A cavity optomechanical magnetometer is demonstrated. The magnetic field induced expansion of a magnetostrictive material is resonantly transduced onto the physical structure of a highly compliant optical microresonator, and read-out optically with ultra-high sensitivity. A peak magnetic field sensitivity of 400 nT Hz −1/2 is achieved, with theoretical modeling predicting the possibility of sensitivities below 1 pT Hz −1/2 . This chipbased magnetometer combines high-sensitivity and large dynamic range with small size and room temperature operation.Ultra-low field magnetometers are essential components for a wide range of practical applications including geology, mineral exploration, archaeology, defence and medicine [1]. The field is dominated by superconducting quantum interference devices (SQUIDs) operating at cryogenic temperatures [2]. Magnetometers capable of room temperature operation offer significant advantages both in terms of operational costs and range of applications. The state-of-the-art are magnetostrictive magnetometers with sensitivities in the range of fT Hz −1/2 [3, 4], and atomic magnetometers which achieve impressive sensitivities as low as 160 aT Hz −1/2 [5] but with limited dynamic range due to the nonlinear Zeeman effect [2,6]. Recently, significant effort has been made to miniaturize room temperature magnetometers. However both atomic and magnetostrictive magnetometers remain generally limited to millimeter or centimeter size scales. Smaller microscale magnetometers have many potential applications in biology, medicine, and condensed matter physics [7,8]. A particularly important application is magnetic resonance imaging, where by placing the magnetometer in close proximity to the sample both sensitivity and resolution may be enhanced [9], potentially enabling detection of nuclear spin noise [10], imaging of neural networks [7], and advances in areas of medicine such as magneto-cardiography[1, 6] and magneto-encephalography [11].In the past few years, rapid progress has been achieved on NV center based magnetometers. They combine sensitivities as low as 4 nT Hz −1/2 with room temperature operation, optical readout and nanoscale size [12] and are predicted theoretically to reach the fT Hz −1/2 range [13]. This has allowed three-dimensional magnetic field imaging at the micro scale using ensembles of NV-centers [7], and magnetic resonance [14] and field imaging[13] at the nanoscale using single NV centers. In spite of these extraordinary achievements applications are hampered by fabrication issues and the intricacy of the read-out schemes [15]. Furthermore miniaturization is limitied by the bulky read-out optics, the magnetic field coils for state preparation and the microwave excitation device [7].In this letter we present the concept of a cavity optomechanical field sensor which combines room temperature operation and high sensitivity with large dynamic range and small size. The sensor leverages results from the emergent field of cavity optomechanics where ultra-sensitive force and positi...

Nonlinear forces allow motion of a mechanical oscillator to be squeezed below the zero-point motion.Of existing methods, mechanical parametric amplification is relatively accessible, but previously thought to be limited to 3 dB of squeezing in the steady state. We consider the effect of applying continuous weak measurement and feedback to this system. If the parametric drive is optimally detuned from resonance, correlations between the quadratures of motion allow unlimited steady-state squeezing. Compared to backaction evasion, we demonstrate that the measurement strength, temperature and efficiency requirements for quantum squeezing are significantly relaxed. DOI: 10.1103/PhysRevLett.107.213603 PACS numbers: 42.50.Dv, 85.85.+j Recent experiments have demonstrated impressive progress in cooling towards the ground state and measuring the zero-point motion of mechanical oscillators. This brings within reach the observation of nonclassical phonon states, with applications in quantum information and tests of quantum mechanics [1] The most successful systems to date involve cryogenically cooled high frequency oscillators strongly coupled to optical or microwave fields [2,3]. However, techniques to manipulate quantum states and investigate nonclassical behavior of phonons, apart from creating single phonon states [4], are less well developed.A squeezed state, in which the variance of one quadrature of motion is below the zero-point motion, is the most accessible of quantum resources in optomechanical systems. This can be achieved, for example, by resolved sideband cooling using squeezed or modulated input light [5,6]. Also promising is squeezing via backaction evading measurement (BAE) [7], which is close to being realized [8]. These schemes would allow for ultrasensitive force detection [9] and normal mode entanglement [10] but are constrained by the requirement of strong coupling to the optical mode. Additional downsides are the requirement of ultralow temperatures and the side-effect of parametric instability due to strong radiation pressure [8].Electrostatic forces, on the other hand, are strong enough to create nonclassical states in an oscillator by driving it into the nonlinear regime [1]. It has been predicted that micro-and nanoelectromechanical systems (MEMS/NEMS) can be engineered in this way to excite arbitrary Fock states [11] and induce macroscopic quantum tunnelling [12]. In a similar fashion, mechanical squeezing can be achieved via mechanical parametric amplification (MPA) [13]. MPA exploits nonlinearities in the electrostatic driving field [14], the resonator's intrinsic motion [15] or a coupled charge qubit [16]. A periodic modulation in the oscillator's spring constant at twice its resonance frequency gives rise to an in-phase amplified quadrature and an out-of-phase damped quadrature. The amplified gain approaches infinity at threshold, whereas the squeezing due to damping is limited to a factor of 1 half. This is a long-standing problem that also limits the intracavity variance of an optical ...

Predation is thought to shape the macroscopic properties of animal groups, making moving groups more cohesive and coordinated. Precisely how predation has shaped individuals' fine-scale social interactions in natural populations, however, is unknown. Using high-resolution tracking data of shoaling fish (Poecilia reticulata) from populations differing in natural predation pressure, we show how predation adapts individuals' social interaction rules. Fish originating from high predation environments formed larger, more cohesive, but not more polarized groups than fish from low predation environments. Using a new approach to detect the discrete points in time when individuals decide to update their movements based on the available social cues, we determine how these collective properties emerge from individuals' microscopic social interactions. We first confirm predictions that predation shapes the attraction–repulsion dynamic of these fish, reducing the critical distance at which neighbours move apart, or come back together. While we find strong evidence that fish align with their near neighbours, we do not find that predation shapes the strength or likelihood of these alignment tendencies. We also find that predation sharpens individuals' acceleration and deceleration responses, implying key perceptual and energetic differences associated with how individuals move in different predation regimes. Our results reveal how predation can shape the social interactions of individuals in groups, ultimately driving differences in groups' collective behaviour.

