manufacture of quantum sensors. As a demonstration we have constructed two key components using additive manufacturing, namely magnetic shielding and vacuum chambers. The initial prototypes for magnetic shields show shielding factors within a factor of 3 of conventional approaches. The vacuum demonstrator device shows that 3D-printed titanium structures are suitable for use as vacuum chambers, with the test system reaching base pressures of 5 ± 0.5 × 10⁻¹⁰ mbar. These demonstrations show considerable promise for the use of additive manufacturing for cold atom based quantum technologies, in future enabling improved integrated structures, allowing for the reduction in size, weight and assembly complexity.

Spin-Orbit Interactions and Quantum Spin Dynamics in Cold Ion-Atom Collisions

We present accurate ab initio and quantum scattering calculations on a prototypical hybrid ion-atom system Yb^{+}-Rb, recently suggested as a promising candidate for the experimental study of open quantum systems, quantum information processing, and quantum simulation. We identify the second-order spin-orbit (SO) interaction as the dominant source of hyperfine relaxation in cold Yb^{+}-Rb collisions. Our results are in good agreement with recent experimental observations [L. Ratschbacher et al., Phys. Rev. Lett. 110, 160402 (2013)] of hyperfine relaxation rates of trapped Yb^{+} immersed in an ultracold Rb gas. The calculated rates are 4 times smaller than is predicted by the Langevin capture theory and display a weak T^{-0.3} temperature dependence, indicating significant deviations from statistical behavior. Our analysis underscores the deleterious nature of the SO interaction and implies that light ion-atom combinations such as Yb^{+}-Li should be used to minimize hyperfine relaxation and decoherence of trapped ions in ultracold atomic gases.

Effective Markovian description of decoherence in bound systems

Effective descriptions accounting for the evolution of quantum systems that are acted on by a bath are desirable. As the number of bath degrees of freedom increases and full quantum simulations turn out computationally prohibitive, simpler models become essential to understand and gain an insight into the main physical mechanisms involved in the system dynamics. In this regard, vibrational decoherence of an I2 diatomics is tackled here within the framework of Markovian quantum state diffusion. The I2 dynamics are analyzed in terms of an effective decoherence rate, Λ, and the specific choice of the initial state, in particular, Gaussian wave packets and two-state superpositions. It is found that, for Markovian baths, the relevant quantity regarding decoherence is the product of friction (η) and temperature (T); there is no distinction between varying one or the other. It is also observed that decoherence becomes faster as the energy levels involved in the system state correspond to higher eigenvalues. This effect is due to a population redistribution during the dynamical process and an eventual irreversible loss of the initial coherence. These results have been compared with those available in the literature from more detailed semiclassical IVR simulations, finding a good agreement.

Decoherence cross-section in NO + Ar collisions: experimental results and a simple model

Quantum decoherence can be viewed as the mechanism responsible for the quantum-to-classical transition as the initially prepared quantum state interacts with its environment in an irreversible manner. One of the most common mechanisms responsible for the macroscopically observed decoherence involves collisions of an atom or molecule, initially prepared in a coherent superposition of states, with gas particles. In this work, a coherent superposition of quantum internal states of NO molecules is prepared by the interaction between the molecule with both a static and a radiofrequency electric field. Subsequently, NO + Ar collision decoherence experiments are investigated by measuring the loss of coherence as a function of the number of collisions. Data analysis using a model based on the interaction potential of the collisional partners allowed to unravel the molecular mechanism responsible for the loss of coherence in the prepared NO quantum superposition of internal states. The relevance of the present work relies on several aspects. On the one hand, the use of radio-waves introduces a new way for the production of coherent beams. On the other hand, the employed methodology could be useful in investigating the Stereodynamics of chemical reactions with coherent reagents.

Experimental methods of molecular matter-wave optics

We describe the state of the art in preparing, manipulating and detecting coherent molecular matter. We focus on experimental methods for handling the quantum motion of compound systems from diatomic molecules to clusters or biomolecules.Molecular quantum optics offers many challenges and innovative prospects: already the combination of two atoms into one molecule takes several well-established methods from atomic physics, such as for instance laser cooling, to their limits. The enormous internal complexity that arises when hundreds or thousands of atoms are bound in a single organic molecule, cluster or nanocrystal provides a richness that can only be tackled by combining methods from atomic physics, chemistry, cluster physics, nanotechnology and the life sciences.We review various molecular beam sources and their suitability for matter-wave experiments. We discuss numerous molecular detection schemes and give an overview over diffraction and interference experiments that have already been performed with molecules or clusters.Applications of de Broglie studies with composite systems range from fundamental tests of physics up to quantum-enhanced metrology in physical chemistry, biophysics and the surface sciences.Nanoparticle quantum optics is a growing field, which will intrigue researchers still for many years to come. This review can, therefore, only be a snapshot of a very dynamical process.

