Quantum-classical Transition Research Articles

Magnon antibunching in a nanomagnet

We investigate the correlations of magnons inside a nanomagnet and identify a regime of parameters where the magnons become antibunched, i.e., where there is a large probability for occupation of the single-magnon state. This antibunched state is very different from magnons at thermal equilibrium and microwave-driven coherent magnons. We further obtain the steady state analytically and describe the magnon dynamics numerically, and ascertain the stability of such antibunched magnons over a large window of magnetic anisotropy, damping and temperature. This means that the antibunched magnon state is feasible in a wide class of low-damping magnetic nanoparticles. To detect this quantum effect, we propose to transfer the quantum information of magnons to photons by magnon-photon coupling and then measure the correlations of photons to retrieve the magnon correlations. Our findings may provide a promising platform to study quantum-classical transitions and for designing a single magnon source.

Effects of time-energy correlation strength in molecular entangled photon spectroscopy

In this paper, we explore the time-energy domain quantum-classical transition comparing a classical pump-probe experiment on a diatomic molecule to its quantum enhanced counterpart, where the pump and probe pulses are substituted by the signal and idler beams of a spontaneous parametric down conversion (SPDC) source. Absorption of biphotons generated with SPDC exploits quantum time-energy entanglement to enhance the overall yield and selectivity of the process, when compared with a classical pump-probe setup, while maintaining femtosecond time resolution. We systematically study the effects of correlation strength on process efficiency and selectivity, comparing the results to classical pump-probe spectra. An excitation scheme to improve the yield based on spectral narrowing of biphotons is shown. The results indicate that the quantum improvements in yield are caused by a more efficient use of the total power available for the process.

Ladder climbing and autoresonant acceleration of the spherical plasma density wave

Ladder climbing (LC) and autoresonance (AR) of the spherical plasma density wave are studied for the first time. The governing equation of the perturbed spherical density wave in the energy level space based on a hydrodynamic model of the electron plasma is presented, and it is demonstrated that the quantum LC and classical AR transition can be achieved in the spherical plasma. The asymptotic thresholds of the LC and AR transition of the spherical plasma wave are obtained analytically and confirmed numerically. We find that the spherical wave energy is concentrated to the sphere center as the density wave climbs to the higher level, the spherical plasma behaves obvious compression character, and the perturbed density of the sphere center even can be amplified to 100 times larger of the initial perturbed density. Compared to the one-dimensional case, the energy spectrum of the spherical plasma wave shifts upward, and the energy level spacing of the spherical plasma wave is broadened. These result in the facts that the spherical plasma needs the larger driving strength to achieve the LC and AR, while the total perturbed density of the spherical plasma always is larger than that of the one-dimensional case.

Quantum-classical mechanics: Luminescence spectra in polymethine dyes and J-aggregates. Nature of the small Stokes shift

Abstract It can be shown that the joint and full-fledged (beyond the adiabatic approximation) motion of light electrons and very heavy nuclei in molecular and chemical physics in the framework of quantum mechanics can be only singular. This singularity is damped in a new theoretical approach called dozy-chaos mechanics or quantum-classical mechanics. Earlier, the effectiveness of the damping procedure for the above singularity was demonstrated in the simplest case of quantum-classical mechanics (of quantum-classical transitions), namely, by quantum-classical mechanics of elementary electron-charge transfers in condensed media and its applications to the shape of optical absorption bands in polymethine dyes and their aggregates and to other problems. In this article, on the basis of the quantum-classical mechanics of elementary electron-charge transfers, we find out the nature of the luminescence band shape and the small Stokes shift in polymethine dyes and J-aggregates. The very small experimental value of the Stokes shift (1 nm in the J-band) is explained by two factors, both of which are associated with a high degree of self-organization of molecular quantum transitions in J-aggregates. The first of these is related to the stimulation of the electronic transition in the J-chromophore by the chaotic dynamics (weak dozy chaos) of the reorganization of the nuclear environment, which leads to the well-known narrow and red-shifted absorption J-band. The second factor is associated with the spontaneous loosening of the excited electronic state immediately before the act of the photon’s creation by the electron in spontaneous emission. For polymethine dyes and J-aggregates, the universal effect of spontaneous dynamic loosening turns out to be abnormally strong, it must be supposed, due to the very extended π -electron systems undergoing the quantum-classical transitions there. A quantitative explanation is also given for the position and shape of the optical bands in J-aggregates for luminescence and optical absorption in the case of an admixture of monomers of a polymethine dye in an aqueous solution. The experimental fact of the absence of the optical band of the monomers on the shortwave wing of the J-band of luminescence with its apparent presence on the shortwave wing of the J-band of optical absorption is explained by a significant increase in the dynamic self-organization of quantum-classical transitions in J-aggregates as compared to just a small increase in the dynamic self-organization of these transitions in monomers upon the change from optical absorption to luminescence.

