We propose a technique for polarizing and cooling finite many-body classical systems using feedback control. The technique requires the system to have one collective degree of freedom conserved by the internal dynamics. The fluctuations of other degrees of freedom are then converted into the growth of the conserved one. The proposal is validated using numerical simulations of classical spin systems in a setting representative of Nuclear Magnetic Resonance experiments. In particular, we were able to achieve 90 percent polarization for a lattice of 1000 classical spins starting from an unpolarized infinite temperature state.
We consider feedback cooling in a cavityless levitated optomechanics setup, and we investigate the possibility to improve the feedback implementation. We apply optimal control theory to derive the optimal feedback signal both for quadratic (parametric) and linear (electric) feedback. We numerically compare optimal feedback against the typical feedback implementation used for experiments. In order to do so, we implement a tracking scheme that takes into account the modulation of the laser intensity. We show that such a tracking implementation allows us to increase the feedback strength, leading…
In this paper, results of quantum calculations are presented for feedback cooling of an optically trapped nanoparticle in the laser-shot-noise-dominant regime. We numerically investigate the system using both parametric and force feedback cooling schemes. For the same measurement efficiency, the cooling limit from the force feedback is lower than that from the parametric feedback. We also develop a set of semi-classical equations for feedback cooling that accurately match the quantum results. It is demonstrated, by rescaling the semi-classical equations, that the cooling dynamics is uniquely d…
Based on a real-time measurement of the motion of a single ion in a Paul trap, we demonstrate its electro-mechanical cooling below the Doppler limit by homodyne feedback control (cold damping). The feedback cooling results are well described by a model based on a quantum mechanical Master Equation.
We show that in the regime of ground-state cooling, simple expressions can be derived for the performance of resolved-sideband cooling --- an example of coherent feedback control --- and optimal linear measurement-based feedback cooling for a harmonic oscillator. These results are valid to leading order in the small parameters that define this regime. They provide insight into the origins of the limitations of coherent and measurement-based feedback for linear systems, and the relationship between them. These limitations are not fundamental bounds imposed by quantum mechanics, but are due to t…
We demonstrate feedback cooling of the motion of a single rubidium atom trapped in a high-finesse optical resonator to a temperature of about 160 μK. Time-dependent transmission and intensity-correlation measurements prove the reduction of the atomic position uncertainty. The feedback increases the 1/e storage time into the one second regime, 30 times longer than without feedback. Feedback cooling therefore rivals state-of-the-art laser cooling, but with the advantages that it requires less optical access and exhibits less optical pumping.
We develop a theory of quantum feedback cooling of a single ion trapped in front of a mirror. By monitoring the motional sidebands of the light emitted into the mirror mode we infer the position of the ion, and act back with an appropriate force to cool the ion. We derive a feedback master equation along the lines of the quantum feedback theory developed by Wiseman and Milburn, which provides us with cooling times and final temperatures as a function of feedback gain and various system parameters.
Measurement-based control has emerged as an important technique to prepare mechanical resonators in pure quantum states for applications in quantum information processing and quantum sensing. Conventionally this has required two separate channels, one for probing the motion and another one acting back on the resonator. In this work, we analyze and experimentally demonstrate a technique of single-laser feedback cooling, where one laser is used for both probing and controlling the mechanical motion. We show using an analytical model and experiments that feedback cooling is feasible in this mode …
We theoretically investigate the rigid body dynamics of an optically levitated nanodumbbell under parametric feedback cooling and provide a simplified model for describing the motion. Differing from previous studies, the spin of the nanoparticle about its symmetry axis is considered non-negligible. Simulations reveal that standard parametric feedback cooling can extract energy from two of the five rotational degrees of freedom when the nanoparticle is levitated using a linearly polarized laser beam. The dynamics after feedback cooling are characterized by a normal mode describing precession ab…
We realise a phase-sensitive closed-loop control scheme to engineer the fluctuations of the pump field which drives an optomechanical system, and show that the corresponding cooling dynamics can be significantly improved. In particular, operating in the counter-intuitive "anti-squashing" regime of positive feedback and increased field fluctuations, sideband cooling of a nanomechanical membrane within an optical cavity can be improved by 7.5~dB with respect to the case without feedback. Close to the quantum regime of reduced thermal noise, such feedback-controlled light would allow going well b…
We revisit the problem of preparing a mechanical oscillator in the vicinity of its quantum-mechanical ground state by means of feedback cooling based on continuous optical detection of the oscillator position. In the parameter regime relevant to ground state cooling, the optical back-action and imprecision noise set the bottleneck of achievable cooling and must be carefully balanced. This can be achieved by adapting the phase of the local oscillator in the homodyne detection realizing a so-called variational measurement. The trade-off between accurate position measurement and minimal disturban…
All three motional modes of a charged dielectric nanoparticle in a Paul trap are cooled by direct feedback to temperatures of a few mK. We test two methods, one based on electrical forces and the other on optical forces; for both methods, we find similar cooling efficiencies. Cooling is characterized for both feedback forces as a function of feedback parameters, background pressure, and the particle's position.
