Quantum Mechanical Limit Research Articles

Addressing the Hubble tension in Yukawa cosmology?

In Yukawa cosmology, a recent discovery revealed a relationship between baryonic matter and the dark sector. The relation is described by the parameter α and the long-range interaction parameter λ - an intrinsic property of the graviton. Applying the uncertainty relation to the graviton raises a compelling question: Is there a quantum mechanical limit to the measurement precision of the Hubble constant (H0)? We argue that the uncertainty relation for the graviton wavelength λ can be used to explain a running of H0 with redshift. We show that the uncertainty in time has an inverse correlation with the value of the Hubble constant. That means that the measurement of the Hubble constant is intrinsically linked to length scales (redshift) and is connected to the uncertainty in time. On cosmological scales, we found that the uncertainty in time is related to the look-back time quantity. For measurements with a high redshift value, there is more uncertainty in time, which leads to a smaller value for the Hubble constant. Conversely, there is less uncertainty in time for local measurements with a smaller redshift value, resulting in a higher value for the Hubble constant. Therefore, due to the uncertainty relation, the Hubble tension is believed to arise from fundamental limitations inherent in cosmological measurements. Finally, our findings indicate that the mass of the graviton fluctuates with specific scales, suggesting a possible mass-varying mechanism for the graviton.

Driven generalized quantum Rayleigh-van der Pol oscillators: Phase localization and spectral response.

Driven classical self-sustained oscillators have been studied extensively in the context of synchronization. Using the master equation, this work considers the classically driven generalized quantum Rayleigh-van der Pol oscillator, which is characterized by linear dissipative gain and loss terms as well as three nonlinear dissipative terms. Since two of the nonlinear terms break the rotational phase space symmetry, the Wigner distribution of the quantum mechanical limit cycle state of the undriven system is, in general, not rotationally symmetric. The impact of the symmetry-breaking dissipators on the long-time dynamics of the driven system are analyzed as functions of the drive strength and detuning, covering the deep quantum to near-classical regimes. Phase localization and frequency entrainment, which are required for synchronization, are discussed in detail. We identify a large parameter space where the oscillators exhibit appreciable phase localization but only weak or no entrainment, indicating the absence of synchronization. Several observables are found to exhibit the analog of the celebrated classical Arnold tongue; in some cases, the Arnold tongue is found to be asymmetric with respect to vanishing detuning between the external drive and the natural oscillator frequency.

Molecular collisions: From near-cold to ultra-cold

In the past two decades, the revolutionary technologies of creating cold and ultracold molecules have provided cutting-edge experiments for studying the fundamental phenomena of collision physics. To a large degree, the recent explosion of interest in the molecular collisions has been sparked by dramatic progress of experimental capabilities and theoretical methods, which permit molecular collisions to be explored deep in the quantum mechanical limit. Tremendous experimental advances in the field have already been achieved, and the authors, from an experimental perspective, provide a review of these studies for exploring the nature of molecular collisions occurring at temperatures ranging from the Kelvin to the nanoKelvin regime, as well as for applications of producing ultracold molecules.

Neutrinos in curved spacetime: Particle mixing and flavor oscillations

We present a quantum field theoretical approach to the vacuum neutrino oscillations in curved space, we analyze the non--trivial interplay between quantum field mixing and field quantization in curved space and derive new oscillation formulae. We compute the formulae explicitly in the spatially flat FLRW metrics for universes dominated by a cosmological constant and by radiation. We evaluate the transition probabilities in the Schwarzschild black hole metric, and we show that the Hawking radiation affects the oscillations of neutrinos. We show that our results are consistent with those of previous analyses when the quantum mechanical limit is considered.

The standard quantum limit of coherent beam combining

Coherent beam combining refers to the process of generating a bright output beam by merging independent input beams of individually diffusing relative phases by locking them to each other. We report the first quantum mechanical noise limit calculations for coherent beam combining and compare our results to quantum-limited amplification. Our coherent beam combining scheme is based on an optical Fourier transformation which renders the scheme compatible with integrated optics combined with feed-back stabilization of the relative phases. The scheme can be layed out for an arbitrary number of input beams and approaches the shot noise limit for a large number of inputs.

Anomalously Large Spectral Shifts near the Quantum Tunnelling Limit in Plasmonic Rulers with Subatomic Resolution.

The resonance wavelength of a coupled plasmonic system is extremely sensitive to the distance between its metallic surfaces, resulting in "plasmon rulers". We explore this behavior in the subnanometer regime using self-assembled monolayers of bis-phthalocyanine molecules in a nanoparticle-on-mirror (NPoM) construct. These allow unprecedented subangstrom control over spacer thickness via choice of metal center, in a gap-size regime at the quantum-mechanical limit of plasmonic enhancement. A dramatic shift in the coupled plasmon resonance is observed as the gap size is varied from 0.39 to 0.41 nm. Existing theoretical models are unable to account for the observed spectral tuning, which requires inclusion of the quantum-classical interface, emphasizing the need for new treatments of light at the subnanoscale.

