Classical Analog Research Articles

Structured light analogy of quantum squeezed states

Quantum optics has advanced our understanding of the nature of light and enabled applications far beyond what is possible with classical light. The unique capabilities of quantum light have inspired the migration of some conceptual ideas to the realm of classical optics, focusing on replicating and exploiting non-trivial quantum states of discrete-variable systems. Here, we further develop this paradigm by building the analogy of quantum squeezed states using classical structured light. We have found that the mechanism of squeezing, responsible for beating the standard quantum limit in quantum optics, allows for overcoming the “standard spatial limit” in classical optics: the light beam can be “squeezed” along one of the transverse directions in real space (at the expense of its enlargement along the orthogonal direction), where its width becomes smaller than that of the corresponding fundamental Gaussian mode. We show that classical squeezing enables nearly sub-diffraction and superoscillatory light focusing, which is also accompanied by the nanoscale phase gradient of the size in the order of λ/100 (λ/1000), demonstrated in the experiment (simulations). Crucially, the squeezing mechanism allows for continuous tuning of both features by varying the squeezing parameter, thus providing distinctive flexibility for optical microscopy and metrology beyond the diffraction limit and suggesting further exploration of classical analogies of quantum effects.

2,3-Bis(2-pyridyl)thieno[3,4-b]pyrazine and its ruthenium(II) complexes: a new bidentate bridging ligand for enhanced metal-metal communication.

A new bidentate bridging ligand, bis(2-pyridyl)thieno[3,4-b]pyrazine is reported, along with its mono- and bi-metallic Ru(II) complexes as representative examples. Spectroscopic, electrochemical and X-ray crystallographic characterization of these species is reported, with the separation of the two Ru(III)/Ru(II) couples of the bimetallic complex suggesting better metal-metal communication than classical polypyridyl analogues.

Optical orbital angular momentum analogy to the Stern-Gerlach experiment.

Symmetry breaking has been shown to reveal interesting phenomena in physical systems. A notable example is the fundamental work of Otto Stern and Walther Gerlach [Stern and Zerlach, Z. Physik9, 349 (1922)10.1007/BF01326983] nearly 100 years ago demonstrating a spin angular momentum (SAM) deflection that differed from classical theory. Here we use non-separable states of SAM and orbital angular momentum (OAM), known as vector vortex modes, to demonstrate how a classical optics analogy can be used to reveal this non-separability, reminiscent of the work carried out by Stern and Gerlach. We show that by implementing a polarization insensitive device to measure the OAM, the SAM states can be deflected to spatially resolved positions.

Exponentially localized interface eigenmodes in finite chains of resonators

AbstractThis paper studies wave localization in chains of finitely many resonators. There is an extensive theory predicting the existence of localized modes induced by defects in infinitely periodic systems. This work extends these principles to finite‐sized systems. We consider one‐dimensional, finite systems of subwavelength resonators arranged in dimers that have a geometric defect in the structure. This is a classical wave analog of the Su–Schrieffer–Heeger model. We prove the existence of a spectral gap for defectless finite dimer structures and find a direct relationship between eigenvalues being within the spectral gap and the localization of their associated eigenmode. Then, for sufficiently large‐size systems, we show the existence and uniqueness of an eigenvalue in the gap in the defect structure, proving the existence of a unique localized interface mode. To the best of our knowledge, our method, based on Chebyshev polynomials, is the first to characterize quantitatively the localized interface modes in systems of finitely many resonators.

A Method Evaluating Spontaneous Polarization from X-Ray Diffraction Data ∼ A Classical Analogue to the Method Using Berry Phase

A Method Evaluating Spontaneous Polarization from X-Ray Diffraction Data ∼ A Classical Analogue to the Method Using Berry Phase

On the possibility of implementing a quantum entanglement distribution in a biosystem: Microtubules

The paper considers the possibility of implementing a quantum entanglement distribution in the cell microtubule. It has been shown that a quantum entanglement distribution proposed in the paper determines the process of quantum state teleportation through microtubule tryptophan chain. The work shows that the system of tryptophans in a microtubule essentially is a quantum network that consists of: spatially spaced nodes — tryptophans, quantum communication channels connecting tryptophans and qubits transmitted through these communication channels. The connection between the process of quantum teleportation in living nature and its classical analogue is discussed. The quantum protocol established in the work determines the possible principle of quantum information transmission in biosystems and also in the similar nanostructures.