Cooling to the motional ground state is an important first step in the preparation of nonclassical states of mesoscopic mechanical oscillators. Light-mediated coupling to a remote atomic ensemble has been proposed as a method to reach the ground state for low frequency oscillators. The ground state can also be reached using optical measurement followed by feedback control. Here we investigate the possibility of enhanced cooling by combining these two approaches. The combination, in general, outperforms either individual technique, though atomic ensemble-based cooling and feedback cooling each …
We analyze the laser cooling of polarizable particles by continuous dispersive position detection and active feedback. The magnitude of the dissipative force is proportional to the particles' photon scattering rate into the detector, while its velocity dependence is determined by the programmable frequency dependence of the loop gain. The method combines final temperatures near the recoil limit with large velocity capture range, and is applicable to multilevel atoms or molecules.
We model the cooling of open optical and optomechanical resonators via optical feedback in the Linear Quadratic Gaussian setting of stochastic control theory. We show that coherent feedback control schemes, in which the resonator is embedded in an interferometer to achieve all-optical feedback, can outperform the best possible measurement-based schemes in the quantum regime of low steady-state excitation number. Such performance gains are attributed to the coherent controller's ability to process non-commuting output field quadratures simultaneously without loss of fidelity, and may provide im…
Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here, we implement quantum feedback control of a micro-mechanical oscillator for the first time with a squeezed probe field. This allows quantum-enhanced feed…
We propose a simple optomechanical model in which a mechanical oscillator quadrature could be "cooled" well below its equilibrium temperature by applying a suitable feedback to drive the orthogonal quadrature by means of the homodyne current of the radiation field used to probe its position.
We demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force, and we demonstrate rapid parametric feedback cooling of all three motional degrees of freedom from room temperature to a few mK. A single laser at 1550nm, and a single photodiode, are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26nm to 160nm are trapped without feedback to 10$^{-5}$mbar and with feedback engaged the pressure is reduced to 10$^{-6}$mbar. Modifications to the …
Degenerate quantum gases are instrumental in advancing many-body quantum physics and underpin emerging precision sensing technologies. All state-of-the-art experiments use evaporative cooling to achieve the ultracold temperatures needed for quantum degeneracy, yet evaporative cooling is extremely lossy: more than 99.9% of the gas is discarded. Such final particle number limitations constrain imaging resolution, gas lifetime, and applications leveraging macroscopic quantum coherence. Here we show that atomic Bose gases can be cooled to quantum degeneracy using real-time feedback, an entirely ne…
We engineer a quantum bath that enables entropy and energy exchange with a one-dimensional Bose-Hubbard lattice with attractive on-site interactions. We implement this in an array of three superconducting transmon qubits coupled to a single cavity mode; the transmons represent lattice sites and their excitation quanta embody bosonic particles. Our cooling protocol preserves particle number--realizing a canonical ensemble-- and also affords the efficient preparation of dark states which, due to symmetry, cannot be prepared via coherent drives on the cavity. Furthermore, by applying continuous m…
Cooling the motion of a massive mechanical oscillator into its quantum ground state plays an essential role in observing macroscopic quantum effects in mechanical systems. Here we propose a measurement-based feedback cooling protocol in cavity magnomechanics that is able to cool the mechanical vibration mode of a macroscopic ferromagnet into its ground state. The mechanical mode couples to a magnon mode via a dispersive magnetostrictive interaction, and the latter further couples to a microwave cavity mode via the magnetic-dipole interaction. A feedback loop is introduced by measuring the ampl…
We propose a domino-cooling method to realize simultaneous ground-state cooling of a coupled mechanical-resonator chain through an optomechanical cavity working in the unresolved-sideband regime. This domino-effect cooling is realized by combining the cold-damping feedback on the first mechanical resonator with nearest-neighbor couplings between other neighboring mechanical resonators. We obtain analytical results for the effective susceptibilities, noise spectra, final mean phonon numbers, and cooling rates of these mechanical resonators, and find the optimal-cooling condition for these reson…
We consider a possible route to ground state cooling of a levitated nanoparticle, magnetically trapped by a strong permanent magnet, using a combination of measurement and feedback. The trap frequency of this system is much lower than those involving trapped ions or nano-mechanical resonators. Minimisation of environmental heating is therefore challenging as it requires control of the system on a timescale comparable to the inverse of the trap frequency. We show that these traps are an excellent platform for performing optimal feedback control via real-time state estimation, for the preparatio…