Universal few-body physics and cluster formation

A recent rejuvenation of experimental and theoretical interest in the physics of few- body systems has provided deep, fundamental insights into a broad range of problems. Few-body physics is a cross-cutting discipline not restricted to conventional subject ar- eas such as nuclear physics or atomic or molecular physics. To a large degree, the recent explosion of interest in this subject has been sparked by dramatic enhancements of experimental capabilities in ultracold atomic systems over the past decade, which now permit atoms and molecules to be explored deep in the quantum mechanical limit with controllable two-body interactions. This control, typically enabled by magnetic or electromagnetically-dressed Fano-Feshbach resonances, allows in particular access to the range of universal few-body physics, where two-body scattering lengths far exceed all other length scales in the problem. The Efimov effect, where 3 particles experienc- ing short-range interactions can counterintuitively exhibit an infinite number of bound or quasi-bound energy levels, is the most famous example of universality. Tremendous progress in the field of universal Efimov physics has taken off, driven particularly by a combination of experimental and theoretical studies in the past decade, and prior to the first observation in 2006, by an extensive set of theoretical studies dating back to 1970. Because experimental observations of Efimov physics have usually relied on resonances or interference phenomena in three-body recombination, this connects naturally with the processes of molecule formation in a low temperature gas of atoms or nucleons, and more generally with N-body recombination processes. Some other topics not closely related to the Efimov effect are also reviewed in this article, including ...

System Plus Reservoir Approach to Quantum Brownian Motion of a Rod-Like Particle

Quantum Brownian motion of a rod-like particle is investigated in the frame work of system plus reservoir model. The quantum mechanical and classical limit for both translational and rotational motions are discussed. Correlation functions, fluctuation-dissipation relations and mean squared values of translational and rotational motions are obtained.

Extension of the CPT theorem to non-Hermitian Hamiltonians and unstable states

We extend the CPT theorem to quantum field theories with non-Hermitian Hamiltonians and unstable states. Our derivation is a quite minimal one as it requires only the time-independent evolution of scalar products, invariance under complex Lorentz transformations, and a non-standard but nonetheless perfectly legitimate interpretation of charge conjugation as an antilinear operator. The first of these requirements does not force the Hamiltonian to be Hermitian. Rather, it forces its eigenvalues to either be real or to appear in complex conjugate pairs, forces the eigenvectors of such conjugate pairs to be conjugates of each other, and forces the Hamiltonian to admit of an antilinear symmetry. The latter two requirements then force this antilinear symmetry to be CPT, while forcing the Hamiltonian to be real rather than Hermitian. Our work justifies the use of the CPT theorem in establishing the equality of the lifetimes of unstable particles that are charge conjugates of each other. We show that the Euclidean time path integrals of a CPT-symmetric theory must always be real. In the quantum-mechanical limit the key results of the PT symmetry program of Bender and collaborators are recovered, with the C-operator of the PT symmetry program being identified with the linear component of the charge conjugation operator.

Quantum mechanical limit to plasmonic enhancement as observed by surface-enhanced Raman scattering.

Plasmonic nanostructures enable light to be concentrated into nanoscale 'hotspots', wherein the intensity of light can be enhanced by orders of magnitude. This plasmonic enhancement significantly boosts the efficiency of nanoscale light-matter interactions, enabling unique linear and nonlinear optical applications. Large enhancements are often observed within narrow gaps or at sharp tips, as predicted by the classical electromagnetic theory. Only recently has it become appreciated that quantum mechanical effects could emerge as the feature size approaches atomic length-scale. Here we experimentally demonstrate, through observations of surface-enhanced Raman scattering, that the emergence of electron tunnelling at optical frequencies limits the maximum achievable plasmonic enhancement. Such quantum mechanical effects are revealed for metallic nanostructures with gap-widths in the single-digit angstrom range by correlating each structure with its optical properties. This work furthers our understanding of quantum mechanical effects in plasmonic systems and could enable future applications of quantum plasmonics.

Correction: Corrigendum: Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators

Micromechanical resonators are promising replacements for quartz crystals for timing and frequency references owing to potential for compactness, integrability with CMOS fabrication processes, low cost, and low power consumption. To be used in high performance reference application, resonators should obtain a high quality factor. The limit of the quality factor achieved by a resonator is set by the material properties, geometry and operating condition. Some recent resonators properly designed for exploiting bulk-acoustic resonance have been demonstrated to operate close to the quantum mechanical limit for the quality factor and frequency product (Q-f). Here, we describe the physics that gives rise to the quantum limit to the Q-f product, explain design strategies for minimizing other dissipation sources, and present new results from several different resonators that approach the limit.

Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators

Micromechanical resonators are promising replacements for quartz crystals for timing and frequency references owing to potential for compactness, integrability with CMOS fabrication processes, low cost, and low power consumption. To be used in high performance reference application, resonators should obtain a high quality factor. The limit of the quality factor achieved by a resonator is set by the material properties, geometry and operating condition. Some recent resonators properly designed for exploiting bulk-acoustic resonance have been demonstrated to operate close to the quantum mechanical limit for the quality factor and frequency product (Q-f). Here, we describe the physics that gives rise to the quantum limit to the Q-f product, explain design strategies for minimizing other dissipation sources, and present new results from several different resonators that approach the limit.

Multi‐Charged Conjugated Polyelectrolytes as a Versatile Work Function Modifier for Organic Electronic Devices

Despite the excellent work function adjustability of conjugated polyelectrolytes (CPEs), which induce a vacuum level shift via the formation of permanent dipoles at the CPE/metal electrode interface, the exact mechanism of electron injection through the CPE electron transport layer (ETL) remains unclear. In particular, understanding the ionic motion within the CPE ETLs when overcoming the sizable injection barrier is a significant challenge. Because the ionic functionality of CPEs is a key component for such functions, a rigorous analysis using highly controlled ion density (ID) in CPEs is crucial for understanding the underlying mechanism. Here, by introducing a new series of CPEs with various numbers of ionic functionalities, energy level tuning at such an interface can be determined directly by adjusting the ID in the CPEs. More importantly, these series CPEs indicate that two different mechanisms must be invoked according to the CPE thickness. The formation of permanent interfacial dipoles is critical with respect to electron injection through CPE ETL (≤ 10 nm, quantum mechanical tunneling limit), whereas electron injection through thick CPE ETL (20–30 nm) is dominated by the reorientation of the ionic side chains under a given electric field.

Sensitivity of force-detected NMR spectroscopy with resonator-induced polarization

In the low-temperature regime where the thermal polarization $P$ is of order unity and spin-lattice relaxation is ``frozen out,'' resonator-induced relaxation can be used to polarize a nuclear-spin sample for optimal detection sensitivity. We characterize the potential of resonator-induced polarization for enhancing the sensitivity of nuclear-magnetic-resonance spectroscopy. The sensitivities of two detection schemes are compared, one involving detection of a polarized sample dipole and the other involving detection of spin-noise correlations in an unpolarized sample. In the case where the dominant noise source is instrument noise associated with resonator fluctuations and with detection of the mechanical motion, a simple criterion can be used to compare the two schemes. Polarizing the sample improves sensitivity when $P$ is larger than the signal-to-noise ratio for detection of a fully-polarized spin during a single transient. Even if the instrument noise is decreased to a level near the quantum-mechanical limit, it is larger than spin noise for unpolarized samples containing up to a few tens of nuclei. Under these conditions, spin polarization of order unity would enhance spectroscopic detection sensitivity by an order of magnitude or more. In the limiting case where signal decay is due to resonator-induced dissipation during ideal spin locking, and where resonator fluctuations are the noise source, the only parameter of the spin-resonator system that affects the sensitivity per spin is the ratio of frequency to temperature. A balance between the coupling strength, the noise power, and the signal lifetime causes the cancellation of other parameters from the sensitivity formula. Partial cancellation of parameters, associated with a balance between the same three quantities, occurs more generally when the resonator is both the dominant noise source and the dominant source of signal decay. An intrinsic sensitivity limit exists for resonant detection of coherent spin evolution, due to the fact that the detector causes signal decay by enhancing the spins' spontaneous emission. For a single-spin sample, the quantum-limited signal-to-noise ratio for resonant detection is $1/3$. In contrast to the sensitivity, the time required for sample polarization between transients depends strongly on resonator parameters. We discuss resonator design and show that for a torsional resonator, the coupling is optimal when the resonator's magnetization remains aligned with the applied field during the mechanical oscillations.

Nonlinear optical properties of novel tunable, one dimensional molecular superlattice polymers (heteroarylene methines) containing alternating aromatic and quinoid segments

We have investigated the spectral dispersion of second molecular hyperpolarizability γ (−ω′; ω, −ω, ω) of three derivatives of heteroarylene methine by antiresonant ring interferometric nonlinear spectroscopic technique using femtosecond modelocked Ti:sapphire laser in the spectral range of 725–820 nm. The observed dispersion of γ has been explained in the framework of three-essential states model involving the ground state, a one-photon excited state and a two-photon excited state. The spectral response of the hyperpolarizability has been correlated with the electronic and chemical structures of the three derivatives of heteroarylene methine. The estimated γ values have been compared to the fundamental quantum mechanical limit. We have found for the first time that the heteroarylene methines approach this limit within a factor of 2 while even the best known molecule so far falls short of this limit by a factor of 30.