Phonon pumping by modulating the ultrastrong vacuum

The vacuum (i.e., the ground state) of a system in ultrastrong light-matter coupling contains particles that cannot be emitted without any dynamical perturbation and is thus called virtual. We propose a protocol for inducing and observing real mechanical excitations of a mirror enabled by the virtual photons in the ground state of a tripartite system, where a resonant optical cavity is ultrastrongly coupled to a two-level system (qubit) and, at the same time, optomechanically coupled to a mechanical resonator. Real phonons are coherently emitted when the frequency of the two-level system is modulated at a frequency comparable to that of the mechanical resonator and, therefore much lower than the optical frequency. We demonstrate that this hybrid effect is a direct consequence of the virtual photon population in the ground state. Within a classical physics analogy, attaching a weight to a spring only changes its resting position, whereas dynamically modulating the weight makes the system oscillate. In our case, however, the weight is the vacuum itself. We propose and accurately characterize a hybrid superconducting-optomechanical setup based on available state-of-the-art technology, where this effect can be experimentally observed.

Study on the passivation properties of austenitic stainless steel 316LN based on the point defect model

The Point Defect Model was successfully developed to study the passivation of 316LN. Steel's passive film exhibits n-type semi-conductivity with interstitial cations as the dominant point defect. The transfer coefficients αi and rate constants ki are independent of the applied potential but vary with temperature. The electronic structure of the barrier layer (bl) is discussed as a degenerate defect semiconductor in which the bl comprises essentially the depletion zone with the electronic charge and the electron-hole charge being concentrated at the metal/bl and the bl/solution interfaces, respectively. The closest classical analog is postulated to be a tunnel diode.

Adiabatic driving, geometric phases, and the geometric tensor for classical states

We use the Hilbert space formulation of classical mechanics, known as the Koopman–von Neumann formalism, to study adiabatic driving, geometric phases, and the geometric tensor for classical states. In close relation to what happens to a quantum state, a classical Koopman–von Neumann eigenstate will acquire a geometric phase factor expiΦ after a closed variation of the parameters λ in its associated Hamiltonian. The explicit form of Φ is then derived for integrable systems, and its relation with the Hannay angle is shown. Additionally, we use quantum formulas to write an adiabatic gauge potential that generates adiabatic unitary flow between classical eigenstates, and we explicitly show the relationship between the potential and the classical geometric phase. We also define a classical analog of the geometric tensor, thus defining a Fubini–Study metric for classical states, and we use the singularities of the tensor to link the transition from Arnold–Liouville integrability to chaos with some of the mathematical formalism of quantum phase transitions. While the formulas and definitions we use originate in quantum mechanics, all the results found are purely classical, no classical or semiclassical limit is ever taken.

MACE: A Machine-learning Approach to Chemistry Emulation

The chemistry of an astrophysical environment is closely coupled to its dynamics, the latter often found to be complex. Hence, to properly model these environments a 3D context is necessary. However, solving chemical kinetics within a 3D hydro simulation is computationally infeasible for even a modest parameter study. In order to develop a feasible 3D hydro-chemical simulation, the classical chemical approach needs to be replaced by a faster alternative. We present mace, a Machine-learning Approach to Chemistry Emulation, as a proof-of-concept work on emulating chemistry in a dynamical environment. Using the context of AGB outflows, we have developed an architecture that combines the use of an autoencoder (to reduce the dimensionality of the chemical network) and a set of latent ordinary differential equations (that are solved to perform the temporal evolution of the reduced features). Training this architecture with an integrated scheme makes it possible to successfully reproduce a full chemical pathway in a dynamical environment. mace outperforms its classical analog on average by a factor of 26. Furthermore, its efficient implementation in PyTorch results in a sublinear scaling with respect to the number of hydrodynamical simulation particles.

