Characterization of non-linearities through mechanical squeezing in levitated optomechanics

Setter, Ashley; Vovrosh, Jamie

doi:10.1063/1.5116121

Cited by 17 publications

(14 citation statements)

References 23 publications

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“…Moreover, all the simulations have been performed using parameters of current underdamped experiments 12 , together with the parameters of cubic optical potential 29 , 30 directly motivating our predictions to be experimentally tested to witness these new nonlinear mechanical phenomena. However, the analysis of the presented regime is also applicable to other underdamped experiments 31 – 33 . The first point worth experimentally verifying, shown in Figs.…”

Section: Conclusion For Experimental Testsmentioning

confidence: 92%

“…In the low pressure limit the particle is deep in the underdamped regime so that the instantaneous particle speed and acceleration become new transient quantities to be first explored and later exploited for applications. In this paper we simulate and analyse nonlinear ballistic effects for instantaneous velocity and acceleration induced by the initial position uncertainty, and predict the experimental regime where such phenomena are visible using parameters for current setups in laboratories 12 , 31 – 33 . We observe that the only requirement for a reliable experimental observation is a reduction of initial velocity uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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Uncertainty-induced instantaneous speed and acceleration of a levitated particle

Ornigotti

Filip

2021

Sci Rep

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Levitating nanoparticles trapped in optical potentials at low pressure open the experimental investigation of nonlinear ballistic phenomena. With engineered non-linear potentials and fast optical detection, the observation of autonomous transient mechanical effects, such as instantaneous speed and acceleration stimulated purely by initial position uncertainty, are now achievable. By using parameters of current low pressure experiments, we simulate and analyse such uncertainty-induced particle ballistics in a cubic optical potential demonstrating their evolution, faster than their standard deviations, justifying the feasibility of the experimental verification. We predict, the maxima of instantaneous speed and acceleration distributions shift alongside the potential force, while the maximum of position distribution moves opposite to it. We report that cryogenic cooling is not necessary in order to observe the transient effects, while a low uncertainty in initial particle speed is required, via cooling or post-selection, to not mask the effects. These results stimulate the discussion for both attractive stochastic thermodynamics, and extension of recently explored quantum regime.

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Section: Conclusion For Experimental Testsmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Uncertainty-induced instantaneous speed and acceleration of a levitated particle

Ornigotti

Filip

2021

Sci Rep

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“…5 . Moreover, this PSD approach is not suitable for current investigation and use of transient out-of-equilibrium coherent effects faster than any heating of the motion 40 . After the cooling of levitating systems to the ground state 37 , such estimation of the Duffing oscillator from fast transient effects are crucial for upcoming studies of quantum effects 50 – 54 .…”

Section: Experimental Set-up and Data Processingmentioning

confidence: 99%

“…We compare our results with the commonly used PSD method and, unlike Refs. 18,40 , we obtain the Duffing coefficient of nonlinearity without any external driving force which could affect the system parameters and would be undesirable for experimental studies of quantum effects. Moreover, the determined damping coefficient follows well the theoretical prediction down into low pressures.…”

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confidence: 99%

Using the transient trajectories of an optically levitated nanoparticle to characterize a stochastic Duffing oscillator

Flajšmanová

Šiler

Jedlička

et al. 2020

Sci Rep

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We propose a novel methodology to estimate parameters characterizing a weakly nonlinear Duffing oscillator represented by an optically levitating nanoparticle. The method is based on averaging recorded trajectories with defined initial positions in the phase space of nanoparticle position and momentum and allows us to study the transient dynamics of the nonlinear system. This technique provides us with the parameters of a levitated nanoparticle such as eigenfrequency, damping, coefficient of nonlinearity and effective temperature directly from the recorded transient particle motion without any need for external driving or modification of an experimental system. Comparison of this innovative approach with a commonly used method based on fitting the power spectrum density profile shows that the proposed complementary method is applicable even at lower pressures where the nonlinearity starts to play a significant role and thus the power spectrum density method predicts steady state parameters. The technique is applicable also at low temperatures and extendable to recent quantum experiments. The proposed method is applied on experimental data and its validity for one-dimensional and three-dimensional motion of a levitated nanoparticle is verified by extensive numerical simulations. Linear harmonic oscillators are useful idealisations explaining a broad class of phenomena. However, real oscillators are always nonlinear. Typically, they exhibit a soft Duffing nonlinearity turning oscillations to anharmonic one. Despite long-term experimental investigation, new diverse effects have been recently observed in the underdamped Duffing oscillators based on nano-electromechanical systems 1-3 , micro-electromechanical systems 4-8 , nonlinear electric oscillators 9 , particles trapped in nonlinear potentials 10 , solid-state systems 11 , mechanical oscillators with a chemical bond 12 and also proposed for upcoming quantum mechanical oscillators with superconducting qubits 13. They stimulate further investigations of both equilibrium states and transient dynamics of anharmonic oscillators. At long time scales, when dynamics tends to equilibrate, and for short transient times, the anharmonicity can have different impacts. A precise description of transient effects in nonlinear oscillators is therefore essential for our understanding of nonequilibrium physics and applications ranging from nanosensing and thermodynamically engines up to social dynamics 14-23. The faithful characterization of a nonlinear oscillator requires to estimate its parameters beyond standard methodology based either on the equilibrium state (ES) or on the power spectral density (PSD) of particle positions or velocities 24-29. Both these methods presume that values estimated from steady states are valid also during the transient dynamics. Such assumption can, however, lead to significant systematic errors in the values of estimated parameters, e.g. in the case of a nonlinear oscillator with large amplitudes, as we demonstrate in this paper. Currently, optomec...

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“…A straightforward generalization of our schemes should allow the creation of two-mode squeezing between two motional modes of the particle; in this context, we note that both parametric [47] and dissipative [48] two-mode me- chanical squeezing have been realized in optomechanical systems. In the long term, full quantum control of motion should be possible, first in the Gaussian (via linear coupling of all three motional modes to the same cavity mode) and later in the non-Gaussian regime (when nonlinear optomechanical interactions or mechanical potentials are added [49][50][51][52]).…”

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confidence: 99%

Strong mechanical squeezing for a levitated particle by coherent scattering

Černotík

Filip

2020

Phys. Rev. Research

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Levitated particles are a promising platform for precision sensing of external perturbations and probing the boundary between quantum and classical worlds. A critical obstacle for these applications is the difficulty of generating nonclassical states of motion which have not been realized so far. Here, we show that squeezing of the motion of a levitated particle below the vacuum level is feasible with available experimental parameters. Using amplitude modulation of the trapping beam and coherent scattering of trapping photons into a cavity mode, we explore several strategies to achieve strong phase-sensitive suppression of mechanical fluctuations and discuss conditions for preparing nonclassical mechanical squeezing. Our results pave the way to full optomechanical control of levitated particles in the quantum regime.

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Characterization of non-linearities through mechanical squeezing in levitated optomechanics

Cited by 17 publications

References 23 publications

Uncertainty-induced instantaneous speed and acceleration of a levitated particle

Uncertainty-induced instantaneous speed and acceleration of a levitated particle

Using the transient trajectories of an optically levitated nanoparticle to characterize a stochastic Duffing oscillator

Strong mechanical squeezing for a levitated particle by coherent scattering

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