Quantum Potential Research Articles

Mechanical properties of the particle associated with the Laguerre–Gauss beams via the quantum potential point of view

The aim of the present work is to show that the Laguerre–Gauss beams determine a Hamiltonian system with two degrees of freedom for a particle of mass m = 1 under the action of the quantum potential determined by these beams. We show that the integral curves of the Poynting vector constitute a particular subset of solutions to the corresponding Hamilton equations and that the geometrical light rays associated with these twisted beams turn out to be the tangent straight lines to the exact optics energy trajectories at the zeroes of the quantum potential. By using the Hamiltonian formulation, we determine the velocity, the linear momentum, the angular momentum, the torque, and the areal velocity characterizing the particle associated with the Laguerre–Gauss beams.

Holographic realization of the prime number quantum potential.

We report the experimental realization of the prime number quantum potential VN (x), defined as the potential entering the single-particle Schrödinger Hamiltonian with eigenvalues given by the first N prime numbers. Using computer-generated holography, we create light intensity profiles suitable to optically trap ultracold atoms in these potentials for different N values. As a further application, we also implement a potential whose spectrum is given by the lucky numbers, a sequence of integers generated by a different sieve than the familiar Eratosthenes's sieve used for the primes. Our results pave the way toward the realization of quantum potentials with arbitrary sequences of integers as energy levels and show, in perspective, the possibility to set up quantum systems for arithmetic manipulations or mathematical tests involving prime numbers.

Torsion Fields Generated by the Quantum Effects of Macro-bodies

We generalize Einstein’s General Relativity (GR) by assuming that all matter (including macro-objects) has quantum effects. An appropriate theory to fulfill this task is Gauge Theory Gravity (GTG) developed by the Cambridge group. GTG is a “spin-torsion” theory, according to which, gravitational effects are described by a pair of gauge fields defined over a flat Minkowski background spacetime. The matter content is completely described by the Dirac spinor field, and the quantum effects of matter are identified as the spin tensor derived from the spinor field. The existence of the spin of matter results in the torsion field defined over spacetime. Torsion field plays the role of Bohmian quantum potential which turns out to be a kind of repulsive force as opposed to the gravitational potential which is attractive. The equivalence principle remains and essential in this theory so that GR is relegated to a locally approximate theory wherein the quantum effects (torsion) are negligible. As a toy model, we assume that the macro matter content can be described by the covariant Dirac equation and apply this theory to the simplest radially symmetric and static gravitational systems. Consequently, by virtue of the cosmological principle, we are led to a static universe model in which the Hubble redshifts arise from the torsion fields.

Eliminating the Wavefunction from Quantum Dynamics: The Bi-Hamilton–Jacobi Theory, Trajectories and Time Reversal

We observe that Schrödinger’s equation may be written as two real coupled Hamilton–Jacobi (HJ)-like equations, each involving a quantum potential. Developing our established programme of representing the quantum state through exact free-standing deterministic trajectory models, it is shown how quantum evolution may be treated as the autonomous propagation of two coupled congruences. The wavefunction at a point is derived from two action functions, each generated by a single trajectory. The model shows that conservation as expressed through a continuity equation is not a necessary component of a trajectory theory of state. Probability is determined by the difference in the action functions, not by the congruence densities. The theory also illustrates how time-reversal symmetry may be implemented through the collective behaviour of elements that individually disobey the conventional transformation (mathrm{T}) of displacement (scalar) and velocity (reversal). We prove that an integral curve of the linear superposition of two vectors can be derived algebraically from the integral curves of one of the constituent vectors labelled by integral curves associated with the other constituent. A corollary establishes relations between displacement functions in diverse trajectory models, including where the functions obey different symmetry transformations. This is illustrated by showing that a (mathrm{T}-obeying) de Broglie-Bohm trajectory is a sequence of points on the (non-mathrm{T}) HJ trajectories, and vice versa.