Quantum interference of large organic molecules

The wave nature of matter is a key ingredient of quantum physics and yet it defies our classical intuition. First proposed by Louis de Broglie a century ago, it has since been confirmed with a variety of particles from electrons up to molecules. Here we demonstrate new high-contrast quantum experiments with large and massive tailor-made organic molecules in a near-field interferometer. Our experiments prove the quantum wave nature and delocalization of compounds composed of up to 430 atoms, with a maximal size of up to 60 Å, masses up to m=6,910 AMU and de Broglie wavelengths down to λ(dB)=h/mv≃1 pm. We show that even complex systems, with more than 1,000 internal degrees of freedom, can be prepared in quantum states that are sufficiently well isolated from their environment to avoid decoherence and to show almost perfect coherence.

Sympathetic cooling of polyatomic molecules with S-state atoms in a magnetic trap

We present a rigorous theoretical study of low-temperature collisions of polyatomic molecular radicals with (1)S(0) atoms in the presence of an external magnetic field. Accurate quantum scattering calculations based on ab initio and scaled interaction potentials show that collision-induced spin relaxation of the prototypical organic molecule CH(2)(X(3)B(1)) (methylene) and nine other triatomic radicals in cold (3)He gas occurs at a slow rate, demonstrating that cryogenic buffer-gas cooling and magnetic trapping of these molecules is feasible with current technology. Our calculations further suggest that it may be possible to create ultracold gases of polyatomic molecules by sympathetic cooling with alkaline-earth atoms in a magnetic trap.

Stochastic simulation algorithm for the quantum linear Boltzmann equation

We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The algorithm leads to a numerically efficient stochastic simulation procedure for the most general form of this integrodifferential equation, which involves a five-dimensional integral over microscopically defined scattering amplitudes that account for the gas interactions in a nonperturbative fashion. The simulation technique is used to assess various limiting forms of the quantum linear Boltzmann equation, such as the limits of pure collisional decoherence and quantum Brownian motion, the Born approximation, and the classical limit. Moreover, we extend the method to allow for the simulation of the dissipative and decohering dynamics of superpositions of spatially localized wave packets, which enables the study of many physically relevant quantum phenomena, occurring e.g., in the interferometry of massive particles.

Nitric oxide beam intensity oscillations induced by the combined action of a static and a radio frequency electric field

This paper details an experimental and theoretical investigation in which a simplified version of the molecular beam electric resonance technique is employed that requires the use of a C-field only. In the experiment the forward intensity of a NO beam is measured as a function of the frequency of the oscillating electric field over the 900-1460 kHz range. Specifically, the interaction of the NO beam with a radio frequency (rf) field of 1.12 kV/m amplitude and -610 kV/m (2) of gradient at the horizontal plane during 72 micros produces a series of oscillations in the transmitted beam intensity. The theoretical analysis shows how the interaction between a beam of NO molecules and both a static and oscillating rf field produces interferences in the forward beam intensity and how the observed interferences are due to superposition of molecular internal states. Furthermore, the interference model reproduces satisfactorily the observed beam intensity oscillations. The present technique could be useful for the development of new schemes to achieve coherent control of molecular processes using radiowaves.

Quantum physics meets biology

Quantum physics and biology have long been regarded as unrelated disciplines, describing nature at the inanimate microlevel on the one hand and living species on the other hand. Over the past decades the life sciences have succeeded in providing ever more and refined explanations of macroscopic phenomena that were based on an improved understanding of molecular structures and mechanisms. Simultaneously, quantum physics, originally rooted in a world-view of quantum coherences, entanglement, and other nonclassical effects, has been heading toward systems of increasing complexity. The present perspective article shall serve as a "pedestrian guide" to the growing interconnections between the two fields. We recapitulate the generic and sometimes unintuitive characteristics of quantum physics and point to a number of applications in the life sciences. We discuss our criteria for a future "quantum biology," its current status, recent experimental progress, and also the restrictions that nature imposes on bold extrapolations of quantum theory to macroscopic phenomena.

Creation and detection of a mesoscopic gas in a nonlocal quantum superposition

We investigate the scattering of a quantum matter wave soliton on a barrier in a one-dimensional geometry, and we show that it can lead to mesoscopic quantum superposition states, where the atomic gas is in a coherent superposition of being in the half-space to the left of the barrier and being in the half-space to the right of the barrier. We propose an interferometric method to reveal the coherent nature of this superposition, and we discuss in detail the experimental feasibility.

