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Levitated nanoparticles are being investigated as ultrasensitive sensors of forces and accelerations, with applications ranging from fundamental physics phenomena such as dark matter or quantum gravity to real world applications. Quantum cooling in up to 2 motional modes was achieved recently, and attention is now turning to multimode and multiparticle regimes. We investigate here the spectral characteristics of collective motion of $\Ntot= 2-20 $ nanoparticle modes interacting via the optical light of a cavity. We find output spectra of collective motion typically exhibit two dominant generic features: a broad spectral feature, the collective bright mode (CBM) as expected; but we introduce also the mechanical mode comb (MC) a -- not previously studied -- spectral feature. We investigate numerically, and can also precisely reproduce all the intricate details of the MC spectra, including ponderomotive squeezing, with a simple closed-form expression. We show the mechanical comb can autonomously repair loss of teeth due to nanoparticle loss, a feature that may offer robustness to a levitated sensor of external forces.

For applications of solid state quantum computing and quantum simulations, high fidelity initialisation of thermally mixed electronic and nuclear spin qubits is essential. Whereas electronic spins can readily be initialised optically to high fidelity, initialisation of the nuclear spins requires alternative approaches, such as dynamic nuclear polarisation (DNP) via the electronic spin. Pulse-based DNP methods, such as PulsePol, are already widely utilised. By means of repeated application of PulsePol sequences, interspersed with re-initialisation of the electronic spin, high levels of nuclear polarisation -- termed hyperpolarisation -- have been achieved. From theoretical analysis of these protocols perfect nuclear initialisation is expected; however, in practice, saturation below $\sim$ 95$\%$ is seen in experiment. We develop an analytical model to describe hyperpolarisation dynamics, predicting non-maximal nuclear polarisation saturation in the asymptotic limit for realistic nuclear spin clusters. We argue that perfect initialisation of a typical nuclear cluster using this method may not, in general, be possible even with an arbitrarily large number of repetitions.

Efficient hyperpolarisation of nuclear spins via optically active defect centers, such as the nitrogen vacancy (NV) center in diamond, has great potential for enhancing NMR based quantum information processing and nanoscale magnetic resonance imaging. Recently, pulse-based protocols have been shown to efficiently transfer optically induced polarisation of the electron defect spin to surrounding nuclear spins -- at particular resonant pulse intervals. In this work, we investigate the performance of these protocols, both analytically and experimentally, with the electronic spin of a single NV defect. We find that whenever polarisation resonances of nuclear spins are near-degenerate with a `blocking' spin, which is single spin with stronger off-diagonal coupling to the electronic central spin, they are displaced out of the central resonant region -- without, in general, significant weakening of the resonance. We analyse the underlying physical mechanism and obtain a closed form expression for the displacement. We propose that spin blocking represents a common but overlooked effect in hyperpolarisation of nuclear spins and suggest solutions for improved protocol performance in the presence of (naturally occurring) blocking nuclear spins.

Optomechanical devices are being harnessed as sensors of ultraweak forces for applications ranging from inertial sensing to the search for the elusive dark matter. For the latter, there is a focus on detection of either higher energy single recoils or ultralight, narrowband sources; a directional signal is expected. However, the possibility of searching for a stochastic stream of weak impulses, or more generally a directional broadband signal, need not be excluded; with this and other applications in mind, we investigate the experimental signature of Gaussian white noise impulses with a well defined direction $\Psi$ on a levitated nanosphere, trapped and 3D cooled in an optical tweezer. We find that cross-correlation power spectra offer a calibration-free distinctive signature of the presence of a directional but stochastic microscopic force and its orientation quadrant, unlike normal power spectral densities (PSDs). We obtain excellent agreement between theoretical and experimental results. With calibration we are able to measure the angle $\Psi$, akin to a force compass in a plane. We discuss prospects for extending this technique into quantum regime and compare the expected behaviour of quantum baths and classical baths.