Quantum correlation interferometry in reflection: Application to the quantum–classical transition, decoherence, and indirect measurement

A three-body quantum correlation is calculated for two particles reflecting from a mirror. Correlated interference, a consequence of conservation of energy and momentum, occurs for states in which the order of reflection is indeterminate. The resulting quantum joint probability density function exhibits interference with diverse characteristics, depending on the coherence lengths of the substates. Marginal probability density functions can contain information about the quantum nature of all three bodies, even if only one particle is measured. Microscopic particles reflecting from a mesoscopic or macroscopic mirror are used to illustrate unique features of this three-body correlation interferometry. The microscopic momentum exchanged then generates mirror substates which interfere to produce quantum effects which do not vanish with increasing mirror mass, while the small displacement between these mirror states can yield negligible environmental decoherence times.

Coherence-Length Effects in Fast Atom Diffraction at Grazing Incidence

Coherence properties of projectiles, found relevant in ion-atom collisions, are investigated by analyzing the influence of the degree of coherence of the atomic beam on interference patterns produced by grazing-incidence fast-atom diffraction (GIFAD or FAD). The transverse coherence length of the projectiles, which depends on the incidence conditions and the collimating setup, determines the overall characteristics of GIFAD distributions. We show that for atoms scattered from a LiF(001) surface after a given collimation, we can modify the interference signatures of the angular spectra by varying the total impact energy, while keeping the normal energy as a constant. Also, the role played by the geometry of the collimating aperture is analyzed, comparing results for square and circular openings. Furthermore, we study the spot-beam effect, which is due to different focus points of the impinging particles. We show that when a region narrower than a single crystallographic channel is coherently illuminated by the atomic beam, the spot-beam contribution strongly affects the visibility of the interference structures, contributing to the gradual quantum-classical transition of the projectile distributions.

Experimental test of decoherence theory using electron matter waves

A controlled decoherence environment is studied experimentally by free electron interaction with semiconducting and metallic plates. The results are compared with physical models based on decoherence theory to investigate the quantum-classical transition. The experiment is consistent with decoherence theory and rules out established Coulomb interaction models in favor of plasmonic excitation models. In contrast to previous decoherence experiments, the present experiment is sensitive to the onset of decoherence.

Trajectory-based understanding of the quantum–classical transition for barrier scattering

The quantum–classical transition of wave packet barrier scattering is investigated using a hydrodynamic description in the framework of a nonlinear Schrödinger equation. The nonlinear equation provides a continuous description for the quantum–classical transition of physical systems by introducing a degree of quantumness. Based on the transition equation, the transition trajectory formalism is developed to establish the connection between classical and quantum trajectories. The quantum–classical transition is then analyzed for the scattering of a Gaussian wave packet from an Eckart barrier and the decay of a metastable state. Computational results for the evolution of the wave packet and the transmission probabilities indicate that classical results are recovered when the degree of quantumness tends to zero. Classical trajectories are in excellent agreement with the transition trajectories in the classical limit, except in some regions where transition trajectories cannot cross because of the single-valuedness of the transition wave function. As the computational results demonstrate, the process that the Planck constant tends to zero is equivalent to the gradual removal of quantum effects originating from the quantum potential. This study provides an insightful trajectory interpretation for the quantum–classical transition of wave packet barrier scattering.

