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Direct Measurement of Photon Recoil from a Levitated Nanoparticle

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Direct Measurement of Photon Recoil from a Levitated Nanoparticle Selected for a Viewpoint in Physics week ending PRL 116, 243601 (2016) PHYSICAL REVIEW LETTERS 17 JUNE 2016 Direct Measurement of Photon Recoil from a Levitated Nanoparticle Vijay Jain,1,2 Jan Gieseler,1 Clemens Moritz,3 Christoph Dellago,3 Romain Quidant,4,5 and Lukas Novotny1,* 1Photonics Laboratory, ETH Zürich, 8093 Zürich, Switzerland 2Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA 3Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria 4ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain 5ICREA—Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain (Received 19 December 2015; published 13 June 2016) The momentum transfer between a photon and an object defines a fundamental limit for the precision with which the object can be measured. If the object oscillates at a frequency Ω0, this measurement backaction adds quanta ℏΩ0 to the oscillator’s energy at a rate Γrecoil, a process called photon recoil heating, and sets bounds to coherence times in cavity optomechanical systems. Here, we use an optically levitated Γ nanoparticle in ultrahigh vacuum to directly measure recoil. By means of a phase-sensitive feedback scheme, we cool the harmonic motion of the nanoparticle from ambient to microkelvin temperatures and measure its reheating rate under the influence of the radiation field. The recoil heating rate is measured for different particle sizes and for different excitation powers, without the need for cavity optics or cryogenic environments. The measurements are in quantitative agreement with theoretical predictions and provide valuable guidance for the realization of quantum ground-state cooling protocols and the measurement of ultrasmall forces. DOI: 10.1103/PhysRevLett.116.243601 Our ability to detect ultraweak forces depends on both the dissipation is often the dominant decoherence mechanism noise and the sensitivity of the measurement. An optical and places a material limit on the sensitivity of the device [7]. position sensor, for example, irradiates an object with light Optically levitated nanoparticles in vacuum have proven and detects the scattered photons. As each photon carries to be versatile platforms for studies of light-matter inter- momentum p ¼ ℏk, we can increase the optical powerpffiffiffiffi to actions [10–15]. Free from mechanical vibrations of the reduce the object’s position uncertainty to Δx ≥ 1=ð2k NÞ, environment, they have been used to investigate non- where N is the number of scattered photons. Increasing the equilibrium fluctuation theorems [16], nonlinear dynamics optical power, however, increases the rate of momentum and synchronization [17], rotational motion [18], ultrasmall kicks from individual photons and results in a force due to forces [15,19], and coupling to internal spin degrees of radiation pressure shot noise (RPSN), which perturbs the freedom [20]. In the context of cavity optomechanics, inspected object. While increasing power reduces our levitated nanoparticles have also been proposed for quan- measurement imprecision, RPSN places limits on the tum ground-state cooling [13,14,21,22] and for gravita- information gained from a system [1,2]. tional wave detection [23,24]. Central to all of these Remarkable advances in microfabrication have resulted experiments is the optical gradient force, which is needed in high-Q mechanical resonators required for enhanced to trap and control the scrutinized nanoparticle. However, force sensitivity. In addition to ground-state cooling [3,4], due to the discrete nature of optical radiation, the trapping recent experiments in cryogenic chambers with silicon force is itself intrinsically noisy and RPSN may influence nitride membranes, cold-atomic clouds, and microwave the motion of the trapped particle via photon recoil heating, devices have verified the influence of RPSN in continuous akin to atomic physics where it limits the temperature of position and force measurements [5–9]. Increasing the Sisyphus cooling to a few microkelvins [25]. circulating optical power in the cavity increases the back- In most situations, photon recoil heating is negligibly action to the resonator, which is manifested as an increase small for macroscopic objects, as the recoil energy in the oscillator’s mean-square displacement. ℏ2k2=ð2mÞ scales inversely with the object’s mass. While cavity optomechanical systems seek to operate in Consequently, to observe this weak effect, the system this shot-noise dominant regime in order to observe macro- has to be sufficiently well isolated. Specifically, the photon scopic quantum phenomena, material impurities limit the recoil rate has to be larger than the thermal decoherence quality factors within