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arXiv:2407.07060 · Physical Review Letters

Imaging-Based Quantum Optomechanics

Christian M. Pluchar, Wenhua He, Jack P. Manley, Nicolas Deshler, Saikat Guha, Dalziel Joseph Wilson

Published May 14, 2025• 7 citations
arXivHTMLPDF

Abstract

In active imaging protocols, information about an object is encoded into the spatial mode of a scattered photon. Recently the quantum limits of active imaging have been explored with levitated nanoparticles, which experience a multimode radiation pressure backaction (the photon recoil force) due to radiative scattering of the probe field. Here we extend the analysis of multimode backaction to compliant surfaces, accessing a broad class of mechanical resonators and fruitful analogies to quantum imaging. As an example, we consider imaging of the flexural modes of a membrane by sorting the spatial modes of a laser reflected from its surface. We show that backaction in this setting can be understood to arise from spatiotemporal photon shot noise, an effect that cannot be observed in single-mode optomechanics. We also derive the imprecision-backaction product in the limit of purely spatial (intermodal) coupling, revealing it to be equivalent to the standard quantum limit for single-mode optomechanical coupling. Finally, we show that optomechanical correlations due to spatiotemporal backaction can give rise to two-mode entangled light, providing a mechanism for entangling desired pairs of spatial modes. In conjunction with high-Q nanomechanics, our findings point to new opportunities at the interface of quantum imaging and optomechanics, including sensors and networks enhanced by spatial mode entanglement.

