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arXiv:1602.08929 · Journal of Optics

All-mechanical quantum noise cancellation for accelerometry: broadband with momentum measurements, narrow band without

Kurt A. Jacobs, Nikolas Tezak, Hideo Mabuchi, Radhakrishnan Balu

Published Feb 25, 2016• 3 citations
arXivHTMLPDF

Abstract

Abstract We show that the ability to make direct measurements of momentum, in addition to the usual direct measurements of position, allows a simple configuration of two identical mechanical oscillators to be used for broadband back-action-free force metrology. This would eliminate the need for an optical reference oscillator in the scheme of Tsang and Caves (2010 Phys. Rev. Lett. 105 123601 ), along with its associated disadvantages. We also show that if one is restricted to position measurements alone then two copies of the same two-oscillator configuration can be used for narrow-band back-action-free force metrology.

DOI
10.1088/2040-8978/18/3/034002

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Abstract We show that the ability to make direct measurements of momentum, in addition to the usual direct measurements of position, allows a simple configuration of two identical mechanical oscillators to be used for broadband back-action-free force metrology. This would eliminate the need for an optical reference oscillator in the scheme of Tsang and Caves (2010 Phys. Rev. Lett. 105 123601 ), along with its associated disadvantages. We also show that if one is restricted to position measurements alone then two copies of the same two-oscillator configuration can be used for narrow-band back-action-free force metrology.
The radiation pressure interaction of light with a mechanical oscillator leads to a fundamental disturbance on the oscillator. This disturbance - measurement backaction - is due to the quantum fluctuations in the amplitude of the light. When the phase of the light is detected to infer the mechanical position, quantum fluctuations in the phase - measurement imprecision - leads to a further uncertainty in the estimate of the position. In this conventional measurement strategy, these two noise sources impose a fundamental limit on the ability to estimate the position of the mechanical object - the so-called standard quantum limit [1]. However, the two noise contributions are in general correlated. The fluctuations in the amplitude quadrature drive the mechanical oscillator, and this backaction driven motion is transduced into the phase quadrature. Correlations thus established [2] form a valuable quantum mechanical resource that can be directly employed for back-action cancellation in the measurement record via “variational measurements” [3].
Quantum mechanics dictates that a measurement without perturbation is not possible. A textbook example is the observation of the position of an object, which imposes a random back action perturbation on the momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty on the measurement of motion. Here we demonstrate that the back action on an oscillator measured in a reference frame of another oscillator with an effective negative mass can be evaded in both position and momentum variables simultaneously. The mechanical oscillator is a millimeter-sized membrane and the reference negative mass oscillator is the collective spin of an atomic ensemble precessing in a magnetic field. Laser light transmitted through the hybrid system of these two disparate oscillators serves as the meter. We first observe the quantum measurement back action on each oscillator. We then demonstrate that back action at the single noise photon level is efficiently suppressed or enhanced depending on the sign of the effective mass of the reference spin oscillator. The two oscillators are separated by one meter but can be placed at a much larger distance as they are interfaced by laser light. The reference spin oscillator is insensitive to gravity and acceleration which can be efficiently detected by the mechanical oscillator in the absence of the measurement back action. The novel hybrid quantum system presented here paves the road to generation of entanglement and distant quantum communication between mechanical and spin systems and to back action free sensing of acceleration and force.
Quantum mechanics sets a limit for the precision of continuous measurement of the position of an oscillator. We show how it is possible to measure an oscillator without quantum back-action of the measurement by constructing one effective oscillator from two physical oscillators. We realize such a quantum mechanics-free subsystem using two micromechanical oscillators, and show the measurements of two collective quadratures while evading the quantum back-action by 8 decibels on both of them, obtaining a total noise within a factor of 2 of the full quantum limit. This facilitates the detection of weak forces and the generation and measurement of nonclassical motional states of the oscillators. Moreover, we directly verify the quantum entanglement of the two oscillators by measuring the Duan quantity 1.4 decibels below the separability bound.