Dissipative tunnelling by means of scaled trajectories

Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schrödinger–Langevin or Kostin quantum–classical transition wave equation is used and applied resulting in a scaled differential equation of motion. A Gaussian wave packet solution to the resulting scaled Kostin nonlinear equation is assumed and compared to the same solution for the scaled linear Caldirola–Kanai equation. The resulting scaled trajectories are obtained at different dynamical regimes and friction cases, showing the gradual decoherence process in this open dynamics. Theoretical results show that the transmission probabilities are always higher in the Kostin approach than in the Caldirola–Kanai approach in the presence or not of an external electric field. This discrepancy should be understood due to the presence of an environment since the corresponding open dynamics should be governed by nonlinear quantum equations, whereas the second approach is issued from an effective Hamiltonian within a linear theory.

Classicalization by phase space measurements

This article provides an illustration of the measurement approach to the quantum–classical transition suitable for beginning graduate students. As an example, we apply this framework to a quantum system with a general quadratic Hamiltonian, and obtain the exact solution of the dynamics for an arbitrary measurement strength using phase space methods.

Quantum-classical transition in dissipative systems through scaled trajectories

A nonlinear quantum–classical transition wave equation is proposed for dissipative systems within the Caldirola-Kanai model. Equivalence of this transition equation to a scaled Schrödinger equation is proved. The dissipative dynamics is then studied in terms of what we call scaled trajectories following the standard procedure used in Bohmian mechanics. These trajectories depend on a continuous parameter allowing us a smooth transition from Bohmian to classical trajectories. Arrival times and actual momentum distribution functions are also analyzed. The propagation of a Gaussian wave packet in a viscid medium under the presence of constant, linear and harmonic potentials is studied. The gradual decoherence process and localization are easily visualized and understood within this theoretical framework.

Quantum plasmonic nanoantennas

We study plasmonic excitations in the limit of few electrons, in one-atom-thick sodium chains. We compare the excitations to classical localized plasmon modes, and we find for the longitudinal mode a quantum-classical transition around 10 atoms. The transverse mode appears at much higher energies than predicted classically for all chain lengths. The electric field enhancement is also considered, which is made possible by considering the effects of electron-phonon coupling on the broadening of the electronic spectra. Large field enhancements are possible on the molecular level allowing us to consider the validity of using molecules as the ultimate small size limit of plasmonic antennas. Additionally, we consider the case of a dimer system of two sodium chains, where the gap can be considered as a picocavity, and we analyze the charge-transfer states and their dependence on the gap size as well as chain size. Our results and methods are useful for understanding and developing ultrasmall, tunable, and novel plasmonic devices that utilize quantum effects that could have applications in quantum optics, quantum metamaterials, cavity-quantum electrodynamics, and controlling chemical reactions, as well as deepening our understanding of localized plasmons in low-dimensional molecular systems.

Chirped-frequency excitation of gravitationally bound ultracold neutrons

Ultracold neutrons confined in the Earth's gravitational field display quantized energy levels that have been observed for over a decade. In recent resonance spectroscopy experiments [T. Jenke et al., Nature Phys. 7, 468 (2011)], the transition between two such gravitational quantum states was driven by the mechanical oscillation of the plates that confine the neutrons. Here we show that, by applying a sinusoidal modulation with slowly varying frequency (chirp), the neutrons can be brought to higher excited states by climbing the energy levels one by one. The proposed experiment should make it possible to observe the quantum-classical transition that occurs at high neutron energies. Furthermore, it provides a technique to realize superpositions of gravitational quantum states, to be used for precision tests of gravity at short distances.

Quantum–classical transition in the Caldeira–Leggett model

The quantum–classical transition in the Caldeira–Leggett model is investigated in the framework of the functional renormalization group method. It is shown that a divergent quadratic term arises in the action due to the heat bath in the model. By removing the divergence with a frequency cutoff we considered the critical behavior of the model. The critical exponents belonging to the susceptibility and the correlation length are determined and their independence of the frequency cutoff and the renormalization scheme is shown.