We study the cooling performance of optical-feedback controllers for open optical and mechanical resonators in the Linear Quadratic Gaussian setting of stochastic control theory. We utilize analysis and numerical optimization of closed-loop models based on quantum stochastic differential equations to show that coherent control schemes, where we embed the resonator in an interferometer to achieve all-optical feedback, can outperform optimal measurement-based feedback control schemes in the quantum regime of low steady-state excitation number. These performance gains are attributed to the cohere…
We demonstrate a new feedback algorithm to cool a single neutral atom trapped inside a standing-wave optical cavity. The algorithm is based on parametric modulation of the confining potential at twice the natural oscillation frequency of the atom, in combination with fast and repetitive atomic position measurements. The latter serve to continuously adjust the modulation phase to a value for which parametric excitation of the atomic motion is avoided. Cooling is limited by the measurement back action which decoheres the atomic motion after only a few oscillations. Nonetheless, applying this fee…
We discuss continuous observation of the momentum of a single atom by employing the high velocity sensitivity of the index of refraction in a driven $Λ$-system based on electromagnetically induced transparency (EIT). In the ideal limit of unit collection efficiency this provides a quantum limited measurement with minimal backaction on the atomic motion. A feedback loop, which drives the atom with a force proportional to measured signal, provides a cooling mechanism for the atomic motion. We derive the master equation which describes the feedback cooling and show that in the Lamb-Dicke limit th…
We propose an optimal protocol using phase-preserving quantum measurements and phase-dependent modulations of the trapping potential at parametric resonance to cool a quantum oscillator to an occupation number of less than one quantum. We derive the optimal phase relationship and duration for the parametric modulations, and compute the lowest-possible occupation number in the steady state. The protocol is robust against moderate amounts of dissipation and phase errors in the feedback loop. Our work has implications for the cooling of levitated mechanical resonators in the quantum regime.
We study cooling and squeezing the fluctuations of a nanomechanical beam using quantum feedback control. In our model, the nanomechanical beam is coupled to a transmission line resonator via a superconducting quantum interference device (SQUID). The leakage of the electromagnetic field from the transmission line resonator is measured using homodyne detection. This measured signal is then used to design a quantum-feedback-control signal to drive the electromagnetic field in the transmission line resonator. Although the control is imposed on the transmission line resonator, this quantum-feedback…
We apply a feedback cooling technique to simultaneously cool the three electromechanical normal modes of the ton-scale resonant-bar gravitational wave detector AURIGA. The measuring system is based on a dc Superconducting Quantum Interference Device (SQUID) amplifier, and the feedback cooling is applied electronically to the input circuit of the SQUID. Starting from a bath temperature of 4.2 K, we achieve a minimum temperature of 0.17 mK for the coolest normal mode. The same technique, implemented in a dedicated experiment at subkelvin bath temperature and with a quantum limited SQUID, could a…
Cooling the centre-of-mass motion is an important tool for levitated optomechanical systems, but it is often not clear which method can practically reach lower temperatures for a particular experiment. We directly compare the parametric and velocity feedback damping methods, which are used extensively for cooling the motion of single trapped particles in a range of traps. By performing experiments on the same particle, and with the same detection system, we demonstrate that velocity damping cools the oscillator to lower temperatures and is more resilient to imperfect experimental conditions. W…
The concept of critical ambient pressure is introduced. The particle escapes from its trap when the ambient pressure becomes comparable with or smaller than a critical value, even if the particle motion is cooled by one of the feedback (or cavity) cooling schemes realized so far. The critical ambient pressure may be so small that it is not a limiting factor in ground-state cooling, but critical feedback cooling rates, which are also introduced, are limiting factors. The particle escapes from its trap if any of the feedback cooling rates becomes comparable with or larger than its critical value…
Cooled, low-loss nanomechanical resonators offer the prospect of directly observing the quantum dynamics of mesoscopic systems. However, the present state of the art requires cooling down to the milliKelvin regime in order to observe quantum effects. Here we present an active feedback strategy based on continuous observation of the resonator position for the purpose of obtaining these low temperatures. In addition, we apply this to an experimentally realizable configuration, where the position monitoring is carried out by a single-electron transistor. Our estimates indicate that with current t…
Imaging-based detection of the motion of the levitated nanoparticles complements a widely-used interferometric detection method, providing a precise and robust way to estimate the position of the particle. Here, we show the camera-based feedback cooling of a charged nanoparticle levitated in a linear Paul trap. A charged nanoparticle levitated in a vacuum was observed by CMOS camera systems. The nanoparticle images were processed in realtime with a microcontroller integrated with a CMOS image sensor. The phase-delayed position signal was fed-back to one of the trap electrodes resulting in the …
