Levitational Photonics

Non-Hermitian dynamics of single or multiple interacting objects. 

Since light is a flow of momentum, optical forces are intrinsically non-conservative. This characteristic appears whenever simple symmetries are broken. Examples include isotropic particles in circularly polarized beams [1], birefringent or non-spherical particles in linearly or circularly polarized beams [2,3], and optically interacting particles in beams with phase decoherence [4].

The forces in these systems can be locally described by a generalized Hooke’s law, having a non-symmetric stiffness matrix, resulting in biased stochastic motion]. For sufficiently high driving, or low dissipation, this bias grows until inertial forces overcome attractive forces causing a bifurcation, the formation of a limit cycle oscillation and, in multi-particle systems, synchronization [5].

[1] Svak, V. et al. Transverse spin forces and non-equilibrium particle dynamics in a circularly polarized vacuum optical trap. Nature Communications 9, 5453 (2018).
[2] Arita, Y., Simpson, S. H., Zemánek, P. & Dholakia, K. Coherent oscillations of a levitated birefringent microsphere in vacuum driven by nonconservative rotation-translation coupling. Science Advances 6,  (2020).
[3] Arita, Y. et al. Cooling the optical-spin driven limit cycle oscillations of a levitated gyroscope. Communications Physics 6, 1–7 (2023).
[4] Liška, V. et al.  PT-like phase transition and limit cycle oscillations in non-reciprocally coupled optomechanical oscillators levitated in vacuum. Nature Physics (2024)
[5] Brzobohatý, O. et al. Synchronization of spin-driven limit cycle oscillators optically levitated in vacuum. Nature Communications 14, 1–10 (2023).

Cooling of motion of single and multiple objects through either active feedback or passive cavity cooling.

Methods for controlling the motion of single particles, optically levitated in vacuum, have developed rapidly in recent years.

The technique of cold damping makes use of feedback-controlled, electrostatic forces to increase dissipation without introducing additional thermal fluctuations. This process has been instrumental in the ground-state cooling of individual electrically charged nanoparticles. Here we show that the same method can be applied to a pair of nanoparticles, coupled by optical binding forces. These optical binding forces are about three orders of magnitude stronger than typical Coulombic inter-particle force and result in a coupled motion of both nanoparticles characterized by a pair of normal modes [1].

We demonstrate cold damping of these normal modes, either independently or simultaneously, to sub-Kelvin temperatures at pressures of 5 10-3  mbar [2]. Experimental observations are captured by a theoretical model, which we use to survey the parameter space more widely and to quantify the limits imposed by measurement noise and time delays.

[1] Svak V. et al. Stochastic dynamics of optically bound matter levitated in vacuum. Optica 8 (2), 220-229 (2021)
[2] Liška V. et al. Cold damping of levitated optically coupled nanoparticles. Optica 10 (9), 1203-1209 (2023) 

Developing experimental protocols for sculpting phase space of a levitated object.

Using the levitated particles close to the quantum ground state for detection of ultra-weak forces or just for the proof of non-classical quantum behavior requires manipulation of the phase space probability density function (PDF or Wigner function). These PDF changes consist of extension, squeezing, amplification, or non-linear deformations.

We demonstrated the function of a linear phase sensitive amplifier [1] and we analyzed its gain, linearity, extension squeezing and coherence.

[1] Duchaň M. et al. Experimental amplification and squeezing of a motional state of an optically levitated nanoparticle arXiv:2403.04302 [quant-ph]

Enhancing the optomechanical interaction between the optical field and a levitated object using photonic structures.

We propose and analyze theoretically a promising design of an optical trap for vacuum levitation of nanoparticles based on a one-dimensional (1D) silicon photonic crystal cavity (PhC). The considered cavity has a quadratically modulated width of the silicon wave guiding structure. The value of trapping stiffnesses in the microcavity  is predicted to be 5 order of magnitudes higher than that reached for optimized optical tweezers, moreover the linear single photon coupling rate can reach MHz level which is 6 order magnitude larger than previously reported values for common bulk cavities.