DOI
10.1103/64xv-3fyx

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In active imaging protocols, information about an object is encoded into the spatial mode of a scattered photon. Recently the quantum limits of active imaging have been explored with levitated nanoparticles, which experience a multimode radiation pressure backaction (the photon recoil force) due to radiative scattering of the probe field. Here we extend the analysis of multimode backaction to compliant surfaces, accessing a broad class of mechanical resonators and fruitful analogies to quantum imaging. As an example, we consider imaging of the flexural modes of a membrane by sorting the spatial modes of a laser reflected from its surface. We show that backaction in this setting can be understood to arise from spatiotemporal photon shot noise, an effect that cannot be observed in single-mode optomechanics. We also derive the imprecision-backaction product in the limit of purely spatial (intermodal) coupling, revealing it to be equivalent to the standard quantum limit for single-mode optomechanical coupling. Finally, we show that optomechanical correlations due to spatiotemporal backaction can give rise to two-mode entangled light, providing a mechanism for entangling desired pairs of spatial modes. In conjunction with high-Q nanomechanics, our findings point to new opportunities at the interface of quantum imaging and optomechanics, including sensors and networks enhanced by spatial mode entanglement.
Multimode optomechanical scattering is ubiquitous in free-space imaging protocols, but its radiation pressure counterpart is challenging to detect with extended objects. Here we demonstrate radiation pressure actuation of a nanomechanical membrane using dynamically structured light from a spatial mode demultiplexer (SPADE). Using single- and two-mode illumination, we directly image the position-dependent intermodal coupling between Hermite-Gauss (HG) modes as mediated by the membrane's motion. As an application, we use multimode radiation pressure feedback to simultaneously cool two nearly degenerate membrane modes. Our results are applicable to diverse mechanical systems and serve as a stepping stone to SPADE-based quantum optomechanics.
Cavity Optomechanics, that is the study of the interaction between an optical cavity mode and a mechanical degree of freedom, has known impressive evolution over the past decade, to become a new field at the union of condensed matter physics and optics. One of the major goals of this discipline is to test and study quantum mechanics using macroscopic systems. Among the most fundamental problems the community aims to address is the question of the quantum limits in position measurement. Quantum mechanics predicts that any measurement comes along with a backaction, which perturbs the state of the measured system. Moreover, it is expected to be conjugated with the quantum noise of the measurement apparatus (called measurement noise) used to probe the system. The optimal sensitivity is reached whenever both the measurement and the backaction noise are identical, a situation which can be assimilated to the acceptance of Heisenberg's inequality for the measurement apparatus. In cavity optomechanics, the mode of an optical cavity is used as a measurement apparatus of the position of a mechanical resonator which is expected to be responsible for the backaction imprecision. However, this so-called radiation pressure quantum backaction has never been observed to date, while it remains a decisive step towards understanding quantum measurement processes. We describe in this manuscript the study of radiation pressure effects in cavity optomechanics. We introduce the optomechanical system we have developed, which consists in a cm-scale ultra high Q (~ 1 000 000) plano-convex mechanical resonator incorporated into a ultra-high finesse (~ 300 000) Fabry-Prot cavity. We present two important results we obtained with this system. First, we were able to report the first direct observation of radiation pressure in real-time, based on establishing pump-probe correlations. We were also able to demonstrate for the first time nonlinear backaction effects related to substantial improvement of position measurement sensitivity. We explain why demonstrating quantum backaction requires ultra-high stability of the optical mode. We present important changes made to the previous experimental setup, notably on the laser source, on the detection and the stabilization of the experiment. We then describe a new optomechanical detection technique providing an independent measurement of the cavity detuning. Finally, we present a proof-of-principle experiment allowing to extract quantum optomechanical correlations at room temperature.
Backaction-evading measurements of mechanical motion can achieve precision below the zero-point uncertainty and quantum squeezing, which makes them a resource for quantum metrology and quantum information processing. We provide an exact expression for the conditional state of an optomechanical system in a two-tone backaction-evading measurement beyond the standard adiabatic approximation and perform extensive numerical simulations to go beyond the usual rotating-wave approximation. We predict the simultaneous presence of conditional mechanical squeezing, intracavity squeezing, and optomechanical entanglement. We further apply an analogous analysis to the multimode optomechanical system of two mechanical and one cavity mode and find conditional mechanical Einstein-Podolski-Rosen entanglement and genuinely tripartite optomechanical entanglement. Our analysis is of direct relevance for ultrasensitive measurements and measurement-based control in high-cooperativity optomechanical sensors operating beyond the adiabatic limit.
We propose here a fully backaction-evading scheme for the measurement of the entanglement between two nanomechanical resonators. The system, which consists of two mechanical oscillators, coupled to a single mode of an electromagnetic resonant cavity through a radiation-pressure interaction term, is driven by two pump tones and four detection tones. As previously discussed in the literature, the former induce entanglement between the two mechanical oscillators, while we show here that a specific choice of phase and amplitude of the detection tones allows for direct pairwise reconstruction of the collective quadrature fluctuations of the mechanical oscillators belonging to quantum-mechanics-free subspaces, thereby providing direct evidence of the entanglement properties of the two mechanical resonators.
We theoretically show that laser recoil heating in free-space levitated optomechanics can be arbitrarily suppressed by shining squeezed light onto an optically trapped nanoparticle. The presence of squeezing modifies the quantum electrodynamical light-matter interaction in a way that enables us to control the amount of information that the scattered light carries about a given mechanical degree of freedom. Moreover, we analyze the trade-off between measurement imprecision and back-action noise and show that optical detection beyond the standard quantum limit can be achieved. We predict that, with state-of-the-art squeezed light sources, laser recoil heating can be reduced by at least 60% by squeezing a single Gaussian mode with an appropriate incidence direction, and by 98% by squeezing a properly mode-matched mode. Our results, which are valid both for motional and librational degrees of freedom, will lead to improved feedback cooling schemes as well as boost the coherence time of optically levitated nanoparticles in the quantum regime.
Why are classical theories often sufficient to describe the physics of our world even though everything around us is entirely composed of microscopic quantum systems? The boundary between these two fundamentally dissimilar theories remains an unsolved problem in modern physics. Position measurements of small objects allow us to probe the area where the classical approximation breaks down. In quantum mechanics, Heisenbergâ s uncertainty principle dictates that any measurement of the position must be accompanied by measurement induced back-action---in this case manifested as an uncertainty in the momentum. In recent years, cavity optomechanics has become a powerful tool to perform precise position measurements and investigate their fundamental limitations. The utilization of optical micro-cavities greatly enhances the interaction between light and state-of-the-art nanomechanical oscillators. Therefore, quantum mechanical phenomena have been successfully observed in systems far beyond the microscopic world. In such a cavity optomechanical system, the fluctuations in the position of the oscillator are transduced onto the phase of the light, while fluctuations in the amplitude of the light disturb the momentum of the oscillator during the measurement. As a consequence, correlations are established between the amplitude and phase quadrature of the probe light. However, so far, observation of quantum effects has been limited exclusively to cryogenic experiments, and access to the quantum regime at room temperature has remained an elusive goal because the overwhelming amount of thermal motion masks the weak quantum effects. This thesis describes the engineering of a high-performance cavity optomechanical device and presents experimental results showing, for the first time, the broadband effects of quantum back-action at room temperature. The device strongly couples mechanical and optical modes of exceptionally high quality factors to provide a measurement sensitivity ∼ ⁣104\sim\!10^4∼104 times below the requirement to resolve the zero-point fluctuations of the mechanical oscillator. The quantum back-action is then observed through the correlations created between the probe light and the motion of the nanomechanical oscillator. A so-called â variational measurementâ , which detects the transmitted light in a homodyne detector tuned close to the amplitude quadrature, resolves the quantum noise due to these correlations at the level of 10\% of the thermal noise over more than an octave of Fourier frequencies around mechanical resonance. Moreover, building on this result, an additional experiment demonstrates the ability to achieve quantum enhanced metrology. In this case, the generated quantum correlations are used to cancel quantum noise in the measurement record, which then leads to an improved relative signal-to-noise ratio in measurements of an external force. In conclusion, the successful observation of broadband quantum behavior on a macroscopic object at room temperature is an important milestone in the field of cavity optomechanics. Specifically, this result heralds the rise of optomechanical systems as a platform for quantum physics at room temperature and shows promise for generation of ponderomotive squeezing in room-temperature interferometers.