We describe a measurement-and-feedback technique to deterministically prepare low-entropy states of atomic spin ensembles. Using quantum non-demolition measurement and incoherent optical feedback, we drive arbitrary states in the spin-orientation space toward the origin of the spin space. We observe 12 dB of spin noise reduction, or a factor of 63 reduction in phase-space volume. We find optimal feedback conditions and show that multi-stage feedback is advantageous. An input-output calculation of quantum noise incorporating realistic quantum noise sources and experimental limitations agrees we…
A promising route to novel quantum technologies are hybrid quantum systems, which combine the advantages of several individual quantum systems. We have realized a hybrid atomic-mechanical experiment consisting of a SiN membrane oscillator cryogenically precooled to 500 mK and optically coupled to a cloud of laser cooled Rb atoms. Here, we demonstrate active feedback cooling of the oscillator to a minimum mode occupation of n = 16 corresponding to a mode temperature of T = 200 μK. Furthermore, we characterize in detail the coupling of the membrane to the atoms by means of sympathetic cooling. B…
Coherent feedback stabilises a system towards a target state without the need of a measurement, thus avoiding the quantum backaction inherent to measurements. Here, we employ optical coherent feedback to remotely cool a nanomechanical membrane using atomic spins as a controller. Direct manipulation of the atoms allows us to tune from strong-coupling to an overdamped regime. Making use of the full coherent control offered by our system, we perform spin-membrane state swaps combined with stroboscopic spin pumping to cool the membrane in a room-temperature environment to ${T}={216}\,\mathrm{mK}$ …
We report on use of a radiation pressure induced restoring force, the optical spring effect, to optically dilute the mechanical damping of a 1 gram suspended mirror, which is then cooled by active feedback (cold damping). Optical dilution relaxes the limit on cooling imposed by mechanical losses, allowing the oscillator mode to reach a minimum temperature of 6.9 mK, a factor of ~40000 below the environmental temperature. A further advantage of the optical spring effect is that it can increase the number of oscillations before decoherence by several orders of magnitude. In the present experimen…
We demonstrate the integration of a mesoscopic ferromagnetic needle with a cavity optomechanical torsional resonator, and its use for quantitative determination of the needle's magnetic properties, as well as amplification and cooling of the resonator motion. With this system we measure torques as small as 32 zNm, corresponding to sensing an external magnetic field of 0.12 A/m (150 nT). Furthermore, we are able to extract the magnetization (1710 kA/m) of the magnetic sample, not known a priori, demonstrating this system's potential for studies of nanomagnetism. Finally, we show that we can mag…
We consider a wide family of optical coherent feedback loops acting on an optomechanical system operating in the linearized regime. We assess the efficacy of such loops in improving key operations, such as cooling, steady-state squeezing and entanglement, as well as optical to mechanical state transfer. We find that mechanical sideband cooling can be enhanced through passive, interferometric coherent feedback, achieving lower steady-state occupancies and considerably speeding up the cooling process; we also quantify the detrimental effect of non-zero delay times on the cooling performance. Ste…
Conventional techniques for laser cooling, by coherent scattering off of internal states or through an optical cavity mode, have so far proved inefficient on mechanical oscillators heavier than a few nanograms. That is because larger oscillators vibrate at frequencies much too small compared to the scattering rates achievable by their coupling to auxiliary modes. Decoherence mechanisms typically observed in heavy low frequency elastically suspended oscillators also differ markedly from what is assumed in conventional treatments of laser cooling. We show that for a low-frequency anelastic oscil…
Optical measurement of the motion of a 940 kHz mechanical resonance of a silicon nitride nanostring resonator is demonstrated with a read out noise imprecision reaching 37 dB below that of the resonator's zero-point fluctuations. Via intensity modulation of the optical probe laser, radiation pressure feedback is used to cool and damp the mechanical mode from an initial room temperature occupancy of $\bar{n}_{b} = 6.5 \times 10^6$ ($T_{b}=295$K) down to a phonon occupation of $\langle n \rangle = 66 \pm 10$, representing a mode temperature of $T_{m} \approx 3$mK. The five decades of cooling is …
We consider the problem of controlling the motion of an atom trapped in an optical cavity using continuous feedback. In order to realize such a scheme experimentally, one must be able to perform state estimation of the atomic motion in real time. While in theory this estimate may be provided by a stochastic master equation describing the full dynamics of the observed system, integrating this equation in real time is impractical. Here we derive an approximate estimation equation for this purpose, and use it as a drive in a feedback algorithm designed to cool the motion of the atom. We examine t…
The quantum limits of stochastic cooling of trapped atoms are studied. The energy subtraction due to the applied feedback is shown to contain an additional noise term due to atom-number fluctuations in the feedback region. This novel effect is shown to dominate the cooling efficiency near the condensation point. Furthermore, we show first results that indicate that Bose--Einstein condensation could be reached via stochastic cooling.