High-Temperature Quantum–Classical Transition in Solid Methane

Some experimental studies have reported that physical properties of solid methane exhibit a number of anomalies in the temperature interval between \(0.5 T _\mathrm{tr}\) and \(T _\mathrm{tr}\) (\(T _\mathrm{tr}\) is triple point of methane). This paper contains an attempt of systematization and theoretical interpretation of the observed anomalies.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

Feedback-induced bistability of an optically levitated nanoparticle: A Fokker-Planck treatment

Optically levitated nanoparticles have recently emerged as versatile platforms for investigating macroscopic quantum mechanics and enabling ultrasensitive metrology. In this article we theoretically consider two damping regimes of an optically levitated nanoparticle cooled by cavityless parametric feedback. Our treatment is based on a generalized Fokker-Planck equation derived from the quantum master equation presented recently and shown to agree very well with experiment [1]. For low damping, we find that the resulting Wigner function yields the single-peaked oscillator position distribution and recovers the appropriate energy distribution derived earlier using a classical theory and verified experimentally [2]. For high damping, in contrast, we predict a double-peaked position distribution, which we trace to an underlying bistability induced by feedback. Unlike in cavity-based optomechanics, stochastic processes play a major role in determining the bistable behavior. To support our conclusions, we present analytical expressions as well as numerical simulations using the truncated Wigner function approach. Our work opens up the prospect of developing bistability-based devices, characterization of phase-space dynamics, and investigation of the quantum-classical transition using levitated nanoparticles.

Trajectory description of the quantum–classical transition for wave packet interference

The quantum–classical transition for wave packet interference is investigated using a hydrodynamic description. A nonlinear quantum–classical transition equation is obtained by introducing a degree of quantumness ranging from zero to one into the classical time-dependent Schrödinger equation. This equation provides a continuous description for the transition process of physical systems from purely quantum to purely classical regimes. In this study, the transition trajectory formalism is developed to provide a hydrodynamic description for the quantum–classical transition. The flow momentum of transition trajectories is defined by the gradient of the action function in the transition wave function and these trajectories follow the main features of the evolving probability density. Then, the transition trajectory formalism is employed to analyze the quantum–classical transition of wave packet interference. For the collision-like wave packet interference where the propagation velocity is faster than the spreading speed of the wave packet, the interference process remains collision-like for all the degree of quantumness. However, the interference features demonstrated by transition trajectories gradually disappear when the degree of quantumness approaches zero. For the diffraction-like wave packet interference, the interference process changes continuously from a diffraction-like to collision-like case when the degree of quantumness gradually decreases. This study provides an insightful trajectory interpretation for the quantum–classical transition of wave packet interference.

Multiparticle Correlations in Mesoscopic Scattering: Boson Sampling, Birthday Paradox, and Hong-Ou-Mandel Profiles.

The interplay between single-particle interference and quantum indistinguishability leads to signature correlations in many-body scattering. We uncover these with a semiclassical calculation of the transmission probabilities through mesoscopic cavities for systems of noninteracting particles. For chaotic cavities we provide the universal form of the first two moments of the transmission probabilities over ensembles of random unitary matrices, including weak localization and dephasing effects. If the incoming many-body state consists of two macroscopically occupied wave packets, their time delay drives a quantum-classical transition along a boundary determined by the bosonic birthday paradox. Mesoscopic chaotic scattering of Bose-Einstein condensates is, then, a realistic candidate to build a boson sampler and to observe the macroscopic Hong-Ou-Mandel effect.

Niels Bohr as philosopher of experiment: Does decoherence theory challenge Bohr׳s doctrine of classical concepts?

Niels Bohr׳s doctrine of the primacy of “classical concepts” is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr׳s doctrine was primarily an epistemological thesis, derived from his understanding of the functional role of experiment. A hitherto largely overlooked disagreement between Bohr and Heisenberg about the movability of the “cut” between measuring apparatus and observed quantum system supports the view that, for Bohr, such a cut did not originate in dynamical (ontological) considerations, but rather in functional (epistemological) considerations. As such, both the motivation and the target of Bohr׳s doctrine of classical concepts are of a fundamentally different nature than what is understood as the dynamical problem of the quantum-to-classical transition. Our analysis suggests that, contrary to claims often found in the literature, Bohr׳s doctrine is not, and cannot be, at odds with proposed solutions to the dynamical problem of the quantum–classical transition that were pursued by several of Bohr׳s followers and culminated in the development of decoherence theory.