In this work we investigate the effect of the H$\alpha$ bandpass width in the correlation between the CaII H&K and H$\alpha$ indices with the aim of improving the H$\alpha$ index to better identify and model the signals coming from activity variability. We used a sample of 152 FGK dwarfs observed with HARPS for more than 13 years with enough cadence to be able to detect rotational modulations and cycles in activity proxies. We calculated the CaII H&K and H$\alpha$ activity indices using a range of bandwidths for H$\alpha$ between 0.1 and 2.0 Ang. We studied the correlation between the indices time series at long and short timescales and analysed the impact of stellar parameters, activity level and variability on the correlations. The correlation between CaII H&K and H$\alpha$ both at short and long timespans is maximised when using narrow H$\alpha$ bandwidths, with a maximum at 0.6 Ang. For some inactive stars, as the activity level increases, the flux in the H$\alpha$ line core increases while the flux in the line wings decreases as the line becomes shallower and broader. The balance between these fluxes can cause stars to show the negative correlations observed in the literature when using a wide bandwidth on H$\alpha$. These anti-correlations may become positive correlations if using the 0.6 Ang bandwidth. Calculating the H$\alpha$ index using a bandpass of 0.6 Ang maximises the correlation between CaII H&K and H$\alpha$ both at short and long timescales. On the other hand, the use of the broader 1.6 Ang, generally used in exoplanet detection to identify stellar activity signals, degrades the signal by including the flux in the line wings. In face to these results we strongly recommend the use of a 0.6 Ang bandwidth when computing the H$\alpha$ index for the identification of activity rotational modulation and magnetic cycle signals in solar-type stars. (Abridged), Comment: 25 pages, 14 figures, 3 tables, accepted for publication in A&A

Levitated nanoparticles are being intensively investigated from two different perspectives: as a potential realisation of macroscopic quantum coherence; and as ultra-sensitive sensors of force, down to the zeptoNewton level, with a range of various applications, including the search for Dark Matter. A future aim is to merge these two strands, enabling the development of quantum-limited sensors. Here we propose that mechanical cross-correlation spectra $S_{xy}(\omega)$ offer new possibilities: once detector misalignment errors are minimised, the spectral shape of $S_{xy}(\omega)$ directly points out the orientation of an external stochastic force, offering something akin to a compass in the $x-y$ plane. We analyse this for detection of microscopic gas currents, but any broad spectrum directed force will suffice, enabling straightforward investigation with laboratory test forces with or without cavities. For a cavity set-up, we analyse misalignment imprecisions between detectors and motional modes due to for example optical back-actions that mask the signature of the directed forces, and show how to suppress them. Near quantum regimes, we quantify the imprecision due to the $x-y$ correlating effect of quantum shot noise imprecision.

Cavity optomechanics offers quantum cooling, quantum control and measurement of small mechanical oscillators. However the optical backactions that underpin quantum control can significantly disturb the oscillator modes: mechanical frequencies are shifted by the optical spring effect and light-matter hybridisation in strong coupling regimes; mechanical modes hybridise with each other via the cavity mode. This is even more pertinent in the field of levitated optomechanics, where optical trapping fully determines the mechanical modes and their frequencies. Here, using the coherent-scattering (CS) set-up that allowed quantum ground state cooling of a levitated nanoparticle, we show that -- when trapping away from a node of the cavity standing wave -- the CS field opposes optical spring shifts and mechanical mode hybridisation. At an optimal cancellation point, independent of most experimental parameters, we demonstrate experimentally that it is possible to strongly cavity cool and control the {\em unperturbed} modes. Suppression of the cavity-induced mode hybridisation in the $x-y$ plane is quantified by measuring the $S_{xy}(\omega)$ correlation spectra which are seen to always be anti-correlated except at the cancellation point where they become uncorrelated. The findings have implications for directional force sensing using CS set-ups., Comment: typos in .v2 corrected

The use of the nuclear spins surrounding electron spin qubits as quantum registers and long-lived memories opens the way to new applications in quantum information and biological sensing. Hence, there is a need for generic and robust forms of control of the nuclear registers. Although adiabatic gates are widely used in quantum information, they can become too slow to outpace decoherence. Here, we introduce a technique whereby adiabatic gates arise from the dynamical decoupling protocols that simultaneously extend coherence. We illustrate this pulse-based adiabatic control for nuclear spins around NV centers in diamond. We obtain a closed-form expression from Landau-Zener theory and show that it reliably describes the dynamics. By identifying robust Floquet states, we show that the technique enables polarisation, one-shot flips and state storage for nuclear spins. These results introduce a new control paradigm that combines dynamical decoupling with adiabatic evolution., Comment: 5 pages

