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arXiv:2110.07714 · Physical Review A

Nonlinear atomic force microscopy: Squeezing and skewness of micromechanical oscillators interacting with a surface

Karl-Peter Marzlin, Bryan Canam, Nisha Rani Agarwal

Published Jan 19, 2022• 1 citation
arXivHTMLPDF

Abstract

We propose a two-frequency driving scheme in dynamic atomic force microscopy that maximizes the interaction time between tip and sample. Using a stochastic description of the cantilever dynamics, we predict large classical squeezing and a small amount of skewness of the tip's phase-space probability distribution. Strong position squeezing will require close contact between tip and surface, while momentum squeezing would also be possible in the van der Waals region of the tip-surface force. Employing a generalized Caldeira-Leggett model, we predict that surface-dependent dissipative forces may be the dominant source of quantum effects and propose a procedure to isolate quantum effects from thermal fluctuations.

DOI
10.1103/physreva.105.012211

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A scheme to squeeze the center-of-mass motional quadratures of a quantum mechanical oscillator below its standard quantum limit is proposed and analyzed theoretically. It relies on the dipole-dipole coupling between a magnetic dipole mounted on the tip of a cantilever to equally oriented dipoles located on a mesoscopic tuning fork. We also investigate the influence of several sources of noise on the achievable squeezing, including classical noise in the driving fork and the clamping noise in the oscillator. A detection of the state of the cantilever based on state transfer to a light field is considered. We investigate possible limitations of that scheme.
We consider the quantum and classical noise limits to position measurement and force detection by an atomic force microscope (AFM) with an optical readout of cantilever position. We model this by treating the cantilever as a perfectly reflecting mirror for a highly damped optical cavity. There are three sources of noise: the shot noise in the output laser measurement, the thermal noise in the cantilever, and the measurement back-action noise. This last source of noise becomes large for good measurements, measurements for which there is a high correlation between the output phase of the light and the changing position of the cantilever. The back action simultaneously drives a diffusion process in momentum and diagonalizes the cantilever state in the position basis. This latter result is ``state reduction.'' Explicit expressions for the rate of the measurement back action in terms of the device parameters are given. We also calculate the signal-to-noise ratio in the limit of a bad cavity. A comparison to recent experiments suggests that current AFMs are not quantum limited.
Driven nonlinear quantum oscillators are a central platform for quantum technologies, yet their dissipative dynamics are typically described using Lindblad or Caldeira-Leggett master equations derived under assumptions that exclude nonlinearities and driving. Here, we derive a generalized Caldeira-Leggett master equation for driven nonlinear oscillators by retaining the full nonlinear and time-dependent system dynamics in the construction of the dissipator. For position- and momentum-dependent system-bath coupling, the dissipator itself becomes dynamically dressed, generating nonlinear and drive-dependent dissipative channels beyond conventional fixed-dissipator approaches. This produces nonlinear damping together with dissipation-induced corrections to the effective drive. The resulting dissipative dynamics suppress large-amplitude excitations and reduce phase-space fluctuations. For a driven Kerr oscillator, this leads to the suppression of bistability, asymmetric resonance responses, and strongly modified fluctuation distributions. More broadly, our results establish a microscopic framework in which nonlinear dynamics and driving directly reshape the dissipative sector of driven open quantum systems.
This work investigates different coupling mechanisms between ultracold atoms and mechanical oscillators. In a first experiment, atom-surface force is used to couple the vibrations of a mechanical cantilever to the motion of a Bose-Einstein condensate in a magnetic microtrap on a chip. The atoms are trapped at sub-micrometer distance from the cantilever surface. Coupling is used to read out the cantilever vibrations with the atoms. Coupling via surface forces could be employed to couple atoms to molecular-scale oscillators such as carbon nanotubes. In a second experiment, coupling via a 1D optical lattice that is formed by a laser beam retroreflected from the cantilever tip. The optical lattice serves as a transfer rod which couples vibrations of the cantilever to the atoms and vice versa.
We simulated the quantum dynamics for magnetic resonance force microscopy (MRFM) in the oscillating cantilever-driven adiabatic reversals (OSCAR) technique. We estimated the frequency shift of the cantilever vibrations and demonstrated that this shift causes the formation of a Schr\"odinger cat state which has some similarities and differences from the conventional MRFM technique which uses cyclic adiabatic reversals of spins. The interaction of the cantilever with the environment is shown to quickly destroy the coherence between the two possible cantilever trajectories. We have shown that using partial adiabatic reversals, one can produce a significant increase in the OSCAR signal.