Dispersive interactions in graphitic nanostructures

The Casimir interaction between graphitic nanostructures, such as carbon nanotubes and graphene sheets, is investigated at the quantum mechanical limit (T=0K) using a quantum electrodynamical approach for absorbing and dispersive media. It is found that the nanotube/nanotube interaction in a double wall carbon nanotube configuration is profoundly affected by the collective low frequency excitations of individual nanotubes. It is shown that pronounced, low frequency peaks in the nanotube electron energy loss spectra are a main factor contributing to the strength of the intertube attraction. The graphene/graphene force is also investigated. It is obtained that the graphene optical transparency is the main reason for the reduced attraction as compared to the one for perfect metals. This study presents a unified approach for electromagnetic interactions in graphitic nanostructures, which is able to account for their unique electronic and response properties and geometry configurations.

A wideband, low-noise superconducting amplifier with high dynamic range

An ideal amplifier has very low noise, operates over a broad frequency range, and has large dynamic range. Unfortunately, it is difficult to obtain all of these characteristics simultaneously. For example, modern transistor amplifiers offer multi-octave bandwidths and excellent dynamic range, but their noise remains far above the limit set by the uncertainty principle of quantum mechanics. Parametric amplifiers can reach the quantum-mechanical limit, but generally are narrow band and have very limited dynamic range. Here we describe a parametric amplifier that overcomes these limitations through the use of a travelling-wave geometry and the nonlinear kinetic inductance of a superconducting transmission line. We measure gain extending over 2 GHz on either side of an 11.56 GHz pump tone and place an upper limit on the added noise of 3.4 photons at 9.4 GHz. The dynamic range is very large, and the concept can be applied from gigahertz frequencies to ∼ 1 THz.

Is it the boundaries or disorder that dominates electron transport in semiconductor `billiards'?

AbstractSemiconductor billiards are often considered as ideal systems for studying dynamical chaos in the quantum mechanical limit. In the traditional picture, once the electron's mean free path, as determined by the mobility, becomes larger than the device, disorder is negligible and electron trajectories are shaped by specular reflection from the billiard walls alone. Experimental insight into the electron dynamics is normally obtained by magnetoconductance measurements. A number of recent experimental studies have shown these measurements to be largely independent of the billiard's exact shape, and highly dependent on sample‐to‐sample variations in disorder. In this paper, we discuss these more recent findings within the full historical context of work on semiconductor billiards, and offer strong evidence that small‐angle scattering at the sub‐100 nm length‐scale dominates transport in these devices. This has important implications for the role these devices can play for experimental tests of ideas in quantum chaos.

Accretion magnetar in the close binary system 4U 2206+54

The magneto-rotational evolution of a neutron star in the massive binary system 4U 2206+54 is discussed in light of the recent discovery of its 5555 s rotational period and its average rate of spin-down. We show that this behavior of the neutron star means that its magnetic field exceeds the quantum mechanical critical limit and it is an accretion magnetar. The system’s evolution is explained by wind driven mass transfer without formation of an accretion disk. The constant character of the x-ray source indicates a steady rate of accretion and raises anew the question of the stability of the boundary of the magnetosphere of a star undergoing spherical accretion. A solution to this problem is also a key to determining the mechanism for the slowing down of the star’s rotation.

Dispersion cancellation with phase-sensitive Gaussian-state light

Franson's paradigm for nonlocal dispersion cancellation [J. D. Franson, Phys. Rev. A {\bf 45,} 3126 (1992)] is studied using two kinds of jointly Gaussian-state signal and reference beams with phase-sensitive cross correlations. The first joint signal-reference state is nonclassical, with a phase-sensitive cross correlation that is at the ultimate quantum-mechanical limit. It models the outputs obtained from continuous-wave spontaneous parametric downconversion. The second joint signal-reference state is classical---it has a proper $P$ representation---with a phase-sensitive cross correlation that is at the limit set by classical physics. Using these states we show that a version of Franson's nonlocal dispersion cancellation configuration has essentially identical quantum and classical explanations \em except rm for the contrast obtained, which is much higher in the quantum case than it is in the classical case. This work bears on Franson's recent paper [J. D. Franson, arXiv:0907:5196 [quant-ph]], which asserts that there is no classical explanation for all the features seen in quantum nonlocal dispersion cancellation.