Back-action Noise Research Articles

Force sensing beyond standard quantum limit with optomechanical "soft" mode induced by nonlinear interaction.

We consider an optomechanical (OM) system that consists of a mechanical and an optical mode interacting through linear and quadratic OM dispersive couplings. The system is operated in unresolved sideband limit with a high quality factor mechanical resonator. Such a system acts as a parametrically driven oscillator, giving access to an intensity-assisted tunability of the spring constant. This enables the operation of the OM system in its "soft mode," wherein the mechanical spring softens and responds with a lower resonance frequency. We show that this soft mode can be exploited to nonlinearize backaction noise, which yields higher force sensitivity beyond the conventional standard quantum limit.

Broadband reduction of quantum radiation pressure noise via squeezed light injection

The Heisenberg uncertainty principle states that the position of an object cannot be known with infinite precision, as the momentum of the object would then be totally uncertain. This momentum uncertainty then leads to position uncertainty in future measurements. When continuously measuring the position of an object, this quantum effect, known as back-action, limits the achievable precision1,2. In audio-band, interferometer-type gravitational-wave detectors, this back-action effect manifests as quantum radiation pressure noise (QRPN) and will ultimately (but does not yet) limit sensitivity3. Here, we present the use of a quantum engineered state of light to directly manipulate this quantum back-action in a system where it dominates the sensitivity in the 10–50 kHz range. We observe a reduction of 1.2 dB in the quantum back-action noise. This experiment is a crucial step in realizing QRPN reduction for future interferometric gravitational-wave detectors and improving their sensitivity. An amplitude squeezed light source that operates down to 1 kHz frequencies—the lowest squeezing frequency—is generated in nonlinear crystal-based systems. By injecting the squeezed light into a microresonator, the quantum radiation pressure noise is reduced by 1.2 dB.

Shot-noise-limited interferometry for measuring a classical force

We propose an interferometry technique, by using electromagnetically induced transparency phenomena, for measuring classical force. The classical force is estimated by measuring the phase at the output of the interferometer. The proposed measurement mechanism satisfies quantum non-demolition measurement conditions leading to back-action evasion. We further derive the sufficient condition under which the thermal noise in the interferometer is negligible. With no back-action noise and no thermal noise, the sensitivity of this technique is limited by shot noise only.

A new quantum speed-meter interferometer: measuring speed to search for intermediate mass black holes

The recent discovery of gravitational waves (GW) by Advanced LIGO (Laser Interferometric Gravitational-wave Observatory) has impressively launched the novel field of gravitational astronomy and allowed us to glimpse exciting objects about which we could previously only speculate. Further sensitivity improvements at the low-frequency end of the detection band of future GW observatories must rely on quantum non-demolition (QND) methods to suppress fundamental quantum fluctuations of the light fields used to readout the GW signal. Here we present a novel concept of how to turn a conventional Michelson interferometer into a QND speed-meter interferometer with coherently suppressed quantum back-action noise. We use two orthogonal polarizations of light and an optical circulator to couple them. We carry out a detailed analysis of how imperfections and optical loss influence the achievable sensitivity. We find that the proposed configuration significantly enhances the low-frequency sensitivity and increases the observable event rate of binary black-hole coalescences in the range of 10^2 - 10^3,M_ odot by a factor of up to ~300.

Improving optomechanical gyroscopes by coherent quantum noise cancellation processing

Coherent quantum noise cancellation (CQNC) method is used to beat standard quantum limit (SQL) for improving the performance of quantum optomechanical gyroscopes. The protocol for realizing CQNC is achieved by constructing an effective negative mass mechanical oscillator, which is simulated by an ancillary cavity. This oscillator shows an antiresponse relative to that of a real mechanical oscillator. Thus, the optomechanical back-action noise is counteracted or restrained, and we could increase our signal by increasing the coupling strength without increasing the noise.

