Nanoparticle Technique Cancels Disruptive Noise in Quantum Experiments

A new technique improves the precision of quantum measurements. Martynas Skrabulis and colleagues from the Photonics Laboratory, and colleagues have developed a method for cancelling unwanted noise between experimental runs, known as shot-to-shot noise, in parametric oscillators. The approach, inspired by spin-echo techniques, effectively suppresses this noise to the fundamental limit imposed by quantum mechanics, potentially enabling more sensitive and accurate quantum sensing and computation. The team implemented and validated their ‘oscillator-echo’ protocol using an optically levitated nanoparticle subject to fluctuating external forces.

Suppression of decoherence in optically levitated nanoparticles for quantum control

A primary challenge hindering operation of mechanical oscillators outside the classical realm is decoherence, a process involving entanglement between the mechanical oscillator and unobserved degrees of freedom. Sophisticated phonon engineering has enabled sufficient suppression of decoherence in tethered mechanical oscillators to reach measurement-based quantum control, even at room temperature. Quantum noise of the probe light dominates the fluctuations acting on the system in this regime.

Optically levitated nanoparticles represent a simple optomechanical platform routinely operated in the backaction-dominated regime. The centre-of-mass motion of such a dipolar scatterer resembles a three-dimensional harmonic oscillator with continuous position measurement. Ultra-high vacuum operation can suppress decoherence due to the thermal bath, reaching the backaction-dominated regime. This approach has enabled cooling the centre-of-mass motion of nanoparticles to the ground state, and initial steps have been taken to expose quantum features of the particle’s mechanical state by squeezing the fluctuations of one mechanical quadrature below its zero-point value.

Quantum control of optically levitated nanoparticles has enabled cooling their centre-of-mass motion to the ground state. These approaches exploit the ability to tune the resonance frequency of optically levitated systems over a wide range by controlling the trapping-laser power, allowing for parametric modulation of the oscillator eigenfrequency. However, experimental stability presents a practical concern, as many experimental repetitions are required to observe the statistical properties of quantum mechanics.

Slow fluctuations of experimental parameters, termed “shot-to-shot noise”, have challenged the levitated-optomechanics community when creating squeezed states of mechanical motion. This noise is considered shot-to-shot when the time between repetitions is long enough for the uncontrolled parameter to change appreciably, and the duration of a single shot is short enough for the noise to remain constant on that timescale. Kamba et al. at the Swiss Federal Institute of Technology in Zurich identified the difference in the centre of mass and the optical trap as the cause of shot-to-shot force noise. At a more abstract level, shot-to-shot noise in optomechanics effectively yields an ensemble broadening, where each ensemble member corresponds to one realization of the experiment.

This phenomenon is reminiscent of the effective dephasing encountered by an ensemble of spins with slightly differing Larmor frequencies. The existence of echo protocols that refocus spin ensembles and cancel ensemble dephasing raises whether similar decoupling techniques exist for state-expansion protocols of mechanical oscillators against shot-to-shot noise. A protocol has been proposed and experimentally realised that cancels shot-to-shot force noise in squeezing protocols for harmonic oscillators relying on stepwise modulation of the oscillator frequency.

Their oscillator-echo protocol embeds the desired squeezing manipulation between two decoupling steps that refocus the ensemble, akin to a spin-echo protocol. They implemented this protocol using an optically levitated nanoparticle and demonstrate shot-to-shot force-noise suppression to the limit where observed quadrature variances are limited by measurement back-action. The experimental setup involves trapping a silica nanoparticle (nominal diameter 100nm, mass 1.2 fg) in an x-polarized laser beam (wavelength 1550nm, power ∼600mW) focused with an aspheric lens (numerical aperture 0.8). The centre-of-mass oscillation frequencies are (Ωz, Ωx, Ωy)/(2π) = (52, 141, 175) kHz, with focus on the motion along z. Cold-damping reduces the centre-of-mass temperature to a phonon population of n = 1.2±0.6, limited by the detection efficiency η = 0.14. Feedback is implemented by acting on the particle (carrying a few elementary charges) with a Coulomb force proportional to the particle speed, derived from the position measurement.