Coherence-induced quantum forces

We introduce a model that explains the phenomenon of correlation-assisted tunneling and puts it in a broader context. This model assumes the existence of an effective force of pure quantum nature between nearby fragments of correlated matter that results due to interference effects. The magnitude of this force depends on the amount of coherence between different locations; it attains a maximum value for fragments in a perfect superfluid state and disappears entirely when the fragments are in the Mott Insulator state. The force can also be explained in terms of the Bohmian quantum potential. We illustrate the implications of this force on the transport of cold atoms through simple potential structures, the triple-well harmonic trap and optical lattices.

The Identification of Mean Quantum Potential with Fisher Information Leads to a Strong Uncertainty Relation

The Cramer-Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show that the identification of the mean quantum potential, an important notion in Bohmian mechanics, with the Fisher information, leads, through the Cramer-Rao bound, to an uncertainty principle which is stronger, in general, than both Heisenberg and Robertson-Schrodinger uncertainty relations, allowing to experimentally test the validity of such an identification.

High Sensitivity Spin Defects in hBN Created by High‐Energy He Beam Irradiation

AbstractRecently the negatively charged boron vacancies () in hexagonal boron nitride (hBN) have been shown as spin defects that have great potential in quantum sensing. However, so far the sensitivity is limited by either photoluminescence (PL) intensity or the optically detected magnetic resonance (ODMR) contrast, and linewidth. In this work, the generation of these spin defects is demonstrated using high‐energy helium ion beams, and ODMR measurements with different laser and microwave powers are performed. The spin defects generated by high‐energy helium ions exhibit a high PL intensity and ODMR contrast while keeping a small linewidth, hence a good sensitivity. By comparing different fluences of helium irradiations, an optimal fluence is determined which is sufficient in creating spin defects without damaging the overall crystal lattice structure. With this optimal fluence, a high signal‐to‐noise ratio ODMR spectrum can be obtained with an accurate measurement of zero‐field splitting frequency, and a best sensitivity as . Moreover, with a focused beam, such spin defects can be created deterministically with nanometer precision.

Emergent gravity at all scales

It has recently been shown that any observed potential can in principle be generated via quantum mechanics using a suitable wave function. In this work, we consider the concrete example of the gravitational potential experienced by a test particle at length scales spanning from the planetary to the cosmological, and determine the wave function that would produce it as its quantum potential. In other words, the observed gravitational interaction at all length scales can be generated by an underlying wave function. We discuss implications of our result.

On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials

This work reports and classifies the most general construction of rational quantum potentials in terms of the generalized Hermite polynomials. This is achieved by exploiting the intrinsic relation between third-order shape-invariant Hamiltonians and the −1/x and −2x hierarchies of rational solutions of the fourth Painlevé equation. Such a relation unequivocally establishes the discrete spectrum structure, composed as the union of a finite- and infinite-dimensional sequence of equidistant eigenvalues separated by a gap. The two indices of the generalized Hermite polynomials define the dimension of the finite sequence and the gap. Likewise, the complete set of eigensolutions decomposes into two disjoint subsets, whose elements are written as the product of a polynomial times a weight function supported on the real line. These polynomials fulfill a second-order differential equation and are alternatively determined from a three-term recurrence relation, the initial conditions of which are also fixed in terms of generalized Hermite polynomials.

Orbital and Spin Dynamics of Electron’s States Transition in Hydrogen Atom Driven by Electric Field

State transition in the multiple-levels system has the great potential applications in the quantum technology. In this article we employ a deterministic approach in complex space to analyze the dynamics of the 1s–2p electron transition in the hydrogen atom. The electron’s spin motion is embodied in the framework of quantum Hamilton mechanics that allows us to examine the transition dynamics more precisely. The transition is driven by an oscillating electric field in the z-direction. The electron’s transition process can be visualized by monitoring its motion in the complex space. The quantum potential and the total energy proposed in this paper provide new indices to observe the dynamic changes of electrons in the transition process.