Ultra-high sensitivity detection of quantum-scale displacements in cavity optomechanics optimises the combined errors from measurement back-action and imprecisions from incoming quantum noises. This sets the well-known Standard Quantum Limit (SQL). Normal quantum cavity optomechanics allows cooling and detection of a single degree of freedom, along the cavity axis. However, a recent breakthrough that allows quantum ground-state cooling of levitated nanoparticles [Delic et al, arxiv:1911.04406], is uniquely 3D in character, with coupling along the $x$, $y$ and $z$ axes. We investigate current experiments and show that the underlying behaviour is far from the addition of independent 1D components and that ground-state cooling and sensing analysis must consider- to date neglected- 3D hybridisation effects. We characterise the additional 3D spectral contributions and find direct and indirect hybridising pathways can destructively interfere suppressing of 3D effects at certain parameters in order to approach, and possibly surpass, the SQL. We identify a sympathetic cooling mechanism that can enhance cooling of weaker coupled modes, arising from optomechanically induced correlations., Comment: added 3D analysis of new quantum-cooled experiments in arxiv:1911.04406 including hybridisation effects

Dynamical decoupling (DD) is a powerful method for controlling arbitrary open quantum systems. In quantum spin control, DD generally involves a sequence of timed spin flips ($\pi$ rotations) arranged to average out or selectively enhance coupling to the environment. Experimentally, errors in the spin flips are inevitably introduced, motivating efforts to optimise error-robust DD. Here we invert this paradigm: by introducing particular control "errors" in standard DD, namely a small constant deviation from perfect $\pi$ rotations (pulse adjustments), we show we obtain protocols that retain the advantages of DD while introducing the capabilities of quantum state readout and polarisation transfer. We exploit this nuclear quantum state selectivity on an ensemble of nitrogen-vacancy centres in diamond to efficiently polarise the $^{13}$C quantum bath. The underlying physical mechanism is generic and paves the way to systematic engineering of pulse-adjusted protocols with nuclear state selectivity for quantum control applications.

The ability to initialise nuclear spins, which are typically in a mixed state even at low temperature, is a key requirement of many protocols used in quantum computing and simulations as well as in magnetic resonance spectroscopy and imaging. Yet, it remains a challenging task that typically involves complex and inefficient protocols, limiting the fidelity of ensuing operations or the measurement sensitivity. We introduce here a class of dynamical nuclear spin state selective (DNSS) protocols which, when applied to a polarised electron spin such as the nitrogen-vacancy (NV) centre in diamond, permit the addressing of selected nuclear states of the mixture. It works by splitting the underlying eigenstates into two distinct symmetries dependent on the nuclear spin state, and independent of the electron-nuclear coupling strength. As a particular example, we show that DNSS is achievable by simply introducing a detuning in the common Carr-Purcell-Meiboom-Gill (CPMG) protocol, where the state selection is then controlled by the inter-pulse spacing. This approach offers advantages in ultra-high fidelity initialisation of nuclear registers, ensemble polarisation and single-gate manipulation of nuclei.

Characteristic dips appear in the coherence traces of a probe qubit when dynamical decoupling (DD) is applied in synchrony with the precession of target nuclear spins, forming the basis for nanoscale nuclear magnetic resonance (NMR). The frequency of the microwave control pulses is chosen to match the qubit transition but this can be detuned from resonance by experimental errors, hyperfine coupling intrinsic to the qubit, or inhomogeneous broadening. The detuning acts as an additional static field which is generally assumed to be completely removed in Hahn echo and DD experiments. Here we demonstrate that this is not the case in the presence of finite pulse-durations, where a detuning can drastically alter the coherence response of the probe qubit, with important implications for sensing applications. Using the electronic spin associated with a nitrogen-vacancy centre in diamond as a test qubit system, we analytically and experimentally study the qubit coherence response under CPMG and XY8 dynamical decoupling control schemes in the presence of finite pulse-durations and static detunings. Most striking is the splitting of the NMR resonance under CPMG, whereas under XY8 the amplitude of the NMR signal is modulated. Our work shows that the detuning error must not be neglected when extracting data from quantum sensor coherence traces.

