Back-action Noise Research Articles

Microwave quantum diode

The fragile nature of quantum circuits is a major bottleneck to scalable quantum applications. Operating at cryogenic temperatures, quantum circuits are highly vulnerable to amplifier backaction and external noise. Non-reciprocal microwave devices such as circulators and isolators are used for this purpose. These devices have a considerable footprint in cryostats, limiting the scalability of quantum circuits. As a proof-of-concept, here we report a compact microwave diode architecture, which exploits the non-linearity of a superconducting flux qubit. At the qubit degeneracy point we experimentally demonstrate a significant difference between the power levels transmitted in opposite directions. The observations align with the proposed theoretical model. At − 99 dBm input power, and near the qubit-resonator avoided crossing region, we report the transmission rectification ratio exceeding 90% for a 50 MHz wide frequency range from 6.81 GHz to 6.86 GHz, and over 60% for the 250 MHz range from 6.67 GHz to 6.91 GHz. The presented architecture is compact, and easily scalable towards multiple readout channels, potentially opening up diverse opportunities in quantum information, microwave read-out and optomechanics.

Enhancing force sensing in a squeezed optomechanical system with quantum non-demolition measurement

A theoretical scheme is proposed to enhance the sensitivity of force sensors with quantum non-demolition measurement (QND) in an optomechanical setup assisted by four-tone optical driving and an optical parametric amplifier (OPA). With the help of special drive, the system can be simplified as the typical type of QND for force sensing, so that the backaction noise can be evaded to surpass the standard quantum limit. Besides, the added noise can be suppressed owing to the modified optical susceptibility resulting from the OPA. By introducing two oscillators coupling with two charged bodies respectively, the signal can be enhanced with the nonlinearity caused by Coulomb interaction, while the noise presents an exponential decrease. Moreover, considering the homodyne detection effect, the range of system parameters and frequency bands will be broadened. The present investigation may provide a route toward simultaneously evading backaction noise, reducing the mechanical thermal noise, and enhancing the external signal, which can be an alternative design for sensitive devices.

Entanglement-enhanced optomechanical sensing

Optomechanical systems have been exploited in ultrasensitive measurements of force, acceleration and magnetic fields. The fundamental limits for optomechanical sensing have been extensively studied and now well understood—the intrinsic uncertainties of the bosonic optical and mechanical modes, together with backaction noise arising from interactions between the two, dictate the standard quantum limit. Advanced techniques based on non-classical probes, in situ ponderomotive squeezed light and backaction-evading measurements have been developed to overcome the standard quantum limit for individual optomechanical sensors. An alternative, conceptually simpler approach to enhance optomechanical sensing rests on joint measurements taken by multiple sensors. In this configuration, a pathway to overcome the fundamental limits in joint measurements has not been explored. Here we demonstrate that joint force measurements taken with entangled probes on multiple optomechanical sensors can improve the bandwidth in the thermal-noise-dominant regime or the sensitivity in the shot-noise-dominant regime. Moreover, we quantify the overall performance of entangled probes with the sensitivity–bandwidth product and observe a 25% increase compared with that of classical probes. The demonstrated entanglement-enhanced optomechanical sensors would enable new capabilities for inertial navigation, acoustic imaging and searches for new physics. Joint force measurements with entangled optical probes on two optomechanical sensors are demonstrated. The force sensitivity is improved by 40% in the shot-noise-dominant regime. The sensing bandwidth is improved by 20% in the thermal noise limit.

