Quantum Friction Research Articles

Fluctuational electrodynamics in and out of equilibrium

Dispersion forces between neutral material bodies are due to fluctuations of the polarization of the bodies. For bodies in equilibrium these forces are often referred to as Casimir–Lifshitz forces. For bodies in relative motion, in addition to the Casimir–Lifshitz force, a lateral frictional force (“quantum friction”, in the zero temperature limit) comes into play. The widely accepted theory of the fluctuation-induced forces is based on the “fluctuational electrodynamics”, when the Maxwell equations are supplemented by random current sources responsible for the fluctuations of the medium polarization. The first part of our paper touches on some conceptual issues of the theory, such as the dissipation-less limit and the link between Rytov’s approach and quantum electrodynamics. We point out the problems with the dissipation-less plasma model (with its unphysical double pole at zero frequency) which still appears in the literature. The second part of the paper is devoted to “quantum friction”, in a broad sense, and it contains some novel material. In particular, it is pointed out that in weakly dissipative systems the friction force may not be a stationary process. It is shown, using an “exact” (nonperturbative) quantum treatment, that under appropriate conditions, an instability can occur when the kinetic energy (due to the relative motion between the bodies) is transformed into coherent radiation, exponentially growing in intensity (the instability gets eventually limited by nonlinear effects). We also discuss a setup when the two bodies are at rest but a constant electric current is flowing in one of the bodies. One may say that only the electron component of one body is dragged with respect to the other body, unlike the usual setup when the two bodies are in relative motion. Clearly, there are differences in the frictional forces between the two setups.

Local orbital formulation of the Floquet theory of projectile electronic stopping

A recently proposed theoretical framework for the description of electronic quantum friction for constant-velocity nuclear projectiles traversing periodic crystals is here implemented using a local basis representation. The theory requires a change of reference frame to that of the projectile, and a basis set transformation for the target basis functions to a gliding basis is presented, which is time-periodic but does not displace in space with respect to the projectile, allowing a local-basis Floquet impurity-scattering formalism to be used. It is illustrated for a one-dimensional single-band tight-binding model, as the simplest paradigmatic example, displaying the qualitative behaviour of the formalism. The time-dependent non-orthogonality of the gliding basis requires care in the proper (simplest) definition of a local projectile perturbation. The Fermi level is tilted with a slope given by the projectile velocity, which complicates integration over occupied states. It is solved by a recurrent application of the Lippmann-Schwinger equation, in analogy with previous non-equilibrium treatment of electron ballistic transport. Aiming towards a first-principles mean-field-like implementation, the final result is the time-periodic particle density in the region around the projectile, describing the stroboscopically stationary perturbation cloud around the projectile, out of which other quantities can be obtained, such as the electronic stopping power.

A nuclear quadrupolar spin quantum heat engine

We give an implementable scheme which uses intrinsic quadrupolar nuclear spin interactions to harvest efficient energy from a quantum Otto cycle. We employ realistic parameter regimes for the 23Na nucleus in sodium nitrate. The processes of the cycle are accomplished by orienting the sample with respect to the static magnetic field. The effects of stroke duration on the work output and efficiency are revealed in detail. Finite-time adiabatic transformations leading to quantum friction are found to substantially reduce cycle outputs which are stimulated from the non-secular parts of the quadrupolar interaction. An estimation for the power output at maximum efficiency is also given. We show that with the precise control and manipulation of the intrinsic nuclear spin interactions, for example in an advanced nuclear magnetic resonance setup, makes our scheme implement as a powerful quantum Otto cycle.

Quantum friction theory drags experiments toward realization

While quantum friction has yet to be unambiguously detected, changing the geometry and material of the system could increase the force enough for physical measurements.

Wading through the void: Exploring quantum friction and nonequilibrium fluctuations

When two or more objects move relative to one another in vacuum, they experience a drag force, which, at zero temperature, usually goes under the name of quantum friction. This contactless non-conservative interaction is mediated by the fluctuations of the material-modified quantum electrodynamic vacuum and, hence, is purely quantum in nature. Numerous investigations have revealed the richness of the mechanisms at work, thereby stimulating novel theoretical and experimental approaches and identifying challenges and opportunities. In this Perspective, we provide an overview of the physics surrounding quantum friction and a perspective on recent developments.