Interesting experimental signatures of quantum cavity optomechanics arise because the quantum back-action induces correlations between incident quantum shot noise and the cavity field. While the quantum linear theory of optomechanics (QLT) has provided vital understanding across many experimental platforms, in certain new set-ups it may be insufficient: analysis in the time domain may be needed, but QLT obtains only spectra in frequency space; and nonlinear behavior may be present. Direct solution of the stochastic equations of motion in time is an alternative, but unfortunately standard methods do not preserve the important optomechanical correlations. We introduce two-timescale stochastic Langevin (T2SL) propagation as an efficient and straightforward method to obtain time traces with the correct correlations. We show that T2SL, in contrast to standard stochastic simulations, can efficiently simulate correlation phenomena such as ponderomotive squeezing and reproduces accurately cavity sideband structures on the scale of the applied quantum noise and even complicated features entirely submerged below the quantum shot noise imprecision floor. We investigate nonlinear regimes and find where comparison is possible, that the method agrees with analytical results obtained with master equations at low temperatures and in perturbative regimes., Comment: Replaces previous version, with improved presentation

A growing number of experimental set-ups in cavity optomechanics exploit periodically driven fields. However, such set-ups are not amenable to analysis using simple, yet powerful, closed-form expressions of linearized optomechanics, which have provided so much of our present understanding of experimental optomechanics. In the present paper, we formulate a new method to calculate quantum noise spectra in modulated optomechanical systems, which we analyze, compare, and discuss with two other recently proposed solutions: we term these (i) frequency-shifted operators (ii) Floquet and (iii) iterative analysis. We prove that (i) and (ii) yield equivalent noise spectra, and find that (iii) is an analytical approximation to (i) for weak modulations. We calculate the noise spectra of a doubly-modulated system describing experiments of levitated particles in hybrid electro-optical traps. We show excellent agreement with Langevin stochastic simulations in the thermal regime and predict squeezing in the quantum regime. Finally, we reveal how experimentally inaccessible spectral components of a modulated system can be measured in heterodyne detection through an appropriate choice of modulation frequencies.

The extraordinary sensitivity of the output field of an optical cavity to small quantum-scale displacements has led to breakthroughs such as the first detection of gravitational waves \cite{LIGO,LIGODC} and of the motions of quantum ground-state cooled mechanical oscillators \cite{Teufel2011,Chan2011}. While heterodyne detection of the cavity field preserves asymmetries which provide a key signature that mechanical oscillators has attained the quantum regime, detection of a rotating quadrature of the light averages out important quantum correlations, yielding a weaker signal and lower sensitivity than homodyne detection. In turn, homodyning, detects a single optical quadrature, but loses the important quantum sideband asymmetries. In the present work we present and experimentally demonstrate a technique, involving judicious construction of the autocorrelators of the output current using filter functions, which can restore the lost correlations (whether classical or quantum), drastically augmenting the useful information extracted: the filtering adjusts for moderate errors in the locking phase of the local oscillator, allowing efficient single-shot measurement of hundreds of different field quadratures and rapid mapping of detailed features from a simple heterodyne trace. One may also control whether the correlations are recovered in isolation or interfere with the usual stationary heterodyne sidebands. In the latter case we obtain a spectrum of hybrid homodyne-heterodyne character, with motional sidebands of combined amplitudes comparable to homodyne. We term such recovery of lost heterodyne correlations with filter functions r-heterodyning: although investigated here in a thermal regime, its robustness and generality represents a promising new approach to sensing of quantum-scale displacements., Comment: Phys.Rev.Lett., accepted

Homodyne and heterodyne detection represent "twin-pillars" of quantum displacement sensing using optical cavities, having permitted major breakthroughs including detection of gravitational waves and of the motion of quantum ground-state cooled mechanical oscillators. Both can suffer disadvantages as diagnostics in quantum optomechanics, either through symmetrisation (homodyne), or loss of correlations (heterodyne). We show that, for modest heterodyne beat frequencies ($\Omega \sim \omega_M/10 \gg \Gamma$), judicious construction of the autocorrelation of the measured current can either recover (i) a spectrum with strong sidebands but without an imprecision noise floor (ii) a spectrum which is a hybrid, combining both homodyne and heterodyne sideband features. We simulate an experimental realisation with stochastic numerics and find excellent agreement with analytical quantum noise spectra. We term such retrospective recovery of lost heterodyne correlations "r-heterodyning": as the method simply involves post-processing of a normal heterodyne time signal, there is no additional experimental constraint other than on the magnitude of $\Omega$.