Control scheme for polarization circulation speed meter using a dual-retardation waveplate

In interferometric gravitational wave detectors, quantum radiation pressure noise, which is a back action of the measurement, will limit their sensitivities at low frequencies. Speed meters are one of the solutions to reduce the back action noise and improve the sensitivities, and furthermore, they can surpass the standard quantum limit over a wide range of frequencies. The Polarization Circulation Speed Meter is the latest incarnation of the speed meter concept in the sense that it requires a slight modification in the conventional interferometer designs; however, its control scheme has not been developed. The main difficulty is the length and alignment control of the cavity formed by the polarization circulation mirror and the input test masses, whose round-trip phase shift should be kept to $\pi$. In this article, we propose a new control scheme using a dual-retardation waveplate, called Dual-Retardance Control (DRC). In addition, we compare the shot noise level of the DRC to another simpler scheme by dithering. Finally, we design the experimental setup for the demonstration of the DRC and show the expected results through the transfer function measurement.

Enhanced weak force sensing based on atom-based coherent quantum noise cancellation in a hybrid cavity optomechanical system

The weak force sensing based on a coherent quantum noise cancellation (CQNC) scheme is presented in a hybrid cavity optomechanical system containing a trapped ensemble of ultracold atoms and an optical parametric amplifier (OPA). In the proposed system, the back-action noise can be completely eliminated at all frequencies and through the proper choice of the OPA parameters, and the noise spectral density can also be reduced at lower frequencies. This leads to a significant enhancement in the sensitivity of the cavity optomechanical weak force sensor, and the noise spectral density also surpasses the standard quantum limit (SQL) even for the small input power at the lower detection frequency. Furthermore, the experimental feasibility of this scheme is also briefly discussed. This study can be used for the realization of a force sensor based on hybrid cavity optomechanical systems and for the coherent quantum control in macroscopic systems.

Optomechanical sideband asymmetry explained by stochastic electrodynamics

Within the framework of stochastic electrodynamics we derive the noise spectrum of a laser beam reflected from a suspended mirror. The electromagnetic field follows Maxwell's equations and is described by a deterministic part that accounts for the laser field and a stochastic part that accounts for thermal and zero-point background fluctuations.Likewise, the mirror motion satisfies Newton's equation of motion and is composed of deterministic and stochastic parts, similar to a Langevin equation. We consider a photodetector that records the power of the field reflected from the mirror interfering with a frequency-shifted reference beam (heterodyne interferometry). We theoretically show that the power spectral density of the photodetector signal is composed of four parts: (i) a deterministic term with beat notes, (ii) shot noise, (iii) the actual heterodyne signal of the mirror motion and (iv) a cross term resulting from the correlation between measurement noise (shot noise) and backaction noise (radiation pressure shot noise). The latter gives rise to the Raman sideband asymmetry observed with ultracold atoms, cavity optomechanics and with levitated nanoparticles. Our classical theory fully reproduces experimental observations and agrees with the results obtained by a quantum theoretical treatment.

Homodyne coherent quantum noise cancellation in a hybrid optomechanical force sensor

In this paper we propose an experimentally viable scheme to enhance the sensitivity of force detection in a hybrid optomechanical setup assisted by squeezed vacuum injection, beyond the standard quantum limit (SQL). The scheme is based on a combination of the coherent quantum noise cancellation (CQNC) strategy with a variational homodyne detection of the cavity output spectrum in which the phase of the local oscillator is optimized. In CQNC, realizing a negative-mass oscillator in the system leads to exact cancellation of the backaction noise from the mechanics due to destructive quantum interference. Squeezed vacuum injection enhances this cancellation and allows sub-SQL sensitivity to be reached in a wide frequency band and at much lower input laser powers. We show here that the adoption of variational homodyne readout enables us to enhance this noise cancellation up to $40\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}$ compared to the standard case of detection of the optical output phase quadrature, leading to a remarkable force sensitivity of the order of ${10}^{\ensuremath{-}19}\phantom{\rule{0.28em}{0ex}}\mathrm{N}/\sqrt{\mathrm{Hz}}$, about $70%$ enhancement compared to the standard case. Moreover, we show that at nonzero cavity detuning, the signal response can be amplified at a level three to five times larger than that in the standard case without variational homodyne readout, improving the signal-to-noise ratio. Finally, the variational readout CQNC developed in this paper may be applied to other optomechanical-like platforms such as levitated systems and multimode optomechanical arrays or crystals as well as Josephson-based optomechanical systems.