A broadband multidimensional variational measurement allows overcoming the Standard Quantum Limit (SQL) of a classical mechanical force detection for a mechanical oscillator. In this measurement quantum back action, which perturbs the evolution of a mechanical oscillator, can be completely removed in a broad detection frequency band after post-processing. The measurement is performed by optical pumping of the central optical mode and analyzing the light escaping the two other optical modes, which have the frequency separation with the central mode equal to the mechanical frequency. To realize such a scheme in practice one either needs to use a very long optical interferometer or should utilize optical modes belonging to different mode families. In the second case the modes have different geometries and their coupling with the mechanical mode is not identical. Here we analyze a general case of the non-symmetric measurement scheme, in which the coupling strengths with the light modes are not equal to each other, and take into account optical losses. We found that the back action can be completely excluded from the measurement result in the case of the asymmetric lossless system. The nonzero loss limits the sensitivity. An experimental implementation of the proposed scheme is discussed.
Broadband multidimensional variational measurement allows overcoming the standard quantum limit (SQL) in detecting a classical mechanical force acting on a mechanical oscillator. In this measurement quantum back action, which perturbs the evolution of a mechanical oscillator, can be completely removed in a broad frequency band after post-processing. In this paper we show that optical losses inside the cavity restrict back action exclusion due to the loss noise. We also analyze the effect of two-photon (nondegenerate) and conventional (degenerate) squeezing in order to improve sensitivity with accounting for optical losses. We consider mainly internal squeezing.
Advances in precision optomechanical measurement underpin a wide range of technologies, from inertial sensors to the detection of gravitational waves and the exploration of fundamental physics. For such applications, the ultimate sensitivity is limited by quantum noise: shot noise, which stems from the stochastic arrival of photons, dominates at high frequencies, while Quantum Back-Action (QBA) noise—arising from the random radiation-pressure force exerted by the light field—prevails at low frequencies. The interplay between these two contributions defines the Standard Quantum Limit (SQL) of interferometry, a power-dependent trade-off that constrains further performance improvements. Although several sub-SQL techniques have been demonstrated, they typically enhance narrow-band sensitivity or require long filter cavities. Coherent Quantum Noise Cancellation (CQNC), first proposed by Tsang and Caves, offers a broadband solution by introducing an Effective Negative-Mass Oscillator (ENMO) that destructively interferes with the QBA noise across the entire spectrum except at the mechanical resonance of the opto-mechanically coupled system. A mathematically equivalent scheme for broadband QBA evasion has been demonstrated—for example, using atomic ensembles. The operation of this scheme is restricted to specific atomic transition wavelengths and is therefore unsuitable for many optomechanical platforms. This thesis reports the first all-optical, table-top realisation of an ENMO capable of Coherent Quantum Noise Cancellation in quantum optomechanical sensors. The scheme employs an optical analogue of the optomechanical interaction, generated through a combination of parametric down-conversion and beam-splitting processes, yielding a tunable, wavelength-flexible, and compact system. The achieved parameters satisfy the CQNC targets established in earlier theoretical work, and the current system predicts a broadband quantum-noise reduction of 3.6 dB (77% suppression of QBA noise(in dB)) at the frequency of maximum suppression. With further reduction of intracavity losses, the projected cancellation improves to 11.9 dB (81% suppression (in dB)). The experimental realisation features two polarisation-coupled optical resonators that host a two-mode squeezing interaction; the optical resonators possess distinct detunings and linewidths. The interdependent nature of the ENMO system motivated the development of an in-situ characterisation method, which is essential for integrating the ENMO with an optomechanical system in practical applications. Adequately addressing the system’s complexity required the development of five specialised experimental techniques for parameter tuning and comprehensive characterisation. Beyond quantum-noise cancellation, this system lends itself to application in quantum-information and quantum-communication tasks, including an on-demand, high-purity single-photon source and a quantum memory. Owing to the optical platform’s immunity to thermal decoherence, it can be operated at room temperature, and the parametric down-conversion process affords flexibility in wavelength selection. The results presented here advance the state of the art in broadband quantum noise reduction in a broad class of optomechanical devices, with immediate relevance for emerging quantum-technology applications.