[1] Maňka T. et al. Simulation of optomechanical interaction of levitated nanoparticle with photonic crystal micro cavity. Optics Express 32 (5), 7185-7196 (2023)

Advanced analysis of optical and random forces acting on the levitated particle

Precise knowledge of an optical force profile is needed for design of sensing or quantum protocols. Quite often, only a limited amount of data is available, or the particle is in a non-stationary state far from thermal equilibrium. We develop novel methods for characterization of such optical fields based on theory of non-Markovian random processes [1] or ensemble averaging of transient trajectories [2].

[1] Šiler M. et al. Bayesian Estimation of Experimental Parameters in Stochastic Inertial Systems: Theory, Simulations, and Experiments with Objects Levitated in Vacuum. Phys. Rev. Applied 19, 064059 (2023)

[2] Flajšmanová J., et al. Using the transient trajectories of an optically levitated nanoparticle to characterize a stochastic Duffing oscillator. Sci Rep 10, 14436 (2020).

Dynamics of microscopic particles in various optical light fields

We employ the state-of-the art techniques to study the dynamics of  microscopic objects in carefully designed optical light fields, e.g. we  have demonstrated counterintuitive  transport of micro particles   against photon flow in so cold Tractor beam and its utilization  for  passive sorting of micro  objects according their size. Recently,  we studied behavior of particles in highly non-linear cubic potential  and transport in rocking ratchet system.

• Tractor beam in the micro world. We have demonstrated counterintuitive transport of micro particles against photon flow and its utilization for passive sorting of micro objects according their size. Read the article in Nature Photonics
• Dynamics of micro particle in highly non-linear cubic potential. Read the article in Scientific Reports and Physical Review Letters.
• Optical ratchets. A fully reconfigurable two-dimensional rocking ratchet system was employed to omnidirectional transport of micro particles. Read the article in Physical Review Letters

Optically assembled soft matter

 We study the optically mediated interaction between assembled  microscopic objects - optical binding - that gives a rise to attractive  and repulsive forces and dramatically influence the way such objects  assemble and self-organize. This offers routes for colloidal  self-assembly, crystallization, and organization of templates for  biological and colloidal sciences. We focus not only on opto-mechanical  aspects of optical mater but also on its photonic properties.

• Gripped by light: Optical binding. The topic of optical binding was reviewed in Review of Modern Physics
• Optical binding of microobjects. We created extended longitudinally optically bound chains of microparticles of various shapes with the use of counter-propagating light fields. Read our articles in Physical Review Letters, Physical review A
• Particle transport in tractor beam enhanced by the optical binding. Here we demonstrate that motion of two optically bound objects in a tractor beam strongly depends on theirs mutual distance and spatial orientation. Read article in Light: Science & Applications

Modelling of optical tweezers

We are using several theoretical approaches to model interaction of  light with a particle(s) in optical traps. We use in house developed  codes for the Rayleigh approximation, Generalized Lorenz-Mie scattering  based on approaches of Barton as well as the T-Matrix method, Coupled  Dipoles Method and commercially available Finite Elements Method (Comsol  Multiphysics). We focus mainly on the interaction of a non-spherical  particle or large ensemble of particles in structured or interference  light fields. Furthermore, we analyse both the thermal effects connected  to trapping as well as stochastic behaviour of particle ensembles.

• Optical printing. Optical printing is a powerful all-optical method that allows the incorporation of colloidal nanoparticles (NPs) onto substrates with nanometric precision. Read the article in ACS Nano
• Optical binding of nanowires. Using a novel numerical model we uncover rich behaviour of optically bound dielectric nanowires. Read the article in Nano Letters
• Morphology of plasmonic nanoparticle dictates optical forces. We demonstrate confinement of large gold nanoparticles in an optical trap based on very low numerical aperture optics. Read the article in Scientific Reports