Quantum backaction evading measurements of a silicon nitride membrane resonator

Quantum backaction disturbs the measurement of the position of a mechanical oscillator by introducing additional fluctuations. In a quantum backaction measurement technique, the backaction can be evaded, although at the cost of losing part of the information. In this work, we carry out such a quantum backaction measurement using a large 0.5 mm diameter silicon nitride membrane oscillator with 707 kHz frequency, via a microwave cavity readout. The measurement shows that quantum backaction noise can be evaded in the quadrature measurement of the motion of a large object.

Back action evading electro-optical transducer

Electro-optical transducers are utilized for upconversion of radio frequency (RF) signals to the optical frequency domain to study the RF signals with optical tools. The transducers frequently impact the RF system and introduce additional noise, including optical shot noise as well as quantum back action noise, limiting the measurement accuracy. In this paper, we theoretically study a technique based on a high efficiency electro-optical phase modulation effect that allows back action evading detection of an RF field quadrature. The main idea of the proposed method is independent homodyne detection of two (Stokes and anti-Stokes) optical modes. It allows subsequent postprocessing of the detected signals, which, in turn, results in a broadband back action evading measurement leading to the high sensitivity evaluation of the RF signals.

Force Sensing in an Optomechanical System with Feedback-Controlled In-Loop Light

Quantum control techniques applied at macroscopic scales provide us with opportunities in fundamental physics and practical applications. Among them, measurement-based feedback allows efficient control of optomechanical systems and quantum-enhanced sensing. In this paper, we propose a near-resonant narrow-band force sensor with extremely low optically added noise in an optomechanical system subject to a feedback-controlled in-loop light. The membrane's intrinsic motion consisting of zero-point motion and thermal motion is affected by the added noise of measurement due to the backaction noise and imprecision noise. We show that, in the optimal low-noise regime, the system is analogous to an optomechanical system containing a near quantum-limited optical parametric amplifier coupled to an engineered reservoir interacting with the cavity. Therefore, the feedback loop enhances the mechanical response of the system to the input while keeping the optically added noise of measurement below the standard quantum limit. Moreover, the system based on feedback offers a much larger amplification bandwidth than the same system with no feedback.

Squeezed-Light Enhancement and Backaction Evasion in a High Sensitivity Optically Pumped Magnetometer.

We study the effect of optical polarization squeezing on the performance of a sensitive, quantum-noise-limited optically pumped magnetometer. We use Bell-Bloom (BB) optical pumping to excite a ^{87}Rb vapor containing 8.2×10^{12} atoms/cm^{3} and Faraday rotation to detect spin precession. The sub-pT/sqrt[Hz] sensitivity is limited by spin projection noise (photon shot noise) at low (high) frequencies. Probe polarization squeezing both improves high-frequency sensitivity and increases measurement bandwidth, with no loss of sensitivity at any frequency, a direct demonstration of the evasion of measurement backaction noise. We provide a model for the quantum noise dynamics of the BB magnetometer, including spin projection noise, probe polarization noise, and measurement backaction effects. The theory shows how polarization squeezing reduces optical noise, while measurement backaction due to the accompanying ellipticity antisqueezing is shunted into the unmeasured spin component. The method is compatible with high-density and multipass techniques that reach extreme sensitivity.