Gyroscope with two-dimensional optomechanical mirror

We propose an application of two-dimensional optomechanical oscillator as a gyroscope by detecting the Coriolis force which is modulated at the natural frequency of the optomechanical oscillator. Dependence of gyroscope's sensitivity on shot noise, back-action noise, thermal noise, and input laser power is studied. At optimal input laser power, the gyroscope's sensitivity can be improved by increasing the mass or by decreasing the temperature and decay rate of the mechanical oscillator. When the mechanical oscillator's thermal occupation number, nth, is zero, sensitivity improves with decrease in frequency of the mechanical oscillator. For , the sensitivity is independent of the mechanical oscillator's frequency.

Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement

The Standard Quantum Limit in continuous monitoring of a system is given by the trade-off of shot noise and back-action noise. In gravitational-wave detectors, such as Advanced LIGO, both contributions can simultaneously be squeezed in a broad frequency band by injecting a spectrum of squeezed vacuum states with a frequency-dependent squeeze angle. This approach requires setting up an additional long base-line, low-loss filter cavity in a vacuum system at the detector's site. Here, we show that the need for such a filter cavity can be eliminated, by exploiting EPR-entangled signal and idler beams. By harnessing their mutual quantum correlations and the difference in the way each beam propagates in the interferometer, we can engineer the input signal beam to have the appropriate frequency dependent conditional squeezing once the out-going idler beam is detected. Our proposal is appropriate for all future gravitational-wave detectors for achieving sensitivities beyond the Standard Quantum Limit.

General quantum constraints on detector noise in continuous linear measurements

In quantum sensing and metrology, an important class of measurement is the continuous linear measurement, in which the detector is coupled to the system of interest linearly and continuously in time. One key aspect involved is the quantum noise of the detector, arising from quantum fluctuations in the detector input and output. It determines how fast we acquire information about the system and also influences the system evolution in terms of measurement backaction. We therefore often categorize it as the so-called imprecision noise and quantum backaction noise. There is a general Heisenberg-like uncertainty relation that constrains the magnitude of and the correlation between these two types of quantum noise. The main result of this paper is to show that, when the detector becomes ideal, i.e., at the quantum limit with minimum uncertainty, not only does the uncertainty relation takes the equal sign as expected, but also there are two new equalities. This general result is illustrated by using the typical cavity QED setup with the system being either a qubit or a mechanical oscillator. Particularly, the dispersive readout of a qubit state, and the measurement of mechanical motional sideband asymmetry are considered.

Geometric control theory for quantum back-action evasion

Engineering a sensor system for detecting an extremely tiny signal such as the gravitational-wave force is a very important subject in quantum physics. A major obstacle to this goal is that, in a simple detection setup, the measurement noise is lower bounded by the so-called standard quantum limit (SQL), which is originated from the intrinsic mechanical back-action noise. Hence, the sensor system has to be carefully engineered so that it evades the back-action noise and eventually beats the SQL. In this paper, based on the well-developed geometric control theory for classical disturbance decoupling problem, we provide a general method for designing an auxiliary (coherent feedback or direct interaction) controller for the sensor system to achieve the above-mentioned goal. This general theory is applied to a typical opto-mechanical sensor system. Also, we demonstrate a controller design for a practical situation where several experimental imperfections are present.

Standard quantum limit of angular motion of a suspended mirror and homodyne detection of a ponderomotively squeezed vacuum field

Compared to the quantum noise in the measurement of the translational motion of a suspended mirror using laser light, the quantum noise in the measurement of the angular motion of a suspended mirror has not been investigated intensively despite its potential importance. In this article, an expression for the quantum noise in the angular motion measurement is explicitly derived. The expression indicates that one quadrature of the vacuum field of the first-order Hermite-Gaussian mode of light causes quantum sensing noise and the other causes quantum backaction noise, or in other words the first-order vacuum field is ponderomotively squeezed. It is also shown that the Gouy phase shift the light acquires between the mirror and the position of detection of the light corresponds to the homodyne angle. Therefore, the quantum backaction noise can be cancelled and the standard quantum limit can be surpassed by choosing the appropriate position of detection analogously to the cancellation of quantum radiation pressure noise by choosing an appropriate homodyne angle.