Asymmetric transmission through a classical analogue of the Aharonov-Bohm ring

Asymmetric transmission through a classical analogue of the Aharonov-Bohm ring

Simulation of Gaussian wave packets used to illustrate elementary quantum mechanics scenarios

In this paper we numerically solve the time dependent Schrödinger equation for scenarios using wave packets. These examples include the free wave packet, which we use to show the difference between group and phase velocities, the packet in a harmonic oscillator potential with non-trivial initial conditions in one and two dimensions, which is compared with their classical analogs to show how Ehrenfest theorem holds. We also include simulations of the diffraction through the single and double slit potentials, the refraction with a step potential and the dispersion by a central potential. The aim of this paper is to illustrate with simulations, nowadays easy to implement, scenarios that can help explaining the basics of the wave-particle duality.

Information encoding and encryption in acoustic analogues of qubits

Cryptography is crucial in protecting sensitive information and ensuring secure transactions in a time when data security and privacy are major concerns. Traditional cryptography techniques, which depend on mathematical algorithms and secret keys, have historically protected against data breaches and illegal access. With the advent of quantum computers, traditional cryptography techniques are at risk. In this work, we present a cryptography idea using logical phi-bits, which are classical analogues of quantum bits (qubits) and are supported by driven acoustic metamaterials. The state of phi-bits displays superpositions similar to quantum bits, with complex amplitudes and phases. We present a representation of the state vector of single and multi-phi-bit systems. The state vector of multiple phi-bits system lies in a complex exponentially scaling Hilbert space and is used to encode information or messages. By changing the driving conditions of the metamaterial, the information can be encrypted with exceptional security and efficiency. We illustrate experimentally the practicality and effectiveness of encoding and encryption of a message using a 5 phi-bits system and emphasize the scalability of this approach to an N phi-bits system with the same processing time.

Quantum kernels for classifying dynamical singularities in a multiqubit system

Dynamical quantum phase transition is a critical phenomenon involving out-of-equilibrium states and broken symmetries without classical analogy. However, when finite-sized systems are analyzed, dynamical singularities of the rate function can appear, leading to a challenging physical characterization when parameters are changed. Here, we report a quantum support vector machine algorithm that uses quantum Kernels to classify dynamical singularities of the rate function for a multiqubit system. We illustrate our approach using N long-range interacting qubits subjected to an arbitrary magnetic field, which induces a quench dynamics. Inspired by physical arguments, we introduce two different quantum Kernels, one inspired by the ground state manifold and the other based on a single state tomography. Our accuracy and adaptability results show that this quantum dynamical critical problem can be efficiently solved using physically inspiring quantum Kernels. Moreover, we extend our results for the case of time-dependent fields, quantum master equation, and when we increase the number of qubits.

Universality of quantum time dilation

Time dilation is a difference in measured time between two clocks that either move with different velocities or experience different gravitational potentials. Both of these effects stem from the theory of relativity and are usually associated with classically defined trajectories, characterized by position, momentum, and acceleration. However, when spatial degrees of freedom are treated in a quantum way and a clock is allowed to be in a coherent superposition of either two momenta or two heights, additional quantum corrections to classical time dilation appear, called kinematic and gravitational quantum time dilations, respectively. We show that similarly to its classical counterpart, kinematic quantum time dilation is universal for any clock mechanism, while gravitational quantum time dilation is not. We also show that although both of these effects reduce to incoherent averaging of different classical time dilation contributions, there exists an additional quantum time dilation effect that has no classical analog and can be extracted from higher-order corrections to the system’s Hamiltonian.

Non-Hermitian Casimir effect of magnons

There has been a growing interest in non-Hermitian quantum mechanics. The key concepts of quantum mechanics are quantum fluctuations. Quantum fluctuations of quantum fields confined in a finite-size system induce the zero-point energy shift. This quantum phenomenon, the Casimir effect, is one of the most striking phenomena of quantum mechanics in the sense that there are no classical analogs and has been attracting much attention beyond the hierarchy of energy scales, ranging from elementary particle physics to condensed matter physics, together with photonics. However, the non-Hermitian extension of the Casimir effect and the application to spintronics have not yet been investigated enough, although exploring energy sources and developing energy-efficient nanodevices are its central issues. Here we fill this gap. By developing a magnonic analog of the Casimir effect into non-Hermitian systems, we show that this non-Hermitian Casimir effect of magnons is enhanced as the Gilbert damping constant (i.e., the energy dissipation rate) increases. When the damping constant exceeds a critical value, the non-Hermitian Casimir effect of magnons exhibits an oscillating behavior, including a beating one, as a function of the film thickness and is characterized by the exceptional point. Our result suggests that energy dissipation serves as a key ingredient of Casimir engineering.