Electromechanical coupling effect in the detection of nanomechanical motion

The electromechanical coupling in the nanomechanical detection experiment is important as people forever pursue the higher sensitivity. In this work, we have studied theoretically the electromechanical coupling effect on the sensitivity of nanomechanical motion with the mixing current detection method under monostable and bistable regime, respectively. To obtain the sensitivity, the response function, the shot noise and the backaction noise with the coupling in the nanomechanical system consists of the oscillator coupled to a quantum dot are present. It is found that for the monostable state, the higher coupling means higher sensitivity. Both the contributions of shot noise and the backaction noise to the sensitivity are the decreasing function of the coupling. Once the system enters the bistability regime, the telegraph noise dominates instead of the resonance frequency noise, that due to the electron hopping in the bistable regime contributes more noise for the detection, its value is 3 orders of magnitude larger than the contribution of shot noise. As a result, one could find that there is a optimal value of the coupling corresponding to the phase transition point where the sensitivity is the best. Our results provide the pioneer and useful approach for the detection experiment.

Ultraprecision quantum sensing and measurement based on nonlinear hybrid optomechanical systems containing ultracold atoms or atomic Bose–Einstein condensate

In this review, the authors study how a hybrid optomechanical system (OMS), in which a quantum micro- or nano-mechanical oscillator is coupled to the electromagnetic radiation pressure, consisting of an ensemble of ultracold atoms or an atomic Bose–Einstein condensate, can be used as an ultraprecision quantum sensor for measuring very weak signals. As is well-known in any precise quantum measurement, the competition between the shot noise and the backaction noise of measurement executes a limitation on the measurement precision which is the so-called standard quantum limit (SQL). In the case where the intensity of the signal is even lower than the SQL, one needs to perform an ultraprecision quantum sensing to beat the SQL. For this purpose, the authors review three important methods for surpassing the SQL in a hybrid OMS: (i) the backaction evading measurement of a quantum nondemolition variable of the system, (ii) the coherent quantum backaction noise cancelation, and (iii) the so-called parametric sensing, the simultaneous signal amplification, and added noise suppression below the SQL. Furthermore, the authors have shown in this article for the first time how the classical fluctuation of the driving laser phase, the so-called laser phase noise, affects the power spectrum of the output optical field in a standard OMS and induces an additional impression noise which makes the total system noise increase above the SQL. Also, for the first time in this review it has been shown that in the standard OMSs, it is impossible to amplify the signal while suppressing the noise below the SQL simultaneously.

Nonstationary force sensing under dissipative mechanical quantum squeezing

We study the stationary and nonstationary measurement of a classical force driving a mechanical oscillator coupled to an electromagnetic cavity under two-tone driving. For this purpose, we develop a theoretical framework based on the signal-to-noise ratio to quantify the sensitivity of linear spectral measurements. Then, we consider stationary force sensing and study the necessary conditions to minimise the added force noise. We find that imprecision noise and back-action noise can be arbitrarily suppressed by manipulating the amplitudes of the input coherent fields, however, the force noise power spectral density cannot be reduced below the level of thermal fluctuations. Therefore, we consider a nonstationary protocol that involves non-thermal dissipative state preparation followed by a finite time measurement, which allows one to perform measurements with a signal-to-noise much greater than the maximum possible in a stationary measurement scenario. We analyse two different measurement schemes in the nonstationary transient regime, a back-action evading measurement, which implies modifying the drive asymmetry configuration upon arrival of the force, and a nonstationary measurement that leaves the drive asymmetry configuration unchanged. Conditions for optimal force noise sensitivity are determined, and the corresponding force noise power spectral densities are calculated.

Quantum Backaction Cancellation in the Audio Band

We report on the cancellation of quantum back action noise in an optomechanical cavity. We perform two measurements of the displacement of the microresonator, one in reflection of the cavity, and one in transmission of the cavity. We show that measuring the amplitude quadrature of the light in transmission of the optomechanical cavity allows us to cancel the back action noise between 1 kHz and 50 kHz, and obtain a more sensitive measurement of the microresonator's position. To confirm that the back action is eliminated, we measure the noise in the transmission signal as a function of circulating power. By splitting the transmitted light onto two photodetectors and cross correlating the two signals, we remove the contributon from shot noise and measure a quantum noise free thermal noise spectrum. Eliminating the effects of back action in this frequency regime is an important demonstration of a technique that could be used to mitigate the effects of back action in interferometric gravitational wave detectors such as Advanced LIGO.