The nitrogen vacancy (NV) color center in diamond is an enormously important platform for the development of quantum sensors, including for single spin and single molecule NMR. Detection of weak single-spin signals is greatly enhanced by repeated sequences of microwave pulses; in these dynamical decoupling (DD) techniques, the key control parameters swept in the experiment are the time intervals, $\tau$, between pulses. Here we show that, in fact, the pulse duration offers a powerful additional control parameter. While previously, a non-negligible pulse-width has been considered simply a source of experimental error, here we elucidate the underlying quantum dynamics: we identify a landscape of quantum-state crossings which are usually closed (inactive) but may be controllably activated (opened) by adjusting the pulse-width from zero. We identify these crossings with recently observed but unexpected dips (so called spurious dips) seen in the quantum coherence of the NV spin. With this new understanding, both the position and strength of these sharp features may be accurately controlled; they co-exist with the usual broader coherence dips of short-duration microwave pulses, but their sharpness allows for higher resolution spectroscopy with quantum diamond sensors, or their analogues.

Optomechanical coupling between the motion of a mechanical oscillator and a cavity represents a new arena for experimental investigation of quantum effects on the mesoscopic and macroscopic scale.The motional sidebands of the output of a cavity offer ultra-sensitive probes of the dynamics. We introduce a scheme whereby these sidebands split asymmetrically and show how they may be used as experimental diagnostics and signatures of quantum noise limited dynamics. We show split-sidebands with controllable asymmetry occur by simultaneously modulating the light-mechanical coupling $g$ and $\omega_M$ - slowly and out of-phase. Such modulations are generic but already occur in optically trapped set-ups where the equilibrium point of the oscillator is varied cyclically. We analyse recently observed, but overlooked, experimental split-sideband asymmetries; although not yet in the quantum regime, the data suggests that split sideband structures are easily accessible to future experiments.

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 $n_p$, attaining final occupancies of $n_p = 100-1000$. This work puts cavity cooling of a levitated object to the quantum ground-state firmly within reach., Comment: 5 pages

Despite the importance of isotopically purified samples in current experiments, there have been few corresponding studies of spin qubit decoherence using full quantum bath calculations. Isotopic purification eliminates the well-studied nuclear spin baths which usually dominate decoherence. We model the coherence of electronic spin qubits in silicon near so called Clock Transitions (CT) where experiments have electronic $T_{2e}$ times of seconds. Despite the apparent simplicity of the residual decoherence mechanism, this regime is not well understood: the state mixing which underpins CTs allows also a proliferation of contributions from usually forbidden channels (direct flip-flops with non-resonant spins); in addition, the magnitude and effects of the corresponding Overhauser fields and other detunings is not well quantified. For purely magnetic detunings, we identify a regime, potentially favourable for quantum computing, where forbidden channels are completely suppressed but spins in resonant states are fully released from Overhauser fields and applied magnetic field gradients. We show by a general argument that the enhancement between this regime and the high field limit is $< 8$, regardless of density, while enhancements of order 50 are measured experimentally. We propose that this discrepancy is likely to arise from strains of exclusively non-magnetic origin, underlining the potential of CTs for isolating and probing different types of inhomogeneities. We also identify a set of fields, "Dipolar Refocusing Points" (DRPs), where the Hahn echo fully refocuses the effect of the dipolar interaction., Comment: arXiv admin note: text overlap with arXiv:1412.2645

Sensing the internal dynamics of individual nuclear spins or clusters of nuclear spins has recently become possible by observing the coherence decay of a nearby electronic spin: the weak magnetic noise is amplified by a periodic, multi-pulse decoupling sequence. However, it remains challenging to robustly infer underlying atomic-scale structure from decoherence traces in all but the simplest cases. We introduce Floquet spectroscopy as a versatile paradigm for analysis of these experiments, and argue it offers a number of general advantages. In particular, this technique generalises to more complex situations, offering physical insight in regimes of many-body dynamics, strong coupling and pulses of finite duration. As there is no requirement for resonant driving, the proposed spectroscopic approach permits physical interpretation of striking, but overlooked, coherence decay features in terms of the form of the avoided crossings of the underlying quasienergy eigenspectrum. This is exemplified by a set of "diamond" shaped features arising for transverse-field scans in the case of single-spin sensing by NV-centers in diamond. We investigate also applications for donors in silicon showing that the resulting tunable interaction strengths offer highly promising future sensors.

