Wave-particle duality of C(60) molecules

Immobilization of zinc porphyrin complexes on pyridine-functionalized glass surfaces

In order to immobilize sublimable and fluorescent dye molecules on transparent surfaces for the detection of far field molecular interference experiments, we investigate the potential of pyridine-functionalized glass substrates as coordination sites for the zinc complex of tetraphenylporphyrin (ZnTPP). Borosilicate glass is functionalized with 4-(6-(ethoxydimethylsilyl)hexyloxy)pyridine in order to cover the glass surface with pyridine subunits. ZnTPP molecules are deposited by sublimation through mechanical masks of various sizes in a high-vacuum chamber. The resulting micropatterns are analyzed using epifluorescence microscopy which also allows us to define a measure for the quality of molecular immobilization. We observe a reduced mobility and an increased efficiency for the trapping of ZnTPP on pyridine-functionalized surfaces.

Cold-atom-induced control of an optomechanical device

We consider a cavity with a vibrating end mirror and coupled to a Bose-Einstein condensate. The cavity field mediates the interplay between mirror and collective oscillations of the atomic density. We study the implications of this dynamics and the possibility of an indirect diagnostic. Our predictions can be observed in a realistic setup that is central to the current quest for mesoscopic quantumness.

Wave packet interferometry with attosecond precision and picometric structure

Wave packet (WP) interferometry is applied to the vibrational WPs of the iodine molecule. Interference fringes of quantum waves weave highly regular space-time images called "quantum carpets." The structure of the carpet has picometre and femtosecond resolutions, and changes drastically depending on the amplitudes and phases of the vibrational eigenstates composing the WP. In this review, we focus on the situation where quantum carpets are created by two counter-propagating nuclear vibrational WPs. Such WPs can be prepared with either a single or double femtosecond (fs) laser pulse. In the single pulse scheme, the relevant situation appears around the half revival time. Similar situations can be generated with a pair of fs laser pulses whose relative phase is stabilized on the attosecond time scale. In the latter case we can design the quantum carpet by controlling the timing between the phase-locked pulses. We demonstrate this carpet design and visualize the designed carpets by the fs pump-probe measurements, tuning the probe wavelength to resolve the WP density-distribution along the internuclear axis with ~3 pm spatial resolution and ~100 fs temporal resolution.

Beyond spontaneously broken symmetry in Bose-Einstein condensates

Spontaneous symmetry breaking (SSB) for Bose-Einstein condensates cannot treat phase off-diagonal effects, and thus cannot explain Bell inequality violations. We describe another situation that is beyond a SSB treatment: an experiment where particles from two (possibly macroscopic) condensate sources are used for conjugate measurements of the relative phase and populations. Off-diagonal phase effects are characterized by a "quantum angle" and observed via "population oscillations," signaling quantum interference of macroscopically distinct states.

Superconducting nanowires fabricated using molecular templates

The application of single molecules as templates for nanodevices is a promising direction for nanotechnology. We use suspended deoxyribonucleic acid molecules or single-walled carbon nanotubes as templates for fabricating superconducting devices and then study these devices at cryogenic temperatures. Because the resulting nanowires are extremely thin, comparable in diameter to the templating molecule itself, their electronic state is highly susceptible to thermal fluctuations. The most important family of these fluctuations are the collective ones, which take the form of Little's phase slips or ruptures of the many-electron organization. These phase slips break the quantum coherence of the superconducting condensate and render the wire slightly resistive (i.e., not fully superconducting), even at temperatures substantially lower than the critical temperature of the superconducting transition. At low temperatures, for which the thermal fluctuations are weak, we observe the effects of quantum fluctuations, which lead to the phenomenon of macroscopic quantum tunneling. The modern fabrication method of molecular templating, reviewed here, can be readily implemented to synthesize nanowires from other materials, such as normal metals, ferromagnetic alloys, and semiconductors.

Wave and particle in molecular interference lithography

The wave-particle duality of massive objects is a cornerstone of quantum physics and a key property of many modern tools such as electron microscopy, neutron diffraction or atom interferometry. Here we report on the first experimental demonstration of quantum interference lithography with complex molecules. Molecular matter-wave interference patterns are deposited onto a reconstructed Si(111) 7x7 surface and imaged using scanning tunneling microscopy. Thereby both the particle and the quantum wave character of the molecules can be visualized in one and the same image. This new approach to nanolithography therefore also represents a sensitive new detection scheme for quantum interference experiments.

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.

A superconducting NbN detector for neutral nanoparticles

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 allows retrieval of 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.