Backaction-evading impulse measurement with mechanical quantum sensors

The quantum measurement of any observable naturally leads to noise added by the act of measurement. Approaches to evade or reduce this noise can lead to substantial improvements in a wide variety of sensors, from laser interferometers to precision magnetometers and more. In this paper, we develop a measurement protocol based upon pioneering work by the gravitational wave community which allows for reduction of added noise from measurement by coupling an optical field to the momentum of a small mirror. As a specific implementation, we present a continuous measurement protocol using a double-ring optomechanical cavity. We demonstrate that with experimentally-relevant parameters, this protocol can lead to significant back-action noise evasion, yielding measurement noise below the standard quantum limit over many decades of frequency.

Truncated Nonlinear Interferometry for Quantum-Enhanced Atomic Force Microscopy.

Nonlinear interferometers that replace beam splitters in Mach-Zehnder interferometers with nonlinear amplifiers for quantum-enhanced phase measurements have drawn increasing interest in recent years, but practical quantum sensors based on nonlinear interferometry remain an outstanding challenge. Here, we demonstrate the first practical application of nonlinear interferometry by measuring the displacement of an atomic force microscope microcantilever with quantum noise reduction of up to 3dB below the standard quantum limit, corresponding to a quantum-enhanced measurement of beam displacement of 1.7 fm/sqrt[Hz]. Further, we minimize photon backaction noise while taking advantage of quantum noise reduction by transducing the cantilever displacement signal with a weak squeezed state while using dual homodyne detection with a higher power local oscillator. This approach may enable quantum-enhanced broadband, high-speed scanning probe microscopy.

Force measurement in squeezed dissipative optomechanics in the presence of laser phase noise.

We investigate the force measurement sensitivity in a squeezed dissipative optomechanics within the free-mass regime under the influence of shot noise (SN) from the photon number fluctuations, laser phase noise from the pump laser, thermal noise from the environment, and optical losses from outcoupling and detection inefficiencies. Generally, squeezed light could generate a reduced SN on the squeezed quadrature and an enlarged quantum backaction noise (QBA) due to the antisqueezed conjugate quadrature. With an appropriate choice of phase angle in homodyne detection, QBA is cancellable, leading to an exponentially improved measurement sensitivity for the SN-dominated regime. By now, the effects of laser phase noise that is proportional to laser power emerge. The balance between squeezed SN and phase noise can lead to an sub-SQL sensitivity at an exponentially lower input power. However, the improvement by squeezing is limited by optical losses because high sensitivity is delicate and easily destroyed by optical losses.

Back-action evading measurement of the collective mode of a Bose–Einstein condensate

In this paper, we investigate theoretically the back-action evading measurement of the collective mode of an interacting atomic Bose–Einstein condensate (BEC) trapped in an optical cavity that is driven coherently by a pump laser with a modulated amplitude. It is shown that, for a specified kind of amplitude modulation of the driving laser, one can measure a generalized quadrature of the collective mode of the BEC indirectly through the output cavity field with a negligible back-action noise in the good-cavity limit. Nevertheless, the on-resonance added noise of measurement is suppressed below the standard quantum limit (SQL), even in the bad cavity limit. Moreover, the measurement precision can be controlled through the s -wave scattering frequency of atomic collisions.

Overcoming standard quantum limit using a momentum measuring interferometer.

We show that back-action noise in the momentum measurement of a damped forced oscillator can be suppressed because of damping. Using this principle, we propose a back-action suppressed interferometer, in which the signal is a function of momentum of atoms in a harmonic trap. We show that the quantum noise limited sensitivity of this interferometer can overcome the standard quantum limit of force sensing, even at frequencies much smaller than the eigen frequency of the harmonic trap.