Analyzing quantum synchronization through Bohmian trajectories

We analyze quantum effects involved in continuous variable synchronization between two self-sustaining resonators in the framework of Bohmian mechanics. Bohmian trajectories provide visual descriptions of significant nonclassical dynamics, which allow us to characterize the level of quantum synchronization more intuitively compared with only utilizing some designed synchronization measures. It is found that in the quantum limit, the Bohmian trajectories will deviate from their corresponding semiclassical limit cycle behavior after they are distorted by the quantum potential. We explore the roles of zero-point fluctuation, superposition, and nonlocal correlation in synchronization dynamics, corresponding to the oscillators in a coherent state, superposition state, and entanglement state, respectively. We also explore the influence of squeezed Hamiltonian on spontaneous synchronization.

Quantum-enhanced radiometry via approximate quantum error correction

Quantum sensing based on exotic quantum states is appealing for practical metrology applications and fundamental studies. However, these quantum states are vulnerable to noise and the resulting quantum enhancement is weakened in practice. Here, we experimentally demonstrate a quantum-enhanced sensing scheme with a bosonic probe, by exploring the large Hilbert space of the bosonic mode and developing both the approximate quantum error correction and the quantum jump tracking approaches. In a practical radiometry scenario, we attain a 5.3 dB enhancement of sensitivity, which reaches 9.1 × 10−4 Hz−1/2 when measuring the excitation population of a receiver mode. Our results demonstrate the potential of quantum sensing with near-term quantum technologies, not only shedding new light on the quantum advantage of sensing, but also stimulating further efforts on bosonic quantum technologies.

Bohmian quantum potential and chaos

We study the quantum potential Q in a system of 2 degrees of freedom with emphasis on the regions where chaos is generated. Q goes to −∞ at the nodal points, where the wave function vanishes. But close to every nodal point, there is an unstable stagnant point in the frame of reference of the moving node, the X-point, which scatters the incoming trajectories and produces chaos. We first study the quantum potential of a wavefunction with a single nodal point, where we also give an analytical approximation of Q close to the node. Then we consider a wavefunction with infinitely many nodal points along a straight line and finally a system with a finite number of scattered nodal points in the configuration space. In all cases we find that the X-points are very close to the local maxima of Q. These maxima of Q form spikes at those times when the nodal points acquire large velocities, as they go to infinity in the inertial frame of reference (x,y).

Existence of global weak solutions to 2D reduced gravity two-and-a-half layer model

We study the global existence of weak solutions to a reduced gravity two-and-a-half layer model appearing in oceanic fluid dynamics in two-dimensional torus. Based on Faedo–Galerkin method and weak convergence method, we construct the global weak solutions which are renormalized in velocity variable, where the technique of renormalized solutions was introduced by Lacroix-Violet and Vasseur (2018). Besides, we prove that the renormalized solutions are weak solutions, which satisfy the basic energy inequality and Bresch–Desjardins entropy inequality, but not the Mellet–Vasseur type inequality. In the proof, we use the reduced gravity two-and-a-half layer model with drag forces and capillary term as approximate system. It should be pointed out that only when the capillary term vanishes, we prove the existence of renormalized solution to the approximation system, which is different from Lacroix-Violet and Vasseur (2018) with the quantum potential.

Optimized mathematical model of experimental characteristics of 14 nm TG N FinFET

Quantum effects play a dominant role in nanometric structures for which we need to use new methods to describe this phenomenon in device characterizations. In this paper an optimized mathematical model for the Tri gate (TG) N FinFET 14 nm transistor is presented. It is based on the “Bohm Quantum Potential (BQP)" theory. The result is a curve fitting of an experimental (IDS,VDS) characteristics. The proposed model uses the Berkeley “PTM (Predictive technology model)"parameters for the simulation.

Freezable bound states in the continuum for time-dependent quantum potentials

In this work, we construct time-dependent potentials for the Schrödinger equation via supersymmetric quantum mechanics. The Schrödinger equations with the generated potentials have a solution with the property that after a particular threshold time tF, when the potentials do no longer change, the evolving solution becomes a bound state in the continuum, its probability distribution freezes. After the factorization of a geometric phase, the solution satisfies a stationary Schrödinger equation with time-independent potential. The procedure can be extended to support more than one bound state in the continuum. Closed expressions for the potential, the bound states in the continuum, and scattering states are given for the examples starting from the free particle.