Quantum feedback cooling of a mechanical oscillator using variational measurements: tweaking Heisenberg’s microscope

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 disturbance can be understood in terms of Heisenberg’s microscope and becomes particularly relevant when the measurement and feedback processes happen to be fast within the quantum coherence time of the system to be cooled. This corresponds to the regime of large quantum cooperativity , which was achieved in recent experiments on feedback cooling. Our method provides a simple path to further pushing the limits of current state-of-the-art experiments in quantum optomechanics.

Force sensing based on coherent quantum noise cancellation in a hybrid optomechanical cavity with squeezed-vacuum injection

We propose and analyse a feasible experimental scheme for a quantum force sensor based on the elimination of backaction noise through coherent quantum noise cancellation (CQNC) in a hybrid atom-cavity optomechanical setup assisted with squeezed vacuum injection. The force detector, which allows for a continuous, broadband detection of weak forces well below the standard quantum limit (SQL), is formed by a single optical cavity simultaneously coupled to a mechanical oscillator and to an ensemble of ultracold atoms. The latter acts as a negative-mass oscillator so that atomic noise exactly cancels the backaction noise from the mechanical oscillator due to destructive quantum interference. Squeezed vacuum injection enforces this cancellation and allows sub-SQL sensitivity to be reached in a very wide frequency band, and at much lower input laser powers.

Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator

Quantum enhanced sensing is a powerful technique in which nonclassical states are used to improve the sensitivity of a measurement. For enhanced mechanical displacement sensing, squeezed states of light have been shown to reduce the photon counting noise that limits the measurement noise floor. It has long been predicted, however, that suppressing the noise floor with squeezed light should produce an unavoidable increase in radiation pressure noise that drives the mechanical system. Such nonclassical radiation pressure forces have thus far been hidden by insufficient measurement strengths and residual thermal mechanical motion. Since the ultimate measurement sensitivity relies on the delicate balance between these two noise sources, the limits of the quantum enhancement have not been observed. Using a microwave cavity optomechanical system, we observe the nonclassical radiation pressure noise that necessarily accompanies any quantum enhancement of the measurement precision. By varying both the magnitude and phase of the squeezing, we optimize the fundamental trade-off between mechanical imprecision and backaction noise in accordance with the Heisenberg uncertainty principle. As the strength of the measurement is further increased, radiation pressure forces eventually dominate the mechanical motion. In this regime, the optomechanical interaction can be exploited as an efficient quantum nondemolition (QND) measurement of the amplitude fluctuations of the light field. By overwhelming mechanical thermal noise with radiation pressure by two orders of magnitude, we demonstrate a mechanically-mediated measurement of the squeezing with an effective homodyne efficiency of 94%. Thus, with strong radiation pressures forces, mechanical motion enhances the measurement of nonclassical light, just as nonclassical light enhances the measurement of the motion.

Quantum nondemolition measurement by pulsed oscillation

Paramagnetic Faraday rotation is a quantum nondemolition measurement method that can generate spin squeezing and improve the measurement precision of a collective spin component beyond the standard quantum limit. In practice, a constant bias magnetic field is used to drive the spin precessing at sufficiently high frequency in order to lift the signal out of low-frequency technical noises. However, continuous measurement of precessing spins introduces back-action noise (BAN) due to the light-shift effect. Two types of back-action-evading (BAE) measurement of collective spin components have been demonstrated recently: continuous measurement of a two-ensemble system and stroboscopic measurement of a single ensemble. Here we propose another single ensemble BAE measurement by periodically modulating the bias field with $\ensuremath{\pi}$ pulses. Our theoretical calculation shows that under experimental settings where pulse-field modulation does not introduce significant decoherences, the proposed method can suppress the BAN and generate spin squeezing faster than the stroboscopic one at the same probe light power. Moreover, if it is combined with synchronous stroboscopic probing, light-shift BAN can be completely eliminated.

