Optomechanical cavity cooling of levitated objects offers the possibility for laboratory investigation of the macroscopic quantum behavior of systems that are largely decoupled from their environment. However, experimental progress has been hindered by particle loss mechanisms, which have prevented levitation and cavity cooling in a vacuum. We overcome this problem with a new type of hybrid electro-optical trap formed from a Paul trap within a single-mode optical cavity. We demonstrate a factor of 100 cavity cooling of 400 nm diameter silica spheres trapped in vacuum. This paves the way for ground-state cooling in a smaller, higher finesse cavity, as we show that a novel feature of the hybrid trap is that the optomechanical cooling becomes actively driven by the Paul trap, even for singly charged nanospheres.

Optomechanics is concerned with the use of light to control mechanical objects. As a field, it has been hugely successful in the production of precise and novel sensors, the development of low-dissipation nanomechanical devices, and the manipulation of quantum signals. Micro-and nano-particles levitated in optical fields act as nanoscale oscillators, making them excellent lowdissipation optomechanical objects, with minimal thermal contact to the environment when operating in vacuum. Levitated optomechanics is seen as the most promising route for studying high-mass quantum physics, with the promise of creating macroscopically separated superposition states at masses of 10 6 amu and above. Optical feedback, both using active monitoring or the passive interaction with an optical cavity, can be used to cool the centre-of-mass of levitated nanoparticles well below 1 mK, paving the way to operation in the quantum regime. In addition, trapped mesoscopic particles are the paradigmatic system for studying nanoscale stochastic processes, and have already demonstrated their utility in state-of-the-art force sensing. * Electronic address: james.millen@kcl.ac.uk arXiv:1907.08198v1 [physics.optics] 18 Jul 2019It is a pleasant coincidence, that whilst writing this review the Nobel Prize in Physics 2018 was jointly awarded to the American scientist Arthur Ashkin, for his development of optical tweezers. By focusing a beam of light, small objects can be manipulated through radiation pressure and/or gradient forces. This technology is now available offthe-shelf due to its applicability in the bio-and medical-sciences, where it has found utility in studying cells and other microscopic entities.The pleasant coincidences continue, when one notes that the 2017 Nobel Prize in Physics was awarded to Weiss, Thorne and Barish for their work on the LIGO gravitational wave detector. This amazingly precise experiment is, ultimately, an optomechanical device, where the position of a mechanical oscillator is monitored via its coupling to an optical cavity. The field of optomechanics is in the ascendency [1], showing great promise in the development of quantum technologies and force sensing. These applications are somewhat limited by unavoidable energy dissipation and thermal loading at the nanoscale [2], which despite impressive progress in soft-clamping technology [3] means that these technologies will likely always operate in cryogenic environments.Enter the work of Ashkin: he showed that dielectric particles could be levitated and cooled under vacuum conditions in 1977 [4]. By levitating particles at low pressures, they naturally decouple from the thermal environment, and since the mechanical mode is the centre-of-mass motion of a particle, energy dissipation via strain vanishes. The field of levitated optomechanics really took off in 2010, when three independent proposals illustrated that levitated nanoparticles could be coupled to optical cavities [5][6][7]. This promises cooling to the quantum regime, and state engineering once you are t...

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of matter. A nonlinear coupling offers access to rich new physics, in both the quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising of a nanosphere levitated and cooled in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere to millikelvin temperatures for indefinite periods of time in high vacuum. We observe cooling of the linear and non-linear motion, leading to a 10 5 fold reduction in phonon number np, attaining final occupancies of np = 100 − 1000. This work puts cavity cooling of a levitated object to the quantum ground-state firmly within reach.Cavity optomechanics, the cooling and coherent manipulation of mechanical oscillators using optical cavities, has undergone rapid progress in recent years [1], with many experimental milestones realized. These include cooling to the quantum level [2,3], optomechanically induced transparency (OMIT) [4], and the transduction [5][6][7] and squeezing [8] of light. These important processes are due to a linear light-matter interaction; linear in both the position of the oscillatorx and the amplitude of the optical fieldâ.Nonlinear optomechanical interactions open up a new range of applications which are so far largely unexplored. In principle, they allow quantum nondemolition (QND) measurements of energy and thus the possibility of monitoring quantum jumps in a macroscopic system [1,9]. They also offer the prospect of observing phonon quantum shot noise [10], nonlinear OMIT [11,12], and the preparation of macroscopic nonclassical states [13]. To achieve a nonlinear interaction one can use optical means, which require strong single-photon coupling to the mechanical system [11,12] but are a considerable experimental challenge. Nonlinearities can also arise from spatial, mechanical effects, by engineering, for example, a light-matter interaction of the form (â+â † )(G 1x +G 2x 2 ). Previous studies investigated the static shift in the cavity resonant frequency [9,14,15] or the quadratic optical spring effect [15] arising from a nonlinear coupling. However, these studies identified the problem of a residual linear G 1 contribution to the coupling. Not only can G 1 allow unwanted back-action, but a large G 2 1 contribution (e.g. [14]) can mask the signatures of true nonlinear G 2 coupling.In this work, we study a nanosphere levitated in a hybrid system formed from a Paul trap and an optical cavity [16] as shown in fig 1. The output of the cavity is used to access the linear and nonlinear dynamics of the particle. We are able to tune the G 1 : G 2 ratio to reach G 2 G 1 , isolating the true nonlinear dynamics. Further, due to the dynamic nature of this experiment, we are able to observe the cooling, in time, of the nonlinear contribution to motion. To ...

We investigate electron paramagnetic resonance spectra of bismuth-doped silicon, at intermediate magnetic fields B ' 0:1-0:6 T, theoretically and experimentally (with 9.7 GHz X-band spectra). We identify a previously unexplored regime of ''cancellation resonances,'' where a component of the hyperfine coupling is resonant with the external field. We show that this regime has experimentally accessible consequences for quantum information applications, such as reduction of decoherence, fast manipulation of the coupled electron-nuclear qubits, and spectral line narrowing. DOI: 10.1103/PhysRevLett.105.067602 PACS numbers: 76.30.Àv, 03.67.Lx, 71.55.Cn, 76.90.+d Following Kane's suggestion [1] for using phosphorusdoped silicon as a source of qubits for quantum computing, there has been intense interest in such systems [2]. The phosphorus system ( 31 P) is appealing in its simplicity: It represents a simple electron-spin qubit S ¼ 1 2 coupled to a nuclear-spin qubit I ¼ 1 2 via an isotropic hyperfine interaction AI:S of moderate strength ( A 2 ¼ 117:5 MHz). However, recent developments [3-5] point to Si:Bi (bismuth-doped silicon) as a very promising new alternative. Two recent studies measured spin-dephasing times of over 1 ms at 10 K, which is longer than comparable (nonisotopically purified) materials, including Si:P [3,4]. Another group implemented a scheme for rapid (on a time scale of $100 s) and efficient (of order 90%) hyperpolarization of Si:Bi into a single spin state [5].Bismuth has an atypically large hyperfine constant A 2 ¼ 1:4754 GHz and nuclear spin I ¼ 9 2 . This makes its EPR spectra somewhat more complex than for phosphorus, and there is strong mixing of the eigenstates for external field B & 0:6 T. Mixing of Si:P states was studied experimentally in Ref. [6], by means of electrically detected magnetic resonance, but at much lower fields B & 0:02 T. Residual mixing in Si:Bi for B ¼ 2-6 T, where the eigenstates are *99:9% pure uncoupled eigenstates of bothÎ z andŜ z , was also proposed as important for the hyperpolarization mechanism of illuminated Si:Bi [5]. In Ref.[4] it was found that even a $30% reduction in the effective paramagnetic ratio df dB (where f is the transition frequency) leads to a detectable reduction in decoherence rates.Below, we present an analysis of EPR spectra for Si:Bi, testing this against experimental spectra. We identify the points for which df dB ¼ 0, explaining them in a unified manner in terms of a series of EPR ''cancellation resonances''; some are associated with avoided level crossings while others, such as a maximum shown in ENDOR [7] spectra at B % 0:37 T in Ref.[4], are of a quite different origin. These cancellation resonances represent, to the best of our knowledge, an unexplored regime in EPR spectroscopy, arising in systems with exceptionally high A and I. They are somewhat reminiscent of the so-called ''exact cancellation'' regime, widely used in ESEEM spectroscopy [7,8] but differ in essential ways: For instance, they affect both electronic and nuclear freq...

The quantum dynamics of atoms subjected to pairs of closely spaced kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the single -kick system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power L @ ÿ0:75 and obtain a regime of near-linear spectral variances which approximate the ''critical statistics'' The -kicked quantum rotor (QKR) is one of the most studied paradigms of quantum chaos. Its implementation using cold atoms in optical lattices [1] provided a convincing demonstration of a range of quantum chaos phenomena including dynamical localization [2], the quantum suppression of chaotic diffusion. Recently, an experimental study [3] of cesium atoms subjected to pairs of kicks (2-KR) showed surprisingly different behavior. The classical phase space is chaotic but is made up of fast-diffusing regions which are partly separated by slow-diffusing ''trapping regions,'' where the classical trajectories stick; the classical analysis revealed a regime of anomalous diffusion corresponding to long-lived correlations between kicks.Further details are given in Ref.[4], but we show here that the 2-KR has some unexpected quantum properties. We show that there is a cellular phase-space structure which arises from a novel oscillatory band structure of the corresponding unitary matrix. One consequence is a new type of localization-delocalization transition not seen in the QKR, where states delocalize from single-to multiple-cell occupancy; we show it has a clear spectral signature. We have also found scaling behavior of the localization lengths associated with a fractional exponent, i.e., L @ ÿ0:75 , whereas for the well-studied QKR, L @ ÿ1 . A similar exponent is found for the decay of return probabilities in the trapping regions, Pt t ÿ0:75 . We argue that the exponent 0.75 corresponds closely to the value obtained for the dominant exponent of the golden ratio cantorus [5,6]. We show that the spectral fluctuations [both the nearest-neighbor statistics (NNS) and spectral variances] show important differences with the QKR in regimes where the delocalization of eigenstates is hindered by cantori bordering the cells. We find a regime approximating the form found in ''critical statistics'': The number variances of the spectra are linear 2 L ' L for L 1, where ' 1=21 ÿ < 1 and ' 0:75.The term critical statistics arose originally in relation to the metal insulator transition (MIT) in systems with disorder [7,8]. A new universal form of the distribution of nearest-neighbor eigenvalue spacings, termed ''semiPoisson,'' Ps s expÿ2s was associated with the MIT [7]. For critical statistics, a very interesting connection has been established between the multifractal characteristics of the wave functions and those of the spec...