All-electric spin control in interference single electron transistors

Single particle interference lies at the heart of quantum mechanics. The archetypal double-slit experiment(1) has been repeated with electrons in vacuum(2,3) up to the more massive C(60) molecules.(4) Mesoscopic rings threaded by a magnetic flux provide the solid-state analogues.(5,6) Intramolecular interference has been recently discussed in molecular junctions.(7-11) Here we propose to exploit interference to achieve all-electrical control of a single electron spin in quantum dots, a highly desirable property for spintronics(12-14) and spin-qubit applications.(15-19) The device consists of an interference single electron transistor,(10,11) where destructive interference between orbitally degenerate electronic states produces current blocking at specific bias voltages. We show that in the presence of parallel polarized ferromagnetic leads the interplay between interference and the exchange interaction on the system generates an effective energy renormalization yielding different blocking biases for majority and minority spins. Hence, by tuning the bias voltage full control over the spin of the trapped electron is achieved.

Two-center double-capture interference in fast He2+ + H2 collisions

We report the first observation of Young-type interference effects in a two-electron transfer process. These effects change strongly as the projectile velocity changes in fast (1.2 and 2.0 MeV) He(2+) + H(2) collisions as manifested in strong variations of the double-electron capture rates with the H(2) orientation. This is consistent with fully quantum mechanical calculations, which ignore sequential electron transfer, and a simple projectile de Broglie wave picture assuming that two-electron transfer probabilities are higher in collisions where the projectile passes close to either one of the H(2) nuclei.

Deterministic ultracold ion source targeting the Heisenberg limit

The major challenges to fabricate quantum processors and future nano-solid-state devices are material modification techniques with nanometer resolution and suppression of statistical fluctuations of dopants or qubit carriers. Based on a segmented ion trap with mK laser-cooled ions we have realized a deterministic single-ion source which could operate with a huge range of sympathetically cooled ion species, isotopes or ionic molecules. We have deterministically extracted a predetermined number of ions on demand and have measured a longitudinal velocity uncertainty of 6.3 m/s and a spatial beam divergence of 600 microrad. We show in numerical simulations that if the ions are cooled to the motional ground state (Heisenberg limit) nanometer spatial resolution can be achieved.

Transverse-coherence properties of the free-electron-laser FLASH at DESY

A general theoretical approach based on the decomposition of statistical fields into a sum of independently propagating transverse modes was used for the analysis of the coherence properties of the new free-electron laser source FLASH operated at 13.7 nm wavelength. The analysis shows that several transverse modes are contributing to the total radiation field of FLASH. The results of theoretical calculations are compared with measurements using Young's double-slit experiment. The coherence lengths in the horizontal and in the vertical directions 20 m downstream from the source are estimated at 300 and 250 microm, respectively.

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.

Nonlocal quantum macroscopic superposition in a high-thermal low-purity state

Quantum state exchange between light and matter is an important ingredient for future quantum information networks as well as other applications. Photons are the fastest and simplest carriers of information for transmission but in general, it is difficult to localize and store photons, so usually one prefers choosing matter as quantum memory elements. Macroscopic superposition and nonlocal quantum interactions have received considerable interest for this purpose over recent years in fields ranging from quantum computers to cryptography, in addition to providing major insights into physical laws. However, these experiments are generally performed either with equipment or under conditions that are unrealistic for practical applications. Ideally, the two can be combined using conventional equipment and conditions to generate a "quantum teleportation"-like state, particularly with a very small amount of purity existing in an overall highly mixed thermal state (relatively low decoherence at high temperatures). In this study we used an experimental design to demonstrate these principles. We performed optical coherence tomography (OCT) using a thermal source at room temperatures of a specifically designed target in the sample arm. Here, position uncertainty (i.e., dispersion) was induced in the reference arm. In the sample arm (target) we placed two glass plates separated by a different medium while altering position uncertainty in the reference arm. This resulted in a chirped signal between the glass plate reflective surfaces in the combined interferogram. The chirping frequency, as measured by the fast Fourier transform (FFT), varies with the medium between the plates, which is a nonclassical phenomenon. These results are statistically significant and occur from a superposition between the glass surface and the medium with increasing position uncertainty, a true quantum-mechanical phenomenon produced by photon pressure from two-photon interference. The differences in chirping frequency with medium disappears when second-order correlations are removed by dual balanced detection, confirming the proposed mechanism. We demonstrated that increasing position uncertainty at one site leads to position uncertainty (quantum position probability amplitude) nonlocally via second-order correlations (two-photon probability amplitude) from a low coherence thermal source (low purity, high local entropy). The implications, first, are that the phenomenon cannot be explained through classical mechanisms but can be explained within the context of quantum mechanics, particularly relevant to the second-order correlations where controversy exists. More specifically, we provide the theoretical framework that these results indicate a nonlocal macroscopic superposition is occurring through a two-photon probability amplitude-induced increase in the target position probability amplitude uncertainty. In addition, as the experiments were performed with a classical source at room temperature, it supports both the quantum-mechanical properties of second-order correlations and that macroscopic superposition is obtainable in a target not in a single coherent state (mixed state). Future work will focus on generalizing the observations outside the current experimental design and creating embodiments that allow practical application of the phenomenon.

Evidence of wave-particle duality for single fast hydrogen atoms

We report the direct observation of interference effects in a Young's double-slit experiment where the interfering waves are two spatially separated components of the de Broglie wave of single 1.3 MeV hydrogen atoms formed close to either target nucleus in H++H2 electron-transfer collisions. Quantum interference strongly influences the results even though the hydrogen atoms have a de Broglie wavelength, lambda_{dB}, as small as 25 fm.

Time-resolved detection of single-electron interference

We demonstrate real-time detection of self-interfering electrons in a double quantum dot embedded in an Aharonov-Bohm interferometer, with visibility approaching unity. We use a quantum point contact as a charge detector to perform time-resolved measurements of single-electron tunneling. With increased bias voltage, the quantum point contact exerts a back-action on the interferometer leading to decoherence. We attribute this to emission of radiation from the quantum point contact, which drives noncoherent electronic transitions in the quantum dots.

Gas-phase formation of large neutral alkaline-earth metal tryptophan complexes

We report on the first observation of isolated large neutral metal amino acid complexes such as Trp(n)Me(k), with Me=Ca, Ba, Sr, cluster combinations covering n=1...33, k=0..2 and masses beyond 6500 u. The cluster beam is generated using UV laser desorption from a mixed powder of alkaline-earth metal salts and tryptophan inside a cluster mixing channel. The particles are detected using VUV photoionization followed by time-of-flight mass spectroscopy. The enhanced stability of metal amino acid clusters over pure amino acid clusters is substantiated in molecular dynamics simulations by determining the gain in binding energy related to the inclusion of the metal atoms.

Delayed-choice test of quantum complementarity with interfering single photons

We report an experimental test of quantum complementarity with single-photon pulses sent into a Mach-Zehnder interferometer with an output beam splitter of adjustable reflection coefficient R. In addition, the experiment is realized in Wheeler's delayed-choice regime. Each randomly set value of R allows us to observe interference with visibility V and to obtain incomplete which-path information characterized by the distinguishability parameter D. Measured values of V and D are found to fulfill the complementarity relation V2+D2 < or =1.

Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment

In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.

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.

Diffraction of fast atomic projectiles during grazing scattering from a LiF(001) surface

Light atoms and molecules with energies from 300 eV to 25 keV are scattered under a grazing angle of incidence from a LiF(001) surface. For impact of neutral projectiles along low index directions for strings of atoms in the surface plane we observe a defined pattern of intensity spots in the angular distribution of reflected particles which is consistently described using concepts of diffraction theory and specific features of grazing scattering of atoms from insulator surfaces. Experimental results for scattering of H, D, 3He, and 4He atoms as well as H2 and D2 molecules can be unequivocally referred to atom diffraction with de Broglie wavelengths as low as about 0.001 Angstroms.

Signatures of strong momentum localization via entanglement of translational and internal states

We show that atoms or molecules subject to fields that couple their internal and translational (momentum) states may undergo a crossover from randomization (diffusion) to strong localization (sharpening) of their momentum distribution. The predicted crossover should be manifest by a drastic change of the interference pattern as a function of the coupling fields.

Axicon lens for coherent matter waves

We have realized a conical matter wave lens. The repulsive potential of a focused laser beam was used to launch a Bose-Einstein condensate into a radially expanding wavepacket whose perfect ring shape was ensured by energy conservation. In spite of significant interactions between atoms, the spatial and velocity widths of the ring along its radial dimension remained extremely narrow, as also confirmed by numerical simulations. Our results open the possibility for cylindrical atom optics without the perturbing effect of mean-field interactions.

Speckle patterns with atomic and molecular de Broglie waves

We have developed a nozzle source that delivers a continuous beam of atomic helium or molecular hydrogen having a high degree of transverse coherence and with adequate optical brightness to enable new kinds of experiments. Using this source we have measured single slit diffraction patterns and the first ever speckle-diffraction patterns using atomic and molecular de Broglie waves. Our results suggest fruitful application of coherent matter beams in dynamic scattering and diffractive imaging at short wavelength and with extreme surface sensitivity.