Fluctuation-induced quantum friction in nanoscale water flows.

The flow of water in carbon nanochannels has defied understanding thus far1, with accumulating experimental evidence for ultra-low friction, exceptionally high water flow rates and curvature-dependent hydrodynamic slippage2-5. In particular, the mechanism of water-carbon friction remains unknown6, with neither current theories7 nor classical8,9 or ab initio molecular dynamics simulations10 providing satisfactory rationalization for its singular behaviour. Here we develop a quantum theory of the solid-liquid interface, which reveals a new contribution to friction, due to the coupling of charge fluctuations in the liquid to electronic excitations in the solid. We expect that this quantum friction, which is absent in Born-Oppenheimer molecular dynamics, is the dominant friction mechanism for water on carbon-based materials. As a key result, we demonstrate a marked difference in quantum friction between the water-graphene and water-graphite interface, due to the coupling of water Debye collective modes with a thermally excited plasmon specific to graphite. This suggests an explanation for the radius-dependent slippage of water in carbon nanotubes4, in terms of the electronic excitations of the nanotubes. Our findings open the way for quantum engineering of hydrodynamic flows through the electronic properties of the confining wall.

Quantum Otto cycle in a superconducting cavity in the nonadiabatic regime

We analyze the efficiency of the quantum Otto cycle applied to a superconducting cavity. We consider its description in terms of a full quantum scalar field in a one-dimensional cavity with a time dependent boundary condition that can be externally controlled to perform and extract work unitarily from the system. We study the performance of this machine when acting as a heat engine as well as a refrigerator. It is shown that, in a non-adiabatic regime, the efficiency of the quantum cycle is affected by the dynamical Casimir effect, that induces a sort of quantum friction that diminishes the efficiency. We also find regions of parameters where the effect is so strong that the machine can no longer function as an engine since the work that would be produced is completely consumed by the quantum friction. However, this effect can be avoided for some particular temporal evolutions of the boundary conditions that do not change the occupation number of the modes in the cavity, leading to a highly improved efficiency.

Quantum dissipation and friction attributed to plasmons

In this paper, we computed quantum friction of two parallel metal plates separated by a small distance moving with constant relative velocity [Formula: see text]. The plasmons as the internal degrees of freedom living on the two plates are coupled to a vacuum field in the gap between the two plates. We got the in–out quantum action which contained all the dynamical information of the system. Furthermore, we associated the imaginary part of the in–out quantum action with dissipation and frictional force. For the case of dispersionless plasmons, the imaginary part of the in–out quantum action is strongly suppressed as [Formula: see text]. The frictional force exhibits the same feature as [Formula: see text]. The difference is that the frictional force increases as [Formula: see text] and decreases as [Formula: see text]. For the case of dispersive plasmons, there is a threshold for the imaginary part of the in–out quantum action and the frictional force, that is, there is no dissipation when the relative velocity [Formula: see text] is not big enough. We gave a classical argument of the existence of the threshold, and this argument matched the mathematical results.

Energetics of quantum vacuum friction: Field fluctuations

Quantum fluctuations can induce a friction on a neutral but polarizable particle and cause it to radiate energy even if the particle is moving in free space filled with blackbody radiation, and is not in contact with or close to any surface or other object. We explore the energetics of such a particle moving uniformly in vacuum, continuing our previous investigations of quantum friction. The intrinsic polarizability of the particle is considered to be purely real before it is dressed by radiation. The particle is then guaranteed to be in the nonequilibrium steady state (NESS), where it absorbs and emits energy at the same rate. We first calculate the quantum frictional power and force on the particle in the rest frame of the blackbody radiation from first principles, namely the Maxwell-Heaviside equations and the Lorentz force law. Then we provide a simpler method of obtaining the same quantities in the rest frame of the particle by using the principle of virtual work. The equivalence of the two approaches is illustrated. The formulas we derive for quantum vacuum frictional power and force are fully relativistic and applicable to finite temperature. In NESS, the quantum vacuum frictional force on the particle is shown to be a true drag, independent of the model for polarizability and the polarization state of the particle. Finally, we give an estimate of the quantum vacuum friction on a gold atom and comment on the feasibility of detecting such quantum vacuum frictional effects.