Suppression of decoherence in fast-atom diffraction at surfaces

Scattering of fast neutral atoms with keV kinetic energies at alkali-halide surfaces under grazing angles displays intriguing diffraction patterns. The surprisingly strong persistence of quantum coherence despite the impulsive interaction with an environment at solid state density and elevated temperatures raises fundamental questions such as to the suppression of decoherence and of the quantum-to-classical crossover. We present an ab initio simulation of the quantum diffraction of fast helium beams at a LiF (100) surface in the 110 direction and compare with recent experimental diffraction data. From the quantitative reconstruction of diffraction images the vertical LiF-surface reconstruction, or buckling, can be determined.

The simplest double slit: interference and entanglement in double photoionization of H2

The wave nature of particles is rarely observed, in part because of their very short de Broglie wavelengths in most situations. However, even with wavelengths close to the size of their surroundings, the particles couple to their environment (for example, by gravity, Coulomb interaction, or thermal radiation). These couplings shift the wave phases, often in an uncontrolled way, and the resulting decoherence, or loss of phase integrity, is thought to be a main cause of the transition from quantum to classical behavior. How much interaction is needed to induce this transition? Here we show that a photoelectron and two protons form a minimum particle/slit system and that a single additional electron constitutes a minimum environment. Interference fringes observed in the angular distribution of a single electron are lost through its Coulomb interaction with a second electron, though the correlated momenta of the entangled electron pair continue to exhibit quantum interference.

Three-dimensional Monte Carlo simulations of the quantum linear Boltzmann equation

Recently the general form of a translation-covariant quantum Boltzmann equation has been derived, which describes the dynamics of a tracer particle in a quantum gas. We develop a stochastic wave function algorithm that enables full three-dimensional Monte Carlo simulations of this equation. The simulation method is used to study the approach to equilibrium for various scattering cross sections and to determine dynamical deviations from Gaussian statistics through an investigation of higher-order cumulants. Moreover, we examine the loss of coherence of superpositions of momentum eigenstates and determine the corresponding decoherence time scales to quantify the transition from quantum to classical behavior of the state of the test particle.

Inelastic electron holography as a variant of the Feynman thought experiment

Using a combination of electron holography and energy filtering, interference fringes produced after inelastic interaction of electrons with hydrogen molecules are examined. Surprisingly, the coherence of inelastic scattering increases when moving from the surface of a hydrogen-containing bubble to the vacuum. This phenomenon can be understood in terms of the Feynman two-slit thought experiment with a variable ambiguity of the which-way registration.

First measurements of the index of refraction of gases for lithium atomic waves

We report the first measurements of the index of refraction of gases for lithium waves. Using an atom interferometer, we have measured the real and imaginary parts of the index of refraction n for argon, krypton, and xenon as a function of the gas density for several velocities of the lithium beam. The linear dependence of (n-1) with the gas density is well verified. The total collision cross section deduced from the imaginary part of (n-1) is in very good agreement with traditional measurements of this quantity. Finally, the real and imaginary parts of (n-1) and their ratio rho exhibit glory oscillations, in good agreement with calculations.

Measurement of decoherence of electron waves and visualization of the quantum-classical transition

Controlled decoherence of free electrons due to Coulomb interaction with a truly macroscopic environment, the electron (and phonon) gas inside a semiconducting plate, is studied experimentally. The quantitative results are compared with different theoretical models. The experiment confirms the main features of the theory of decoherence and can be interpreted in terms of which-path information. In contrast to previous model experiments on decoherence, the obtained interferograms directly visualize the transition from quantum to classical.

Master equation for a quantum particle in a gas

The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of S-matrix theory. This quantum version of the linear Boltzmann equation accounts nonperturbatively for the quantum effects of the scattering dynamics and describes decoherence and dissipation in a unified framework. As a completely positive master equation it incorporates both the known equation for an infinitely massive Brownian particle and the classical linear Boltzmann equation as limiting cases.

Ultimate decoherence border for matter-wave interferometry

Stochastic backgrounds of gravitational waves are intrinsic fluctuations of spacetime which lead to an unavoidable decoherence mechanism. This mechanism manifests itself as a degradation of the contrast of quantum interferences. It defines an ultimate decoherence border for matter-wave interferometry using larger and larger molecules. We give a quantitative characterization of this border in terms of figures involving the gravitational environment as well as the sensitivity of the interferometer to gravitational waves. The known level of gravitational noise determines the maximal size of the molecular probe for which interferences may remain observable. We discuss the relevance of this result in the context of ongoing progresses towards more and more sensitive matter-wave interferometry.

Ericson fluctuations in an open deterministic quantum system: theory meets experiment

We provide numerically exact photoexcitation cross sections of rubidium Rydberg states in crossed, static electric, and magnetic fields, in quantitative agreement with recent experimental results. Their spectral backbone underpins a clear transition towards the Ericson regime, associated with a universal, fluctuating behavior of the cross section of strongly coupled, fragmenting quantum systems.

