Back action evading quantum measurement of motion in a negative mass reference frame
C. Møller, Rodrigo A. Thomas, Georgios Vasilakis, Emil Zeuthen, Yeghishe Tsaturyan, Kasper Jensen, Albert Schließer, Klemens Hammerer, Eugene Simon Polzik
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 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.
The application of quantum mechanics to macroscopic motion suggests many counterintuitive phenomena. While the quantum nature of the motion of individual atoms and molecules has long been successfully studied, an equivalent demonstration of the motion of a near-macroscopic structure remains a challenge in experimental physics. A nanomechanical resonator is an excellent system for such a study. It typically contains > 10 10 atoms, and it may be modeled in terms of macroscopic parameters such as bulk density and elasticity. Yet it behaves like a simple harmonic oscillator, with mass low enough and resonant frequency high enough for its quantum zero-point motion and single energy quanta to be experimentally accessible. In pursuit of quantum phenomena in a mechanical oscillator, two important goals are to prepare the oscillator in its quantum ground state, and to measure its position with a precision limited by the Heisenberg uncertainty principle. In this work we have demonstrated techniques that advance towards both of these goals. Our system comprises a 30 micron × 170 nm, 2.2 pg, 5.57 MHz nanomechanical resonator capacitively coupled to a 5 GHz superconducting microwave resonator. The microwave resonator and nanomechanical resonator are fabricated together onto a single silicon chip and measured in a dilution refrigerator at temperatures below 150 mK. At these temperatures the coupling of the motion to the thermal environment is very small, resulting in a very high mechanical Q, approaching ∼ 10 6 . By driving with a microwave pump signal, we observed sidebands generated by the mechanical motion and used these to measure the thermal motion of the resonator. Applying a pump tone red-detuned from the microwave resonance, we used the microwave field to damp the mechanical resonator, extracting energy and "cooling" the motion in a manner similar to optical cooling of trapped atoms. Starting from a mode temperature of ∼ 150 mK, we reached ∼ 40 mK by this "backaction cooling" technique, corresponding to an occupation factor only ∼ 150 times above the ground state of motion. We also determined the precision of our device in measurement of position. Quantum mechanics dictates that, in a continuous position measurement, the precision may be no better than the zero-point motion of the resonator. Increasing the coupling of the resonator to detector will eventually result in back-action driving of the motion, adding imprecision and enforcing this limit. We demonstrated that our system is capable of precisions approaching this limit, and identified the primary experimental factors preventing us from reaching it: noise added to the measurement by our amplifier, and excess dissipation appearing in our microwave resonator at high pump powers. Furthermore, by applying both red- and blue-detuned phase-coherent microwave pump signals, we demonstrated back-action evading (BAE) measurement sensitive to only a single quadrature of the motion. By avoiding the back-action driving in the measured quadrature, such a technique has the potential for precisions surpassing the limit of the zero-point motion. With this method, we achieved a measurement precision of ∼ 100 fm, or 4 times the quantum zero-point motion of the mechanical resonator. We found that the measured quadrature is insensitive to back-action driving by at least a factor of 82 relative to the unmeasured quadrature. We also identified a mechanical parametric amplification effect which arises during the BAE measurement. This effect sets limits on the BAE performance but also mechanically preamplifies the motion, resulting in a position resolution 1.3 times the zero-point motion. We discuss how to overcome the experimental limits set by amplifier noise, pump power and parametric amplification. These results serve to define the path forward for demonstrating truly quantum-limited measurement and non-classical states of motion in a nearly-macroscopic object.
It is well established that quantum back action (QBA) can be reduced (or even completely canceled) in composite systems by engineering so-called quantum-mechanics-free subspaces (QMFSs) of commuting variables. An important ingredient in this approach is the negative-mass oscillator, a phenomenon that arises in, e.g., polarized spin ensembles and two-tone-driven optomechanical systems. Entanglement established between a system of interest and an auxiliary negative-mass reference system allows measurements of motion, fields and forces with, in principle, unlimited precision. To date, these principles have been developed theoretically and demonstrated experimentally for a number of composite systems. However, the utility of the concept has been limited by the dominating requirement of close proximity of the resonance frequencies of the system of interest and the negative-mass reference system, and by the need to embed the subsystems in a narrowband cavity, which could be problematic while at the same time achieving good overcoupling. Here we propose a general approach which overcomes these limitations by employing periodic modulation of the driving fields (e.g., two-tone driving) in combination with coherent or measurement-based anti-noise paths. This approach makes it possible to engineer a QMFS of two systems with vastly different spectra and with arbitrary signs of their masses, while dispensing with the need to embed the subsystems in a sideband-resolving cavity. We discuss the advantages of this novel approach for applications such as QBA evasion in gravitational wave detection, force sensing, and entanglement generation between disparate systems.
Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement back action of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, back-action evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broad-band squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic spin ensembles, and implementations of the quantum Toffoli gate.
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].