Neutron phase imaging and tomography

We report how a setup consisting of three gratings yields quantitative two- and three-dimensional images depicting the quantum-mechanical phase shifts of neutron de Broglie wave packets induced by the influence of macroscopic objects. Since our approach requires only a little spatial and chromatic coherence it provides a more than 2 orders of magnitude higher efficiency than existing techniques. This dramatically reduces the required measurement time for computed phase tomography and opens up the way for three-dimensional investigations of previously inaccessible quantum-mechanical phase interactions of neutrons with matter.

High finesse opto-mechanical cavity with a movable thirty-micron-size mirror

We report on the demonstration of a high finesse micro-optomechanical system and identify potential applications ranging from optical cooling to weak force detection to massive quantum superpositions. The system consists of a high quality diameter flat dielectric mirror cut from a larger substrate with a focused ion beam and attached to an atomic force microscope cantilever. Cavity ring-down measurements performed on a 25 mm long Fabry-Pérot cavity with the 30 microm mirror at one end show an optical finesse of 2100. Numerical calculations show that the finesse is not diffraction limited and that orders of magnitude higher finesse should be possible. A mechanical quality factor of more than 10(5) at pressures below 10(-3) mbar is demonstrated for the cantilever with a mirror attached.

Magic numbers, excitation levels, and other properties of small neutral He4 clusters (N⩽50)

The ground-state energies and the radial and pair distribution functions of neutral 4He clusters are systematically calculated by the diffusion Monte Carlo method in steps of one 4He atom from 3 to 50 atoms. In addition the chemical potential and the low-lying excitation levels of each cluster are determined with high precision. These calculations reveal that the "magic numbers" observed in experimental 4He cluster size distributions, measured for free jet gas expansions by nondestructive matter-wave diffraction, are not caused by enhanced stabilities. Instead they are explained in terms of an enhanced growth due to sharp peaks in the equilibrium concentrations in the early part of the expansion. These peaks appear at cluster sizes which can just accommodate one more additional stable excitation. The good agreement with experiment provides not only experimental confirmation of the energy level and the chemical potential calculations, but also evidence for a new mechanism which can lead to magic numbers in cluster size distributions. By accounting for the falloff of the radial density distributions at the surface and a size-dependent surface tension, the energy levels are demonstrated to be consistent with a modified Rayleigh model of surface excitations. The compressibility coefficient of these small clusters is found to be one order of magnitude smaller than the bulk compressibility.

Qubit assisted probing of coherence between mesoscopic states of an apparatus

I present a general scheme through which the evidence of a superposition involving distinct states of a mesoscopic system can be probed. The scheme relies on a single qubit being coupled to a mesoscopic harmonic oscillator in such a way that it can be used to both prepare and probe a superposition of states of the oscillator. Two potentially realizable implementations, one with a single flux qubit coupled to an LC circuit, and the other with a single ion-trap qubit coupled to the collective motion of several ions, are proposed.

Radiative correction to the helium dimer interaction energy

The leading-order radiative correction to the helium-helium interaction energy at the equilibrium internuclear distance has been calculated for the first time. The result is -1.27(2) mK. The calculations were performed using a new technique of evaluating expectation values of singular operators in connection with the most accurate wave functions of He(2) available today-the exponentially correlated Gaussian functions.

Molecular beams with a tunable velocity

The merging of molecular beam methods with those of accelerator physics has yielded new tools to manipulate the motion of molecules. Over the last few years, decelerators, lenses, bunchers, traps, and storage rings for neutral molecules have been demonstrated. Molecular beams with a tunable velocity and with a tunable width of the velocity distribution can now be produced, and are expected to become a valuable tool in a variety of physical chemistry and chemical physics experiments. Here we present a compact molecular beam machine, capable of producing 3D spatially focused packets of state-selected accelerated or decelerated molecules.

Direct observation of thitherto unobservable quantum phenomena by using electrons

Fundamental aspects of quantum mechanics, which were discussed only theoretically as "thought experiments" in the 1920s and 1930s, have begun to frequently show up in nanoscopic regions owing to recent rapid progress in advanced technologies. Quantum phenomena were once regarded as the ultimate factors limiting further miniaturization trends of microstructured electronic devices, but now they have begun to be actively used as the principles for new devices such as quantum computers. To directly observe what had been unobservable quantum phenomena, we have tried to develop bright and monochromatic electron beams for the last 35 years. Every time the brightness of an electron beam improved, fundamental experiments in quantum mechanics became possible, and quantum phenomena became observable by using the wave nature of electrons.