"We Died Here, Obedient to Her Laws": The Reception of Sparta in the Lost Cause and Confederate Memorialization

Abstract: Although scholars have explored many aspects of the Lost Cause, few have focused on the presence of classical analogies in its many iterations. Citing Confederate monuments, memorial speeches, and other sources, this essay explores previously under-analyzed classical reception in Confederate memorialization. It argues that white Southerners invoked the ancient Spartans frequently to reinforce specific elements of the Lost Cause mythology. Comparing Confederate soldiers to Spartans, especially in the context of the Battle of Thermopylae, upheld a key Lost Cause belief in the superiority of the Confederate soldier while also deflecting blame for the Confederacy's military loss solely onto the factor of overwhelming US numbers and arms. Former Confederates also identified Confederate women as Spartan to emphasize their loyalty and sacrifice to the South during the war—another major aspect of the Lost Cause. By referencing the classical world in such a manner, postwar white Southerners continued a rich antebellum tradition of citing antiquity to defend conservative Southern values.

Weak Force Sensing Based on Optical Parametric Amplification in a Cavity Optomechanical System Coupled in Series with Two Oscillators

AbstractIn the realm weak force sensing, an important issue is to suppress fundamental noise (quantum noise and thermal noise), as they limit the accuracy of force measurement. In this study, a weak force sensing scheme that combines a degenerate optical parametric amplifier (OPA) and an auxiliary mechanical oscillator into a cavity optomechanical system to reduce quantum noise is investigated. It is demonstrated that the noise reduction of two coupled oscillators depends on their norm mode splitting. and provide a classic analogy and quantum perspective for further clarification. Besides, the noise reduction mechanism of OPA is to reduce the fluctuation of photon number and enhance the squeezing of the cavity field. A specific design is proposed that aimed at enhancing the joint effect of both, beyond what can be achieved using OPA alone or two series coupled oscillators. This scheme provides a new perspective for deeper understanding of cavity field squeezing and auxiliary oscillator in force sensing.

Quantum-to-Classical Neural Network Transfer Learning Applied to Drug Toxicity Prediction.

Toxicity is a roadblock that prevents an inordinate number of drugs from being used in potentially life-saving applications. Deep learning provides a promising solution to finding ideal drug candidates; however, the vastness of chemical space coupled with the underlying matrix multiplication means these efforts quickly become computationally demanding. To remedy this, we present a hybrid quantum-classical neural network for predicting drug toxicity utilizing a quantum circuit design that mimics classical neural behavior by explicitly calculating matrix products with complexity . Leveraging the Hadamard test for efficient inner product estimation rather than the conventionally used swap test, we reduce the number of qubits by half and remove the need for quantum phase estimation. Directly computing matrix products quantum mechanically allows for learnable weights to be transferred from a quantum to a classical device for further training. We apply our framework to the Tox21 data set and show that it achieves commensurate predictive accuracy to the model's fully classical analogue. Additionally, we demonstrate that the model continues to learn, without disruption, once transferred to a fully classical architecture. We believe that combining the quantum advantage of reduced complexity and the classical advantage of noise-free calculation will pave the way for more scalable machine learning models.

The inverted pendulum as a classical analog of the EFT paradigm

The inverted pendulum is a mechanical system with a rapidly oscillating pivot point. Using techniques similar in spirit to the methodology of effective field theories, we derive an effective Lagrangian that allows for the systematic computation of corrections to the so-called Kapitza equation. The derivation of the effective potential of the system requires non-trivial matching conditions, which need to be determined order by order in the power-counting of the problem. The convergence behavior of the series is investigated on the basis of high-order results obtained by this method. The results from this analysis can be used to determine the regions of parameter space, in which the inverted position of the pendulum is stable or unstable to high precision.