There are two distinct techniques of proven effectiveness for extending the coherence lifetime of spin qubits in environments of other spins. One is dynamical decoupling, whereby the qubit is subjected to a carefully timed sequence of control pulses; the other is tuning the qubit towards 'optimal working points' (OWPs), which are sweet-spots for reduced decoherence in magnetic fields. By means of quantum many-body calculations, we investigate the effects of dynamical decoupling pulse sequences far from and near OWPs for a central donor qubit subject to decoherence from a nuclear spin bath. Key to understanding the behavior is to analyse the degree of suppression of the usually dominant contribution from independent pairs of flip-flopping spins within the many-body quantum bath. We find that to simulate recently measured Hahn echo decays at OWPs (lowest-order dynamical decoupling), one must consider clusters of three interacting spins, since independent pairs do not even give finite $T_2$ decay times. We show that while operating near OWPs, dynamical decoupling sequences require hundreds of pulses for a single order of magnitude enhancement of $T_2$, in contrast to regimes far from OWPs, where only about ten pulses are required., Comment: improved introduction and conclusion; added appendices; 11 pages, 5 figures

We note the existence of a set of magnetic field values where a simple Hahn echo sequence refocuses the dynamics of the full dipolar interaction, for spin systems of electron donors in silicon. As the refocussing occurs for both arbitrary coupling strengths and arbitrary times, these dipolar refocusing points (DRPs) offer new possibilities for regulating entanglement due to the always-on spin dipolar interaction. While the experimental effects of DRPs will be strongly diluted in the measured coherences of thermal (unpolarized) spin ensembles, we investigate possible signatures in coherence decays arising from a study of the combined effects of decoherence arising from instantaneous diffusion and direct flip-flops

Hybrid qubit systems combining electronic spins with nearby ("proximate") nuclear spin registers offer a promising avenue towards quantum information processing, with even multi-spin error correction protocols recently demonstrated in diamond. However, for the important platform offered by spins of donor atoms in cryogenically-cooled silicon,decoherence mechanisms of $^{29}$Si proximate nuclear spins are not yet well understood.The reason is partly because proximate spins lie within a so-called "frozen core" region where the donor electronic hyperfine interaction strongly suppresses nuclear dynamics. We investigate the decoherence of a central proximate nuclear qubit arising from quantum spin baths outside, as well as inside, the frozen core around the donor electron. We consider the effect of a very large nuclear spin bath comprising many ($\gtrsim 10^8$) weakly contributing pairs outside the frozen core. We also propose that there may be an important contribution from a few (of order $100$) symmetrically sited nuclear spin pairs ("equivalent pairs"), which were not previously considered as their effect is negligible outside the frozen core. If equivalent pairs represent a measurable source of decoherence, nuclear coherence decays could provide sensitive probes of the symmetries of electronic wavefunctions. For the phosphorus donor system, we obtain $T_{2n}$ values of order 1 second for both the "far bath" and "equivalent pair" models, confirming the suitability of proximate nuclei in silicon as very long-lived spin qubits.

The development of laser cooling coupled with the ability to trap atoms and ions in electromagnetic fields, has revolutionised atomic and optical physics, leading to the development of atomic clocks, high-resolution spectroscopy and applications in quantum simulation and processing. However, complex systems, such as large molecules and nanoparticles, lack the simple internal resonances required for laser cooling. Here we report on a hybrid scheme that uses the external resonance of an optical cavity, combined with radio frequency (RF) fields, to trap and cool a single charged nanoparticle. An RF Paul trap allows confinement in vacuum, avoiding instabilities that arise from optical fields alone, and crucially actively participates in the cooling process. This system offers great promise for cooling and trapping a wide range of complex charged particles with applications in precision force sensing, mass spectrometry, exploration of quantum mechanics at large mass scales and the possibility of creating large quantum superpositions., Comment: 8 pages, 5 figures Updated version includes additional references, new title, and supplementary information included