Testing gravity-driven collapse of the wave function via cosmogenic neutrinos

It is pointed out that the Diósi-Penrose ansatz for gravity-induced quantum state reduction can be tested by observing oscillations in the flavor ratios of neutrinos originating at cosmological distances. Since such a test would be almost free of environmental decoherence, testing the ansatz by means of a next generation neutrino detector such as IceCube would be much cleaner than by experiments proposed so far involving superpositions of macroscopic systems. The proposed microscopic test would also examine the universality of the superposition principle at unprecedented cosmological scales.

The spectra of mixed He3–He4 droplets

The diffusion Monte Carlo technique is used to calculate and analyze the excitation spectrum of 3He atoms bound to a cluster of 4He atoms by using a previously determined optimum filling of single-fermion orbits with well-defined orbital angular momentum L, spin S, and parity quantum numbers. The study concentrates on the energies and shapes of the three kinds of states for which the fermionic part of the wave function is a single Slater determinant: maximum L or maximum S states within a given orbit, and fully polarized clusters. The picture that emerges is that of systems with strong shell effects, whose binding and excitation energies are essentially determined by averages over configuration at fixed number of particles and spin, i.e., by the monopole properties of an effective Hamiltonian.

Indispensable role of quantum theory in the brain dynamics

Recently, Tegmark pointed out that the superposition of ion states involved in the superposition of firing and resting states of a neuron quickly decohere. It undoubtedly indicates that neural networks cannot work as quantum computers, or computers taking advantage of coherent states. Does it also mean that the brain can be modeled as a neural network obeying classical physics? Here we show that it does not mean that the brain can be modeled as a neural network obeying classical physics. A brand new perspective in research of neural networks from quantum theoretical aspect is presented.

From Pedigree Cats to Fluffy-Bunnies

We consider two distinct classes of quantum mechanical entanglement. The first "pedigree" class consists of delicate highly entangled states, which hold great potential for use in future quantum technologies. By focusing on Schrodinger cat states, we demonstrate not only the possibilities these states hold but also the difficulties they present. The second "fluffy-bunny" class is made up of robust states that arise naturally as a result of measurements and interactions between particles. This class of entanglement may be responsible for the classical-like world we see around us.

Towards quantum superpositions of a mirror: an exact open systems analysis

We analyze the recently proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester, assuming that the mirror's dynamics contains a nonunitary term of the Lindblad-type proportional to -[q,[q,rho]], with q the position operator for the center of mass of the mirror, and rho the statistical operator. We derive an exact formula for the fringe visibility for this system. We discuss the consequences of our result for tests of environmental decoherence and of collapse models. In particular, we find that with the conventional parameters for the continuous spontaneous localization model of state vector collapse, maintenance of coherence is expected to within an accuracy of at least 1 part in 10(8). Increasing the apparatus coupling to environmental decoherence may lead to observable modifications of the fringe visibility, with time dependence given by our exact result.

Non-Markovian particle dynamics in continuously controlled quantum gases

For a quantum gas, being subject to continuous feedback of a macroscopic observable, the single-particle dynamics is studied. Despite feedback-induced particle correlations, it is shown that analytic solutions are obtained by formally extending the single-particle Hilbert space by an auxiliary degree of freedom. The particle's motion is then fed by colored noise, which effectively maps quantum-statistical correlations onto the single particle. Thus, the single particle in the continuously controlled gas follows a non-Markovian trajectory in phase space.

A quantum biological hypothesis of human secondary dentinogenesis

It is hypothesized that human coronal secondary dentin (SD) is a final classical mechanical (CM) response to a chain of prior quantum mechanical (QM) transductions of the information of initial CM occlusal loadings of enamel. Such CM energy is transduced into QM quanta (as protons) that are translocated centripetally via clustered water (CW), (as "proton wires"), that is structurally related to both enamel prism sheath and hydroxyapatite crystal hydration shells. These quanta pass into odontoblastic cell processes (OP), lying within dentinal tubules (DT). OP's contain abundant parallel arrays of cylindrical microtubules (MT). These are the sites of two further CW-related QM events: (i) proton translocation associated with conformal changes of MT tubulin protein dimers; and (ii) coherent energetic oscillations within the CW filling the MT's hollow cores. Finally, these quanta pass into the odontoblastic soma, where QM wave function collapse transduces this information into a final CM state that initiates the processes of SD formation. A critical portion of this hypothesis may be experimentally tested.