arXiv subjects

Petr Jákl

Publications and source records attributed to Petr Jákl.

6 recordsLinked to original sources

arXiv2026

Unidirectional Inter-Axial Coupling and Spontaneous Cooling in a~Non-Hermitian Dynamics of a~Levitated Particle

Non-Hermitian dynamics in open systems can give rise to a variety of fascinating non-equilibrium phenomena, ranging from symmetry-breaking transitions to directional energy flow. Parity-time (PT) symmetry breaking determines the occurrence of dynamical instabilities, while non-reciprocal interactions enable asymmetric energy transfer between modes. Here, we present a versatile optomechanical platform based on a vacuum-levitated nanoparticle that allows full control over the coupling of its mechanical modes, including non-reciprocal and non-conservative interactions. By engineering the spatial ellipticity and polarization of the trapping beam, we continuously tune the system from a reciprocal to a strongly non-reciprocal regime. This allows us to observe PT-symmetry phase transitions and to isolate a unidirectional regime in which one mode remains effectively decoupled while driving the other. We demonstrate that elliptical polarisation of the trapping beam spanning unidirectional and reciprocal regimes induces asymmetric intermodal energy transfer. This results in the spontaneous cooling of one mechanical mode without external feedback. Both modes share identical mass, size, charge, and optical environment, providing a clean and robust setting for exploring non-Hermitian dynamics, exceptional-point physics, and energy redistribution in minimal systems. Combined with recent advances in ground-state cooling, our results provide a direct route to realising non-Hermitian phenomena in the quantum regime.

physics.optics↗

arXiv2025

Fermat's Spiral-Based Characterization of Squeezed Nonlinear Motional States of Levitated Nanoparticle

Controlling the state of motion of optically levitated nanoparticles is crucial for the advancement of precision sensing, fundamental tests of physics, and the development of hybrid classical-quantum technologies. Experimentally, such control can be achieved by pulsed modifications of the optical potential confining the nanoparticle. Most frequently, the applied potential pulses are parabolic in nanoparticle position, and they expand/squeeze or displace the initial Gaussian state of motion to a modified Gaussian state. The time-dependent mean values and covariance matrix of the phase-space variables can fully characterize such a state. However, quasi-parabolic optical potentials with added weak Duffing-type nonlinearity, encountered in real-world experiments, can generally distort the state of motion to a non-Gaussian one, for which the description based solely on the mean values and covariance matrix fails. Here, we introduce a nonlinear transformation of the phase-space coordinates using the concept of Fermat's spiral, which effectively removes the state distortion induced by the Duffing-type nonlinearity and enables characterization of the state of motion by the standard Gaussian-state metrics. Comparisons of the experimental data with theoretical models show that the proposed coordinate transformation can recover the ideal behavior of a harmonic oscillator even after extended evolution of the system in the nonlinear potential. The presented scheme enables the separation of the effects of the applied state manipulation, the system's gradual thermalization, and the nonlinearity of the confinement on the experimentally observed dynamics of the system, thereby facilitating the design of advanced protocols for levitated optomechanics.

physics.optics↗

arXiv2025

Nanomechanical State Amplifier Based on Optical Inverted Pendulum

A contactless control of mean values and fluctuations of position and velocity of a nanoobject belongs among the key methods needed for ultra-precise nanotechnology and the upcoming quantum technology of macroscopic systems. An analysis of experimental implementations of such a control, including assessments of linearity and the effects of added noise, is required. Here, we present a protocol of linear amplification of mean values and fluctuations along an arbitrary phase space variable and squeezing along the complementary one, referred to as a nanomechanical state amplifier. It utilizes the experimental platform of a single optically levitating nanoparticle and the three-step protocol combines a controlled fast switching of the parabolic trapping potential to an inverted parabolic potential and back to the parabolic potential. The protocol can be sequentially repeated or extended to shape the nanomechanical state appropriately. Experimentally, we achieve amplification of position with a gain of $|G| \simeq 2$ and a classical squeezing coefficient above 4 dB in as short a timestep as one period of nanoparticle oscillations ($7.6\,μ$s). Amplification in velocity, with the same parameters, squeezes the input noise and enhances force sensing.

quant-ph↗

arXiv2024

Observations of a PT-like phase transition and limit cycle oscillations in non-reciprocally coupled optomechanical oscillators levitated in vacuum

Nanoparticles levitated in an optical trap provide a versatile platform to study mechanical oscillators in a controlled environment with tuneable parameters. Recently, it has become possible to couple two of these optomechanical oscillators. Here, we demonstrate the collective non-Hermitian dynamics of such a pair of non-conservatively coupled oscillators. We take advantage of the tunability of the optical interactions between the particles in our system and set the optical interaction between the particles to be purely non-reciprocal. By continuously varying the relative power of the trapping beams, we take the system through a transition, similar to a parity-time phase transition. A Hopf bifurcation at a critical point results in the formation of collective limit cycle oscillations, resembling those observed in phonon lasers. These coupled levitated oscillators provide a platform for exceptional point optomechanical sensing and can be extended to multi-particle systems, paving the way for the development of topological optomechanical media.

physics.optics↗

arXiv2018

Diffusing Up the Hill: Dynamics and Equipartition in Highly Unstable Systems

Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard statistical analysis of unstable mechanical processes and their applications. A newly proposed approach takes advantage of the local characteristics of the most probable particle motion instead of the divergent averages. We experimentally verify its theoretical predictions for a Brownian particle moving near an inflection in a highly unstable cubic optical potential. The most-likely position of the particle atypically shifts against the force despite the trajectories diverge in the opposite direction. The local uncertainty around the most-likely position saturates even for strong diffusion and enables well-resolved position detection. Remarkably, the measured particle distribution quickly converges to the quasi-stationary one with the same atypical shift for different initial particle positions. The demonstrated experimental confirmation of the theoretical predictions approves the utility of local characteristics for highly unstable systems which can be exploited in thermodynamic processes to uncover energetics of unstable systems.

cond-mat.stat-mech↗

arXiv2017

Omnidirectional Transport in Fully Reconfigurable Two Dimensional Optical Ratchets

A fully reconfigurable two-dimensional (2D) rocking ratchet system created with holographic optical micromanipulation is presented. We can generate optical potentials with the geometry of any Bravais lattice in 2D and introduce a spatial asymmetry with arbitrary orientation. Nontrivial directed transport of Brownian particles along different directions is demonstrated numerically and experimentally, including on-axis, perpendicular and oblique with respect to an unbiased ac driving. The most important aspect to define the current direction is shown to be the asymmetry and not the driving orientation, and yet we show a system in which the asymmetry orientation of each potential well does not coincide with the transport direction, suggesting an additional symmetry breaking as a result of a coupling with the lattice configuration. Our experimental device, due to its versatility, opens up a new range of possibilities in the study of nonequilibrium dynamics at the microscopic level.

cond-mat.soft↗