The decoherence of mixed electron-nuclear spin qubits is a topic of great current importance, but understanding is still lacking: while important decoherence mechanisms for spin qubits arise from quantum spin bath environments with slow decay of correlations, the only analytical framework for explaining observed sharp variations of decoherence times with magnetic field is based on the suppression of classical noise. Here we obtain a general expression for decoherence times of the central spin system which exposes significant differences between quantum-bath decoherence and decoherence by classical field noise. We perform measurements of decoherence times of bismuth donors in natural silicon using both electron spin resonance (ESR) and nuclear magnetic resonance (NMR) transitions, and in both cases find excellent agreement with our theory across a wide parameter range. The universality of our expression is also tested by quantitative comparisons with previous measurements of decoherence around `optimal working points' or `clock transitions' where decoherence is strongly suppressed. We further validate our results by comparison to cluster expansion simulations.

The use of levitated nanospheres represents a new paradigm for the optomechanical cooling of a small mechanical oscillator, with the prospect of realising quantum oscillators with unprecedentedly high quality factors. We investigate the dynamics of this system, especially in the so-called self-trapping regimes, where one or more optical fields simultaneously trap and cool the mechanical oscillator. The determining characteristic of this regime is that both the mechanical frequency $\omega_M$ and single-photon optomechanical coupling strength parameters $g$ are a function of the optical field intensities, in contrast to usual set-ups where $\omega_M$ and $g$ are constant for the given system. We also measure the characteristic transverse and axial trapping frequencies of different sized silica nanospheres in a simple optical standing wave potential, for spheres of radii $r=20-500$\,nm, illustrating a protocol for loading single nanospheres into a standing wave optical trap that would be formed by an optical cavity. We use this data to confirm the dependence of the effective optomechanical coupling strength on sphere radius for levitated nanospheres in an optical cavity and discuss the prospects for reaching regimes of strong light-matter coupling. Theoretical semiclassical and quantum displacement noise spectra show that for larger nanospheres with $r \gtrsim 100$\,nm a range of interesting and novel dynamical regimes can be accessed. These include simultaneous hybridization of the two optical modes with the mechanical modes and parameter regimes where the system is bistable. We show that here, in contrast to typical single-optical mode optomechanical systems, bistabilities are independent of intracavity intensity and can occur for very weak laser driving amplitudes.

We present pulsed electron-nuclear double resonance (ENDOR) experiments which enable us to characterize the coupling between bismuth donor spin qubits in Si and the surrounding spin bath of 29Si impurities which provides the dominant decoherence mechanism (nuclear spin diffusion) at low temperatures (< 16 K). Decoupling from the spin bath is predicted and cluster correlation expansion simulations show near-complete suppression of spin diffusion, at optimal working points. The suppression takes the form of sharply peaked divergences of the spin diffusion coherence time, in contrast with previously identified broader regions of insensitivity to classical fluctuations. ENDOR data suggest that anisotropic contributions are comparatively weak, so the form of the divergences is largely independent of crystal orientation., Comment: Added journal ref., minor improvements

Optomechanical cooling of levitated dielectric particles represents a promising new approach in the quest to cool small mechanical resonators towards their quantum ground state. We investigate two-mode cooling of levitated nanospheres in a self-trapping regime. We identify a rich structure of split sidebands (by a mechanism unrelated to usual strong-coupling effects) and strong cooling even when one mode is blue detuned. We show the best regimes occur when both optical fields cooperatively cool and trap the nanosphere, where cooling rates are over an order of magnitude faster compared to corresponding single-sideband cooling rates., Comment: 8 Pages, 7 figures

Several recent studies have investigated the dynamics of cold atoms in optical lattices subject to AC forcing; the theoretically predicted renormalization of the tunneling amplitudes has been verified experimentally. Recent observations include global motion of the atom cloud, such as giant "Super-Bloch Oscillations" (SBOs). We show that, in order to understand unexplained features of SBOs, in addition to the renormalization of the tunneling, a new and important phase correction must be included. For Fermionic systems with strong attractive interactions, one may engineer different types of collisions and recollisions between bound-pairs and unpaired atoms., Comment: 6 pages, 2 figures

