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arXiv:2602.14992

Rotational Quantum Friction via Spontaneous Decay

Nicolas Schüler, O. J. Franca, Michael Vaz, Hervé Bercegol, Stefan Yoshi Buhmann

quant-phphysics.opticsSubmitted Feb 16, 2026• Announced Feb 17, 2026
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Abstract

A fascinating effect belonging to the field of vacuum forces and fluctuations is that of quantum friction. It refers to the prediction of a dissipative force acting on a moving object due to the quantum vacuum field. In this work, we investigate rotational quantum friction where a diatomic polar molecule rotates around its own center of mass in free space. We quantize the rotational motion and investigate the resulting dissipation due to spontaneous decay. We find in the Markovian regime that a friction torque $\propto Ω^3$ persists even for zero temperature, and in agreement with the classical result in the limit of large rotational quantum number $l$. Within the non-Markovian short-time regime we find a friction $\proptoΩ$.

Comments
7 pages, 2 figures, Submitted

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A fascinating effect belonging to the field of vacuum forces and fluctuations is that of quantum friction. It refers to the prediction of a dissipative force acting on a moving object due to the quantum vacuum field. In this work, we investigate rotational quantum friction where a diatomic polar molecule rotates around its own center of mass in free space. We quantize the rotational motion and investigate the resulting dissipation due to spontaneous decay. We find in the Markovian regime that a friction torque ∝Ω3\propto Ω^3∝Ω3 persists even for zero temperature, and in agreement with the classical result in the limit of large rotational quantum number lll. Within the non-Markovian short-time regime we find a friction ∝Ω\proptoΩ∝Ω.
A nonabsorbing particle rotating in vacuum can lose angular momentum only by converting mechanical energy into electromagnetic radiation. Here, we develop a quantum theory of rotational vacuum friction for small lossless particles and show that axial symmetry qualitatively changes the leading dissipation channel. At zero temperature, the frictional torque scales as M∝Ω7M\proptoΩ^7M∝Ω7 with rotation frequency  Omega\ Omega Omega in anisotropic particles due to the emission of correlated photon pairs whose frequencies sum to 2Ω2Ω2Ω, while a contribution to the torque linear in  Omega\ Omega Omega is found at finite temperature. In contrast, axisymmetric particles are protected against photon-assisted friction regardless of temperature.
Quantum mechanics predicts the occurrence of random electromagnetic field fluctuations, or virtual photons, in vacuum. The exchange of virtual photons between two bodies in relative motion could lead to non-contact quantum vacuum friction or Casimir friction. Despite its theoretical significance, the non-contact Casimir frictional force has not been observed and its theoretical predictions have varied widely. In this work, we report the first measurement of the non-contact Casimir frictional force between two moving bodies. By employing two mechanical oscillators with resonant frequencies far lower than those in Lorentz models of electrons in dielectric materials, we have amplified the Casimir frictional force at low relative velocities by several orders of magnitude. We directly measure the non-contact Casimir frictional force between the two oscillators and show its linear dependence on velocity, proving the dissipative nature of Casimir friction. This advancement marks a pivotal contribution to the field of dissipative quantum electrodynamics and enhances our understanding of friction at the nanoscale.
We quantize the Brownian motion undergone by a free particle in the absence of inertial force (the so-called large friction regime) as described by the diffusion equation early found out by Einstein in 1905. Accordingly, we are able to come up with a time-dependent attractive quantum force F(t) that acts upon the Brownian free particle as a result of quantum-mechanical thermal fluctuations of a heat bath consisting of a set of quantum harmonic oscillators having the same oscillation frequency /omega in thermodynamic equilibrium at temperature T. More specifically, at zero temperature we predict that the zero-point force is given by F^((T=0)) (t)=-[ω/(1+2\omegat)^(3/2)] \sqrt(γ/2), where γis the friction constant with dimensions of mass per time and /eta the Planck constant divided by 2π. For evolution times t~1/ω, ω~0^14 Hz, /gamma~10^(-10) kg/s, and /eta~10^(-34) m^2 kg/s, we find out F^((T=0)) ~10^(-8) N, which exhibits the same magnitude order as the Casimir electromagnetic quantum force, for instance. Thus, we reckon that novel quantum effects arising from our concept of time-dependent thermal quantum force F(t) may be borne out by some experimental set-up in nanotechnology.
For a diatomic molecule interacting with an off-resonant laser field it is shown how quantum vacuum fluctuations of the electromagnetic field act via spontaneous Raman processes on the molecular rotational degree of freedom. Furthermore, the inclusion of the molecule's centre-of-mass and the treatment of associated photon recoil effects is outlined. The obtained results form a basis for describing the combined centre-of-mass and rotational dynamics of the molecule in off-resonant, spatially varying laser fields, such as in the laser focus forming a dipole trap.
We report on a microscopic theory of quantum friction. Our approach investigates the interplay between the dispersive response and the relative center-of-mass motion of two ground-state atoms. This coupling yields a quantum force, which can be expressed as a power series in the velocity. The significance of each contribution depends on its order parity: while even-order terms are reversible, odd-order terms are irreversible and only survive in the presence of an internal dissipation mechanism. In addition, we obtain general, model-independent properties for the work performed by these contributions for arbitrary scattering trajectories. These results enable an unambiguous identification of odd-parity terms with microscopic quantum friction. At room temperature, the dominant microscopic quantum friction is of first order in the velocity and presents a strong quantum character. Our microscopic theory reveals that several properties of quantum friction obtained in specific settings -- such as the cubic dependence on velocity at zero temperature -- are indeed universal features already present at the atomic scale.
Nonlinear friction forces are a problem in classical Brownian motion for a long time [1]. They are described either by Langevin or by Fokker-Planck equations [2-4]. However, the rigorous generalized Langevin equation is linear, which points out that nonlinear friction forces possess a macroscopic hydrodynamic origin [1]. For this reason, they are not present in the modern quantum theory of open systems [5]. The scope of the present paper is to investigate the nonlinear friction effect on quantum mechanics. The analysis is based on a dissipative Madelung quantum hydrodynamics. Thus, the nonlinear friction is a result of nonlinear non-equilibrium thermodynamics in contrast to the traditional mechanical nonlinear friction forces. A quantum particle in vacuum is described by the Schrodinger equation