Quantum sensing protocol for motionally chiral Rydberg atoms

A quantum sensing protocol is proposed for demonstrating the motion-induced chirality of circularly polarised Rydberg atoms. To this end, a cloud of Rydberg atoms is dressed by a bichromatic light field. This allows to exploit the long-lived ground states for implementing a Ramsey interferometer in conjunction with a spin echo pulse sequence for refocussing achiral interactions. Optimal parameters for the dressing lasers are identified. Combining a circularly polarised dipole transition in the Rydberg atom with atomic centre-of-mass motion, the system becomes chiral. The resulting discriminatory chiral energy shifts induced by a chiral mirror are estimated using a macroscopic quantum electrodynamics approach. The presented quantum sensing protocol will also provide an indirect proof for Casimir–Polder quantum friction.

Open Quantum Systems' Decay across Time.

The description of an open quantum system's decay almost always requires several approximations so as to remain tractable. In this Letter, we first revisit the meaning, domain, and seeming contradictions of a few of the most widely used of such approximations: (semigroup) Markovianity, linear response theory, Wigner-Weisskopf approximation, and rotating-wave approximation. Second, we derive an effective time-dependent decay theory and corresponding generalized quantum regression relations for an open quantum system linearly coupled to an environment. This theory covers all timescales and subsumes the Markovian and linear-response results as limiting cases. Finally, we apply our theory to the phenomenon of quantum friction.

Motion-Induced Radiation Due to an Atom in the Presence of a Graphene Plane

We study the motion-induced radiation due to the non-relativistic motion of an atom, coupled to the vacuum electromagnetic field by an electric dipole term, in the presence of a static graphene plate. After computing the probability of emission for an accelerated atom in empty space, we evaluate the corrections due to the presence of the plate. We show that the effect of the plate is to increase the probability of emission when the atom is near the plate and oscillates along a direction perpendicular to it. On the contrary, for parallel oscillations, there is a suppression. We also evaluate the quantum friction on an atom moving at constant velocity parallel to the plate. We show that there is a threshold for quantum friction: friction occurs only when the velocity of the atom is larger than the Fermi velocity of the electrons in graphene.

Casimir Force: Vacuum fluctuation, zero-point energy, and computational electromagnetics

The understanding of the Casimir force foretells applications in micro/nanoelectromechanical sensors and quantum friction. We review the history of quantum theory and Casimir force modeling and, using the homomorphism between electromagnetic oscillations and a linear pendulum with simple harmonic oscillation, we explore various concepts needed for Casimir force calculations. Through the argument principle, we simplify the derivation of Casimir energy and, hence, the Casimir force. Then, we discuss the connection between the Casimir force and computational electromagnetics (CEM), focusing on the method of moments (MOM). Finally, we consider the marriage of these concepts with recently developed broadband fast algorithms. The resulting approaches illustrate that the Casimir force calculation is for various highly complex structures.

Detectable Signature of Quantum Friction on a Sliding Particle in Vacuum

AbstractSpatially separated bodies in a relative motion through vacuum experience a tiny friction force known as quantum friction (QF). This force has so far eluded experimental detection due to its small magnitude and short range. Quantitative details revealing traces of the QF in the degradation of the quantum coherence of a particle are presented. Environmentally induced decoherence for a particle sliding over a dielectric sheet can be decomposed into contributions of different signatures: one solely induced by the electromagnetic vacuum in the presence of the dielectric and another induced by motion. As the geometric phase (GP) has been proved to be a fruitful venue of investigation to infer features of the quantum systems, herein it is proposed to use the accumulated GP acquired by a particle as a QF sensor. Furthermore, an innovative experiment designed to track traces of QF by measuring the velocity dependence of corrections to the GP and coherence is proposed. The experimentally viable scheme presented can spark renewed optimism for the detection of non‐contact friction, with the hope that this non‐equilibrium phenomenon can be readily measured soon.