Theory of decoherence due to scattering events and Lévy processes

A general connection between the characteristic function of a Lévy process and loss of coherence of the statistical operator describing the center of mass degrees of freedom of a quantum system interacting through momentum transfer events with an environment is established. The relationship with microphysical models and recent experiments is considered, focusing on the recently observed transition between a dynamics described by a compound Poisson process and a Gaussian process.

Matter-wave decoherence due to a gas environment in an atom interferometer

Decoherence due to scattering from background gas particles is observed for the first time in a Mach-Zehnder atom interferometer, and compared with decoherence due to scattering photons. A single theory is shown to describe decoherence due to scattering either atoms or photons. Predictions from this theory are tested by experiments with different species of background gas, and also by experiments with different collimation restrictions on an atom beam interferometer.

Quantum description of Einstein's Brownian motion

A fully quantum treatment of Einstein's Brownian motion is given, stressing in particular the role played by the two original requirements of translational invariance and connection between dynamics of the Brownian particle and atomic nature of the medium. The former leads to a clearcut relationship with a generator of translation-covariant quantum-dynamical semi-groups recently characterized by Holevo, the latter to a formulation of the fluctuation-dissipation theorem in terms of the dynamic structure factor, a two-point correlation function introduced in seminal work by Van Hove, directly related to density fluctuations in the medium and therefore to its atomistic, discrete nature. A microphysical expression for the generally temperature dependent friction coefficient is given in terms of the dynamic structure factor and of the interaction potential describing the single collisions. A comparison with the Caldeira-Leggett model is drawn, especially in view of the requirement of translational invariance, further characterizing general structures of reduced dynamics arising in the presence of symmetry under translations.

Mixed quantum-classical treatment of vibrational decoherence

The mixed quantum-classical method based on the Bohmian formulation of quantum mechanics [J. Chem. Phys. 113, 9369 (2000)]] is applied to study the process of vibrational decoherence of I2 in a dense helium environment. Specifically, the revival of vibrational wave packets, detectable by pump-probe spectroscopy, is a quantum phenomena which depends sensitively on the coherence between the vibrational levels excited by the pump pulse. The time-dependent pump-probe revival signal is a very sensitive way of detecting vibrational dephasing induced by an environment. The very good agreement between previous experimental signals and calculations presented in ths work confirms the theoretical approach and provides a promising basis for the prediction and interpretation of future experiments exploiting quantum revivals as a probe of decoherence.

Exact decoherence to pointer states in free open quantum systems is universal

In this Letter it is shown that exact decoherence to minimal uncertainty Gaussian pointer states is generic for free quantum particles coupled to a heat bath. More specifically, the Letter is concerned with damped free particles linearly coupled under product initial conditions to a heat bath at arbitrary temperature, with arbitrary coupling strength and spectral densities covering the Ohmic, sub-Ohmic, and supra-Ohmic regime. Then it is true that there exists a time t(c) such that for times t>t(c) the state can always be exactly represented as a mixture (convex combination) of particular minimal uncertainty Gaussian states, regardless of and independent from the initial state. This exact "localization" is hence not a feature specific to high temperature and weak damping limit, but is a generic property of damped free particles.

Decoherence of matter waves by thermal emission of radiation

Emergent quantum technologies have led to increasing interest in decoherence--the processes that limit the appearance of quantum effects and turn them into classical phenomena. One important cause of decoherence is the interaction of a quantum system with its environment, which 'entangles' the two and distributes the quantum coherence over so many degrees of freedom as to render it unobservable. Decoherence theory has been complemented by experiments using matter waves coupled to external photons or molecules, and by investigations using coherent photon states, trapped ions and electron interferometers. Large molecules are particularly suitable for the investigation of the quantum-classical transition because they can store much energy in numerous internal degrees of freedom; the internal energy can be converted into thermal radiation and thus induce decoherence. Here we report matter wave interferometer experiments in which C70 molecules lose their quantum behaviour by thermal emission of radiation. We find good quantitative agreement between our experimental observations and microscopic decoherence theory. Decoherence by emission of thermal radiation is a general mechanism that should be relevant to all macroscopic bodies.

Wave nature of biomolecules and fluorofullerenes

We demonstrate quantum interference for tetraphenylporphyrin, the first biomolecule exhibiting wave nature, and for the fluorofullerene C60F48 using a near-field Talbot-Lau interferometer. For the porphyrins, which are distinguished by their low symmetry and their abundant occurrence in organic systems, we find the theoretically expected maximal interference contrast and its expected dependence on the de Broglie wavelength. For C60F48, the observed fringe visibility is below the expected value, but the high contrast still provides good evidence for the quantum character of the observed fringe pattern. The fluorofullerenes therefore set the new mark in complexity and mass (1632 amu) for de Broglie wave experiments, exceeding the previous mass record by a factor of 2.