Local-oscillator noise coupling in balanced homodyne readout for advanced gravitational wave detectors

The second generation of interferometric gravitational wave detectors are quickly approaching their design sensitivity. For the first time these detectors will become limited by quantum back-action noise. Several back-action evasion techniques have been proposed to further increase the detector sensitivity. Since most proposals rely on a flexible readout of the full amplitude- and phase-quadrature space of the output light field, balanced homodyne detection is generally expected to replace the currently used DC readout. Up to now, little investigation has been undertaken into how balanced homodyne detection can be successfully transferred from its ubiquitous application in table-top quantum optics experiments to large-scale interferometers with suspended optics. Here we derive implementation requirements with respect to local oscillator noise couplings and highlight potential issues with the example of the Glasgow Sagnac Speed Meter experiment, as well as for a future upgrade to the Advanced LIGO detectors.

Quantum Coherent Feedback Control for Generation System of Optical Entangled State.

The non-measurement based coherent feedback control (CFC) is a control method without introducing any backaction noise into the controlled system, thus is specially suitable to manipulate various quantum optical systems for preparing nonclassical states of light. By simply tuning the transmissivity of an optical controller in a CFC loop attached to a non-degenerate optical parametric amplifier (NOPA), the quantum entanglement degree of the output optical entangled state of the system is improved. At the same time, the threshold pump power of the NOPA is reduced also. The experimental results are in reasonable agreement with the theoretical expectation.

Comparing resolved-sideband cooling and measurement-based feedback cooling on an equal footing: Analytical results in the regime of ground-state cooling

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 the fact that both cooling methods are restricted to use only a linear interaction with the resonator. We compare the performance of the two methods on an equal footing --- that is, for the same interaction strength --- and confirm that coherent feedback is able to make much better use of the linear interaction than measurement-based feedback. We find that this performance gap is caused not by the back-action noise of the measurement but by the projection noise. We also obtain simple expressions for the maximal cooling that can be obtained by both methods in this regime, optimized over the interaction strength.

Converting a real quantum spin bath to an effective classical noise acting on a central spin

We present a cluster expansion method for approximating quantum spin-bath dynamics in terms of a classical Gaussian stochastic process. The cluster expansion produces the two-point correlation function of the approximate classical bath, permitting rapid evaluation of noise-mitigating quantum control strategies without resorting to computationally intensive dynamical decoupling models. Our approximation is valid for the wide class of models possessing negligible back-action and nearly-Gaussian noise. We study several instances of the central spin decoherence problem in which the central spin and randomly-located bath spins are alike and dipolarly coupled. For various pulse sequences, we compare the coherence echo decay computed explicitly quantum mechanically versus those computed using our approximate classical model, and obtain agreement in most, but not all, cases. We demonstrate the utility of these classical noise models by efficiently searching for the 4-pulse sequences that maximally mitigate decoherence in each of these cases, a computationally expensive task in the explicit quantum model.

Coherent cancellation of backaction noise in optomechanical force measurements

Optomechanical detectors have reached the standard quantum limit in position and force sensing where measurement backaction noise starts to be the limiting factor for the sensitivity. A strategy to circumvent measurement backaction, and surpass the standard quantum limit, has been suggested by M. Tsang and C. Caves in Phys. Rev. Lett. 105 123601 (2010). We provide a detailed analysis of this method and assess its benefits, requirements, and limitations. We conclude that a proof-of-principle demonstration based on a micro-optomechanical system is demanding, but possible. However, for parameters relevant to gravitational wave detectors the requirements for backaction evasion appear to be prohibitive.

Quantum mechanics. Mechanically detecting and avoiding the quantum fluctuations of a microwave field.

Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion.