Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator

Moore, Darren W.; Rakhubovsky, Andrey A.; Filip, Radim

doi:10.1088/1367-2630/ab5690

Cited by 11 publications

(5 citation statements)

References 92 publications

(152 reference statements)

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“…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%

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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Section: Experimental Set-up and Data Processingmentioning

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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“…This means that the nonlocal nonlinearity will have the cubic form q i q j q k [49]. In fact this cubic form implies the nullifiers of the 3-cluster will take the form p i − q j q k , suggestive of the nonlinear squeezing resource required for adaptively implementing the cubic phase state via measurement [15,50]. This 3-edge hypergraph bears much similarity to the Union Jack state of Ref [45] and has the ability, through Gaussian measurements, to teleport a 3-edge onto a new set of modes not previously sharing a 3-edge.…”

Section: Multimode Nonlinear Operationsmentioning

confidence: 99%

Quantum hypergraph states in continuous variables

Moore

2019

Phys. Rev. A

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The measurement based, or one-way, model of quantum computation for continuous variables uses a highly entangled state called a cluster state to accomplish the task of computing. Cluster states that are universal for computation are a subset of a class of states called graph states. These states are Gaussian states and therefore require that the homodyne detection (Gaussian measurement) scheme is supplemented with a non-Gaussian measurement for universal computation, a significant experimental challenge. Here we define a new non-Gaussian class of states based on hypergraphs which satisfy the requirements of the Lloyd-Braunstein criteria while restricted to a Gaussian measurement strategy. Our main result is to show that, taking advantage of the intrinsic multimode nonlinearity, a hypergraph consisting of 3-edges can be used to apply a three-mode operation to an input three-mode state. As a special case, this technique can be used to apply the cubic phase gate to a single mode.

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“…The approach, which is an extension of the methods used for implementation of Gaussian operations [16], requires the auxiliary systems prepared in quantum states which approximate eigenstates of specific operators. For Gaussian operations the resources come from the family of squeezed states, for the cubic gate we require states with nonlinear squeezing, which can be prepared in various ways [9,23,27,40,46,47,67].…”

Section: Introductionmentioning

confidence: 99%

Cubic nonlinear squeezing and its decoherence

Kala¹,

Marek²,

Filip³

2021

Preprint

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Squeezed states of the harmonic oscillator are a common resource in applications of quantum technology. If the noise is suppressed in a nonlinear combination of quadrature operators, the quantum states are non-Gaussian and we refer to the noise reduction as nonlinear squeezing. Non-Gaussian aspects of quantum states are often those most vulnerable to decoherence due to imperfections appearing in realistic experimental implementations. We analyze the behavior of quantum states with cubic nonlinear squeezing under loss and dephasing. The properties of nonlinear squeezed states depend on their initial parameters that can be optimized and adjusted to achieve the maximal robustness for the potential applications.

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Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator

Cited by 11 publications

References 92 publications

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

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

Quantum hypergraph states in continuous variables

Cubic nonlinear squeezing and its decoherence

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