Enhanced decoherence for a neutral particle sliding on a metallic surface in vacuum

Bodies in relative motion, spatially separated in vacuum, experience a tiny friction force known as quantum friction. This force has eluded experimental detection so far due to its small magnitude and short range. Herein, we give quantitative details so as to track traces of the quantum friction by measuring coherences in the atom. We notice that the environmentally induced decoherence can be decomposed into contributions of different signature: corrections induced by the electromagnetic vacuum in presence of the dielectric sheet and those induced by the motion of the particle. In this direction, we show that non-contact friction enhances the decoherence of the moving atom. Further, its effect can be enlarged by a thorough selection of the two-level particle and the Drude-Lorentz parameters of the material. In this context, we suggest that measuring decoherence times through velocity dependence of coherences could indirectly demonstrate the existence of quantum friction.

Nonequilibrium thermodynamics of quantum friction

Thermodynamic principles are often deceptively simple and yet surprisingly powerful. We show how a simple rule, such as the net flow of energy in and out of a moving atom under nonequilibrium steady state condition, can expose the shortcomings of many popular theories of quantum friction. Our thermodynamic approach provides a conceptual framework in guiding atom-optical experiments, thereby highlighting the importance of fluctuation-dissipation relations and long-time correlations between subsystems. Our results introduce consistency conditions for (numerical) models of nonequilibrium dynamics of open quantum systems.

Quantum Finite-Time Thermodynamics: Insight from a Single Qubit Engine.

Incorporating time into thermodynamics allows for addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model in order to study this tradeoff from first principles, based on the quantum theory of open systems. We study the quantum origin of irreversibility, originating from heat transport, quantum friction, and thermalization in the presence of external driving. We construct various finite-time engine cycles that are based on the Otto and Carnot templates. Our analysis highlights the role of coherence and the quantum origin of entropy production.

Chiral gravitational waves and primordial black holes in UV-protected Natural Inflation

We consider an UV-protected Natural Inflation scenario involving Chern-Simons-like interactions between the inflaton and some beyond the Standard Model gauge fields. The accelerated expansion of the Universe is supported by a combination of a gravitationally-enhanced friction sensitive to the scale of inflation and quantum friction effects associated with the explosive production of gauge fluctuations. The synergy of these two velocity-restraining mechanisms allows for: i) Natural Inflation potentials involving only sub-Planckian coupling constants, ii) the generation of a dark matter component in the form of primordial black holes, and iii) a potentially observable background of chiral gravitational waves at small scales.

The Quantum Friction and Optimal Finite-Time Performance of the Quantum Otto Cycle.

In this work we considered the quantum Otto cycle within an optimization framework. The goal was maximizing the power for a heat engine or maximizing the cooling power for a refrigerator. In the field of finite-time quantum thermodynamics it is common to consider frictionless trajectories since these have been shown to maximize the work extraction during the adiabatic processes. Furthermore, for frictionless cycles, the energy of the system decouples from the other degrees of freedom, thereby simplifying the mathematical treatment. Instead, we considered general limit cycles and we used analytical techniques to compute the derivative of the work production over the whole cycle with respect to the time allocated for each of the adiabatic processes. By doing so, we were able to directly show that the frictionless cycle maximizes the work production, implying that the optimal power production must necessarily allow for some friction generation so that the duration of the cycle is reduced.

Quantum heat engine based on dynamical materials design

We propose a novel type of quantum heat engine based on the ultrafast dynamical control of the magnetic properties of a nano-scale working body. The working principle relies on nonlinear phononics, an example for dynamical materials design. We describe the general recipe for identifying candidate materials, and also propose Cr$_{2}$O$_{3}$ as a promising working body for a quantum Otto cycle. Using a spin Hamiltonian as a model for Cr$_{2}$O$_{3}$, we investigate the performance in terms of efficiency, output power, and quantum friction. To assess the assumptions underlying our effective spin Hamiltonian we also consider a working substance composed of several unit cells. We show that even without an implementation of transitionless driving, the quantum friction is very low compared to the total produced work and the energy cost of counterdiabatic driving is negligible. This is an advantage of the working substance, as experimentally hard-to-implement shortcuts to adiabaticity are not needed. Moreover, we discuss some remarkable thermodynamic features due to the quantumness of the proposed system such as a non-monotonic dependence of the efficiency on the temperature of the hot-bath. Finally, we explore the dependence of the performance on the system parameters for a generic model of this type of quantum heat engine and identify properties of the energy spectrum required for a well-performing quantum heat engine.