systems that are mechanically clamped rate. Using active feedback to bring a nanoparticle into P ∼ 10−8 to the environment. Furthermore, absorption of radiation ultrahigh vacuum (UHV) ( gas mbar), however, we limits the number of photons that can be used to interrogate significantly reduce the heating due to residual gas mol- the system. Thus, despite cryogenic temperatures, thermal ecules and thereby ascertain for the first time a direct 0031-9007=16=116(24)=243601(5) 243601-1 © 2016 American Physical Society PHYSICAL REVIEW LETTERS week ending PRL 116, 243601 (2016) 17 JUNE 2016 x γ interaction with the radiation field, and fb is the damping introduced by feedback cooling. The different contributions will be discussed in detail. z The trapped particle’s energy changes constantly due to Ω interactions with its environment, and the time evolution of 0 E¯ ω its average energy is predicted by the Fokker-Planck h 0 equation to be [16] m d ¯ ¯ EðtÞ¼−γ½EðtÞ − E∞; ð2Þ y dt E0 where E∞ is the average energy in the steady state (t → ∞) FIG. 1. Illustration of photon recoil heating. A particle with and γ is the rate at which the steady state is reached. Writing m mass is trapped at the focus of a laser beam by means of the the average energy of the particle in terms of discrete optical gradient force. The particle’s center-of-mass temperature ¯ quanta, E ¼ nℏΩ0, we obtain is cooled by parametric feedback and heated by individual photon Ω =2π momentum kicks. 0 is the mechanical oscillation frequency n_ ¼ −γn þ Γ; ð Þ and ℏω0 is the photon energy. The incident light is polarized 3 along the x direction. where n is the mean occupation number and readout of the recoiling rate of photons from a macroscopic E∞ object at room temperature. This places us in the regime of Γ ¼ γ ð4Þ ℏΩ0 strong measurement backaction [8]. To minimize the damping due to residual gas molecules, is the heating rate. It defines the rate at which phonons are we perform our experiments in UHV environments. As reintroduced into the mechanical system. The solution of described in Ref. [11], we first trap a particle by a strongly Eq. (3) is focused laser beam at ambient temperature and gas pres- sure, and then evacuate the vacuum chamber. We use fused −γt nðtÞ¼n∞ þ½n0 − n∞e ; ð5Þ silica particles with radii on the order of R ¼ 50 nm, a laser beam with wavelength λ ¼ 1064 nm and power where n0 is the mean occupation number at an initial time P ¼ 70 0 mW, and an objective of numerical aperture and NA ¼ 0.9 for focusing. The total detection efficiency is ηc ¼ 0.0005. It accounts for the photon collection effi- Γ Γ þ Γ þ Γ n ¼ ¼ th recoil fb ð Þ ciency, the splitting into separate detection paths, optical ∞ γ γ þ γ þ γ 6 losses, detector quantum efficiency, and the efficiency of th rad fb translating a displacement into a phase change between the is the occupation number in the steady state. In Eq. (6) we excitation field and the scattered field [26]. We choose a have written Γ as the sum of a heating rate due to collisions coordinate system whose z axis coincides with the optical Γ with gas molecules ( th), a heating rate due to photon recoil axis and whose x axis defines the direction of polarization Γ kicks ( recoil), and a heating rate due to noise introduced by of the incident light (cf. Fig. 1). the feedback loop (Γ ). ’ fb For small oscillation amplitudes, the particle s motion The surrounding gas at temperature T gives rise to the along the three principal axes is decoupled and we end up damping γ and the thermal decoherence Γ ¼ γ kBT= with three independent harmonic oscillators, each with its th th th ℏΩ0.Forγ > Ω0, the particle’s motion is overdamped Ω γ own oscillation frequency 0 and damping , a result of the and the dynamics are governed by a diffusion equation, as asymmetric shape of the optical potential [11]. For exam- in the case of optical tweezers operated in liquids. At gas y ple, the motion along is described by pressures below 10 mbar, the damping to the nanoparticle is linear in gas pressure [32], 2 1 ÿþ γy_ þ Ω0y ¼ FðtÞ; ð1Þ m R2P γ ≈ 15 8 gas ; ð Þ th . mv 7 with Ω0=2π ¼ 150 kHz (cf. Fig. 2) and F denoting gas fluctuating forces acting on the particle. The corresponding pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P v ¼ 3k T=m m oscillation frequencies for the x and z axes are 123 and where gas is the pressure, gas B gas and gas 49 kHz, respectively. The oscillator’s damping rate can be are the root-mean-square velocity and mass of gas mole- γ ¼ γ þ γ þ γ γ R m ’ written as th rad fb, where th accounts for the cules, and and are the particle s radius and mass, γ interaction with the background gas, rad refers to the respectively. 243601-2 PHYSICAL REVIEW LETTERS week ending PRL 116, 243601 (2016) 17 JUNE 2016 105 ℏω P Here, 0 is the photon energy and scatt is the scattered n=179028 power of the particle.
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