We experimentally surpass the 3 dB limit to steady-state parametric squeezing of a mechanical oscillator. The localization of an atomic force microscope cantilever, achieved by optimal estimation, is enhanced by up to 6.2 dB in one position quadrature when a detuned parametric drive is used. This squeezing is, in principle, limited only by the oscillator Q factor. Used on low temperature, high frequency oscillators, this technique provides a pathway to achieve robust quantum squeezing below the zero-point motion. Broadly, our results demonstrate that control systems engineering can overcome well established limits in applications of nonlinear processes. Conversely, by localizing the mechanical position to better than the measurement precision of our apparatus, they demonstrate the usefulness of mechanical nonlinearities in control applications. DOI: 10.1103/PhysRevLett.110.184301 PACS numbers: 45.80.+r, 05.40.Àa High-quality mechanical oscillators are widely used for weak force detection [1,2], nanoscale manipulation [3,4], and quantum state engineering [5,6]. Such applications often utilize optimal estimation to localize the oscillator, followed by feedback control to confine its position. In a classical context, this type of control is commonly used to linearize the response of sensors driven into their nonlinear regime, resulting in increased dynamic range and suppression of resonance frequency fluctuations [7]. Furthermore, spurred by the growing prospect of accessing new quantum physics [8], similar techniques are now being applied to state-of-the art mechanical oscillators to cool them close to the quantum limit set by mechanical zero-point motion [9,10], and ultimately surpass it via quantum control techniques such as backaction evasion [11][12][13]. However, the level of achievable oscillator localization has always previously been limited to at best the measurement precision, presenting a significant barrier to applications in both quantum and classical regimes.Applications of mechanical oscillators can also benefit from nonlinearities without requiring any measurement. An example of particular relevance to this Letter is mechanical parametric amplification, where direct modulation of the spring constant induces amplification of in-phase motion [14]. This technique is often used in microelectromechanical (MEMS) and nanoelectromechanical systems to boost mechanical signals from in-phase forces above the measurement noise floor [15,16]. Conversely, out-of-phase motion is deamplified and thereby more strongly confined or ''squeezed.'' In principle, squeezing below the zero-point motion variance V g is possible. Such ''quantum squeezing'' has applications in quantum metrology and tests of macroscale entanglement and quantum gravity [8]. However, the emergence of mechanical instability limits the improvement in confinement to at most 50% (or À3 dB) in the steady state [17]. Since a mean thermal occupancy of just half a phonon increases the oscillator's motional variance to twice the zero-point motion var...

We revisit the stochastic master equation approach to feedback cooling of a quantum mechanical oscillator undergoing position measurement. By introducing a rotating wave approximation for the measurement and bath coupling, we can provide a more intuitive analysis of the achievable cooling in various regimes of measurement sensitivity and temperature. We also discuss explicitly the effect of backaction noise on the characteristics of the optimal feedback. The resulting rotating wave master equation has found application in our recent work on squeezing the oscillator motion using parametric driving and may have wider interest.

Detailed quantifications of how predators and their grouping prey interact in three dimensions (3D) remain rare. Here we record the structure and dynamics of fish shoals (Pseudomugil signifer) in 3D both with and without live predators (Philypnodon grandiceps) under controlled laboratory conditions. Shoals adopted two distinct types of shoal structure: “sphere-like” geometries at depth and flat “carpet-like” structures at the water’s surface, with shoals becoming more compact in both horizontal and vertical planes in the presence of a predator. The predators actively stalked and attacked the prey, with attacks being initiated when the shoals were not in their usual configurations. These attacks caused the shoals to break apart, but shoal reformation was rapid and involved individuals adjusting their positions in both horizontal and vertical dimensions. Our analyses revealed that targeted prey were more isolated from other conspecifics, and were closer in terms of distance and direction to the predator compared to non-targeted prey. Moreover, which prey were targeted could largely be identified based on individuals’ positions from a single plane. This highlights that previously proposed 2D theoretical models and their assumptions appear valid when considering how predators target groups in 3D. Our work provides experimental, and not just anecdotal, support for classic theoretical predictions and also lends new insights into predatory–prey interactions in three-dimensional environments.

The strength of the Zeeman splitting induced by an applied magnetic field is an important factor for the realization of spin-resolved transport in mesoscopic devices. We measure the Zeeman splitting for a quantum point contact etched into a Ga0.25In0.75As quantum well, with the field oriented parallel to the transport direction. We observe an enhancement of the Lande g-factor from |g*|=3.8 +/- 0.2 for the third subband to |g*|=5.8 +/- 0.6 for the first subband, six times larger than in GaAs. We report subband spacings in excess of 10 meV, which facilitates quantum transport at higher temperatures.Comment: [Version 2] Revtex4, 11 pages, 3 figures, accepted for publication in Applied Physics Letter

Abstract. We study the position estimation of a mechanical oscillator undergoing both detuned parametric amplification and continuous quantum measurement. This model, which can be utilized to produce squeezed states, is applied to a general optoelectromechanical system. Using a stochastic master equation formalism, we derive general formulae for the reduction in position uncertainty of one quadrature of motion. The filter for extracting the optimal position estimate from the measurement record is derived. We also find that since this scheme does not work far into the back-action-dominated regime, implementing resolved-sideband cooling improves the squeezing only marginally.