High-frequency traveling-wave phononic cavity with sub-micron wavelength

Thin-film gallium nitride (GaN) is a promising platform for phononic integrated circuits that hold great potential for scalable information processing processors. Here, an unsuspended traveling phononic resonator based on a high-acoustic-index-contrast mechanism is realized in GaN-on-Sapphire with a frequency up to 5 GHz, which matches the typical superconducting qubit frequency. A sixfold increment in quality factor is found when temperature decreases from room temperature (Q = 5000) to 7 K (Q = 30 000), and thus, a frequency-quality factor product of 1.5×1014 is obtained. Higher quality factors should be available when the fabrication process is further optimized. Our system shows great potential in hybrid quantum devices via the so-called circuit quantum acoustodynamics.

Energy Landscapes of Carbon Clusters from Tight-Binding Quantum Potentials.

We calculate transformation pathways between fullerene and octahedral carbon clusters and between a buckyball and its bowl-shaped isomer. The energies and gradients are provided by efficient tight-binding potentials, which are interfaced to our Energy Landscape exploration software. From the global energy landscape, we extract the mechanistic and kinetic parameters as a function of temperature, and compare our results to selected density functional theory (DFT) (PBE/cc-pVTZ) benchmarks. Infrared spectra are calculated to provide data for experimental identification of the clusters and differentiation of their isomers. Our results suggest that the formation of buckyballs from a buckybowl will be suppressed at elevated temperatures (above around 5250 K) due to entropic effects, which may provide useful insight into the detection of cosmic fullerenes.

Towards a quantum interface between spin waves and paramagnetic spin baths

Spin waves have risen as promising candidate information carriers for the next generation of information technologies. Recent experimental demonstrations of their detection using electron spins in diamond pave the way towards studying the back-action of a controllable paramagnetic spin bath on the spin waves. Here, we present a quantum theory describing the interaction between spin waves and paramagnetic spins. As a case study we consider an ensemble of nitrogen-vacancy spins in diamond in the vicinity of an Yttrium-Iron-Garnet thin film. We show how the back-action of the ensemble results in strong and tuneable modifications of the spin-wave spectrum and propagation properties. These modifications include the full suppression of spin-wave propagation and, in a different parameter regime, the enhancement of their propagation length by $\sim 50\%$. Furthermore, we show how the spin wave thermal fluctuations induce a measurable frequency shift of the paramagnetic spins in the bath. This shift results in a thermal dispersion force that can be measured optically and/or mechanically with a diamond mechanical resonator. In addition, we use our theory to compute the spin wave-mediated interaction between the spins in the bath. We show that all the above effects are measurable by state-of-the-art experiments. Our results provide the theoretical foundation for describing hybrid quantum systems of spin waves and spin baths, and establish the potential of quantum spins as active control, sensing, and interfacing tools for spintronics.

Electromechanical behaviors in piezotronic quantum wells based on a quantum-corrected phenomenological theory

Piezotronic devices have attracted a great deal of attention due to their potential applications in self-powered tactile sensing, nano-device memory, human-electronic interface, etc. As the size of piezotronic devices shrinks, some interesting quantum effects begin to appear. In this paper, we establish a theory oriented to the engineering application of piezoelectric semiconductors, called quantum-corrected phenomenological (QCP) theory, by coupling the density-gradient theory and the linear piezoelectricity theory through Gauss's law. For numerical verification, we specifically studied the electromechanical behaviors in GaN/AlGaN heterostructure quantum wells (QWs) with both infinite and finite barrier height. The results of electron density, electric potential, and quantum potential are provided, and their dependence on the doping density, the applied stress, and the Al mole fraction is investigated. Some interesting quantum effects are revealed, and their influencing mechanisms are well investigated from a macroscopic perspective. Not only do the conclusions drawn in this paper enrich the fundamental understanding of the piezotronic effect in a QW structure, but also the proposed QCP theory can serve as a valuable tool for future device engineering.