Numerous theoretical and experimental studies have investigated the dynamics of cold atoms subjected to time periodic fields. Novel effects dependent on the amplitude and frequency of the driving field, such as Coherent Destruction of Tunneling have been identified and observed. However, in the last year or so, three distinct types of experiments have demonstrated for the first time, interesting behaviour associated with the driving phase: i.e. for systems experiencing a driving field of general form $V(x)\sin (\omega t + \phi)$, different types of large scale oscillations and directed motion were observed. We investigate and explain the phenomenon of Super-Bloch Oscillations (SBOs) in relation to the other experiments and address the role of initial phase in general. We analyse and compare the role of $\phi$ in systems with homogeneous forces ($V'(x)= const$), such as cold atoms in shaken or amplitude-modulated optical lattices, as well as non-homogeneous forces ($V'(x)\neq const$), such as the sloshing of atoms in driven traps, and clarify the physical origin of the different $\phi$-dependent effects., Comment: 10 pages, 1 figure

There is growing interest in bismuth-doped silicon (Si:Bi) as an alternative to the well-studied proposals for silicon based quantum information processing (QIP) using phosphorus-doped silicon (Si:P). We focus here on the implications of its anomalously strong hyperfine coupling. In particular, we analyse in detail the regime where recent pulsed magnetic resonance experiments have demonstrated the potential for orders of magnitude speedup in quantum gates by exploiting transitions that are electron paramagnetic resonance (EPR) forbidden at high fields. We also present calculations using a phenomenological Markovian master equation which models the decoherence of the electron spin due to Gaussian temporal magnetic field perturbations. The model quantifies the advantages of certain "optimal working points" identified as the $df/dB=0$ regions, where $f$ is the transition frequency, which come in the form of frequency minima and maxima. We show that at such regions, dephasing due to the interaction of the electron spin with a fluctuating magnetic field in the $z$ direction (usually adiabatic) is completely removed., Comment: 15 pages, 9 figures

We investigate theoretically and experimentally the electron paramagnetic resonance (EPR) spectra of bismuth doped silicon (Si:Bi) at intermediate magnetic fields, $B \approx 0.05 -0.6$ T. We identify a previously unexplored EPR regime of "cancellation-resonances"- where part of the hyperfine coupling is resonant with the external field-induced splitting. We show this regime has interesting and experimentally accessible consequences for spectroscopy and quantum information applications. These include reduction of decoherence, fast manipulation of the coupled nuclear-electron qubit system and line narrowing in the multi-qubit case. We test our theoretical analysis by comparing with experimental X-band (9.7 GHz) EPR spectra obtained in the intermediate field regime.

We investigate the effect of periodic driving by an external field on systems with attractive pairing interactions. These include spin systems (like the ferromagnetic XXZ model) as well as ultracold fermionic atoms described by the attractive Hubbard model. We show that a well-known phenomenon seen in periodically driven systems--the renormalization of the exchange coupling strength--acts selectively on bound-pairs of spins/atoms, relative to magnon/bare atom states. Thus one can control the direction and speed of transport of bound-pair relative to magnon/unpaired atom states, and thus coherently achieve spatial separation of these components. Applications to recent experiments on transport with fermionic atoms in optical lattices which consist of mixtures of bound-pairs and bare atoms are discussed., Comment: 6 pages, 3 figures

We show that the dynamics of a doubly-excited 1D Heisenberg ferromagnetic chain, subject to short pulses from a parabolic magnetic field may be analyzed as a pair of quantum kicked rotors. By focusing on the two-magnon dynamics in the kicked XXZ model we investigate how the anisotropy parameter - which controls the strength of the magnon-magnon interaction - changes the nature of the coupling between the two "image" coupled Kicked Rotors. We investigate quantum state transfer possibilities and show that one may control whether the spin excitations are transmitted together, or separate from each other., Comment: 8 pages, 4 figures; extended appendix and corrected typos

We investigate the Quantum Resonance (QR) regime of a periodically kicked atomic Bose-Einstein condensate. We find that the clearest indicator of the nonlinear dynamics is a surprisingly abrupt cut-off which appears on the main "Talbot time" QR. We show that this is due and excitation path combining both Beliaev and Landau processes, with some analogies to nonlinear self-trapping. Investigation of dynamical instability reveals further symptoms of nonlinearity such as a regime of exponential oscillations.