Measurement backaction yields a recoil heating rate Γqb/(2π) = 3.4 ±0.5kHz. A pair of lasers strategically modulates the stiffness of the optical trap. For Gaussian states, the phase-space distribution is fully described by the state’s expectation value d = ⟨v⟩ and its covariance matrix Σ = ⟨vvT ⟩−⟨v⟩⟨v’T. The evolution of the mean d, starting at d0 = ⟨v0⟩, is given by d(θ) = Φr(θ)d0 + df0,r(θ). Measuring Q relative to the minimum of the effective potential, the initial state undergoes a squeezed rotation around the origin superimposed on a linear translation by the displacement vector df0,r(θ) = f0 Ω r2 −1 r [r(1 −cos θ), sin θ]T. The trajectory of d(θ) when starting at the origin d0 = T is an elliptical trajectory around the centre point cf0,r = f0 Ω(r2 −1), 0 T. This oscillation is explained by the shift in the minimum of the potential when the stiffness is reduced by r. Rotation in phase space around cf0,r corresponds to oscillations around this new minimum. The elliptical trajectories of the mean for two values of the constant force f0 are illustrated.

Oscillator-echo technique reaches measurement-backaction limit in levitated nanoparticle experiments

Shot-to-shot noise in experiments squeezing the motion of microscopic oscillators has been suppressed to the measurement-backaction limit, a new record achieved using an optically levitated nanoparticle. The Swiss-based team employed a technique inspired by nuclear magnetic resonance, dubbed ‘oscillator-echo’, to cancel out fluctuations caused by stray electric fields. This breakthrough allows the intrinsic quantum behaviour of the nanoparticle to be isolated, previously masked by external disturbances.

The oscillator-echo protocol works by embedding the squeezing step between two decoupling steps, effectively neutralizing the disruptive force fluctuations before and after. Measurements confirm the technique reduces state variance to the level dictated by the unavoidable noise introduced during measurement itself, a significant improvement in experimental control. This advancement builds upon previous work demonstrating ultrahigh-quality resonators and cooling nanoparticles to their quantum ground state, paving the way for more precise sensing applications.

This level of control was attained by employing a novel technique, ‘oscillator-echo’, inspired by methods used in nuclear magnetic resonance. The protocol strategically places a ‘squeezing’ step, which reduces quantum uncertainty, between two ‘decoupling’ steps that neutralise disruptive external forces. Measurements revealed an optimal modulation value that minimises displacement and lowers the state’s variance to the level dictated by unavoidable measurement noise, a key indicator of success. However, these results do not yet demonstrate sustained quantum states or address the considerable engineering challenges required to scale this technique for practical dark matter detection.

Quantum noise cancellation unlocks precision nanoparticle control

Extending ‘oscillator-echo’ to arrays of levitated nanoparticles, a crucial step towards building more powerful sensors, presents a significant challenge. Maintaining coherent control over multiple, interacting nanoparticles will require overcoming complex electrostatic forces and cross-talk between individual traps. Despite the current limitation to single nanoparticles, this development represents a vital step forward in precision measurement. Random forces affecting the particle’s movement were successfully suppressed to the fundamental limit imposed by quantum mechanics; this ‘oscillator-echo’ technique effectively cancels them.

Achieving this level of control is crucial for building more sensitive detectors for diverse applications, ranging from gravitational wave detection to searching for dark matter particles. This new technique effectively neutralises disruptive forces acting on microscopic particles, allowing for clearer observation of their quantum behaviour. By adapting principles from nuclear magnetic resonance, scientists cancelled out unwanted fluctuations affecting an optically levitated nanoparticle, held in place by light, making it ideal for precision measurements. This level of control, where noise is reduced to the fundamental limit imposed by quantum mechanics, is crucial for advancing sensitive detection technologies. The protocol implemented here embeds a process called ‘squeezing’, reducing quantum uncertainty, between two ‘decoupling’ steps that counteract external disturbances.

The researchers successfully suppressed shot-to-shot force noise to the measurement-backaction limit using an oscillator-echo protocol with an optically levitated nanoparticle. This means they reduced disruptive external forces acting on the particle, allowing for more precise observation of its quantum behaviour. The technique adapts principles from spin-echo protocols to cancel unwanted fluctuations, demonstrating a vital step forward in precision measurement. The authors demonstrated this noise suppression in a single nanoparticle, and acknowledge that extending this to arrays of nanoparticles presents a significant challenge.