Broadband quantum back action evading measurements of a resonant force

Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random quantum back-action (QBA) perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty on the measurement of motion. As a consequence of this randomness, and in accordance with the Heisenberg uncertainty principle, the QBA puts a limitation-the so-called standard quantum limit-on the precision of sensing of position, velocity and acceleration. Here we show that QBA on a macroscopic mechanical oscillator can be evaded if the measurement of motion is conducted in the reference frame of an atomic spin oscillator. The collective quantum measurement on this hybrid system of two distant and disparate oscillators is performed with light. The mechanical oscillator is a vibrational 'drum' mode of a millimetre-sized dielectric membrane, and the spin oscillator is an atomic ensemble in a magnetic field. The spin oriented along the field corresponds to an energetically inverted spin population and realizes a negative-effective-mass oscillator, while the opposite orientation corresponds to an oscillator with positive effective mass. The QBA is suppressed by -1.8 decibels in the negative-mass setting and enhanced by 2.4 decibels in the positive-mass case. This hybrid quantum system paves the way to entanglement generation and distant quantum communication between mechanical and spin systems and to sensing of force, motion and gravity beyond the standard quantum limit.

Quantum mechanics places a fundamental limit on the precision of continuous measurements. The Heisenberg uncertainty principle dictates that as the precision of a measurement of an observable (for example, position) increases, back action creates increased uncertainty in the conjugate variable (for example, momentum). In interferometric gravitational-wave detectors, higher laser powers reduce the position uncertainty created by shot noise(the photon-counting error caused by the quantum nature of the laser) but necessarily do so at the expense of back action in the form of quantum radiation pressure noise (QRPN)1. Once at design sensitivity, the gravitational-wave detectors Advanced LIGO2, VIRGO3 and KAGRA4 will be limited by QRPN at frequencies between 10hertz and 100hertz. There exist several proposals to improve the sensitivity of gravitational-wave detectors by mitigating QRPN5-10, but until now no platform has allowed for experimental tests of these ideas. Here we present a broadband measurement of QRPN at room temperature at frequencies relevant to gravitational-wave detectors. The noise spectrum obtained shows effects due to QRPN between about 2kilohertz and 100kilohertz, and the measured magnitude of QRPN agrees with our model. We now have a testbed for studying techniques with which to mitigate quantum back action, such as variational readout and squeezed light injection7, with the aim of improving the sensitivity of future gravitational-wave detectors.

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.

We apply the strategy of the back action evading measurement of a quadrature component of mechanical motion of a test mass to detection of a classical force acting on the mass (Science, 209, (1980) 547) and study both classical and quantum limitations of the technique. We are considering a resonant displacement transducer interrogated with a dichromatic optical pump as a model system in this study. The transducer is represented by a Fabry Perot cavity with a totally reflecting movable end mirror the resonant force of interest acts upon. The cavity is pumped with two coherent optical carriers equally detuned from one of the cavity resonances. We show that the quantum back action cannot be completely excluded from the measurement result due to the dynamic instability of the opto-mechanical system that either limits the allowable power of the optical pump or calls for introducing an asymmetry to the pump configuration destroying the quantum nondemolition nature of the measurement.

An ultimate limit to the sensitivity achieved by detectors for gravitational radiation is set by quantum fluctuations. All detection systems are subject to this limit, however we shall restrict our attention to the affect of quantum fluctuations on optical detection systems such as the Michelson interferometer. The techniques developed to treat quantum fluctuations in optical systems may prove to be useful in analysing other detection systems. In a Michelson interferometer quantum fluctuations may affect the final measurement in two ways; namely photon counting fluctuations and radiation pressure fluctuations. The effect of these sources of error oil the interferometer detection scheme have been discussed by Caves and by Unruh. Caves suggested that these errors could be reduced by injecting special states of the radiation field with reduced fluctuations into one port of the interferometer. These states called “squeezed states” show reduced fluctuations in one quadrature and enhanced fluctuations in the other4–8. They also play a general role in quantum non demolition (Q.N.D.) measurements9 since the state of a system after certain Q.N.D. measurements (back action evading measurements) resembles a squeezed state.

The act of position measurement alters the motion of an object being measured. This quantum measurement backaction is typically much smaller than the thermal motion of a room-temperature object and thus difficult to observe. By shining laser light through a nanomechanical beam, we measure the beam's thermally driven vibrations and perturb its motion with optical force fluctuations at a level dictated by the Heisenberg measurement-disturbance uncertainty relation. We demonstrate a cross-correlation technique to distinguish optically driven motion from thermally driven motion, observing this quantum backaction signature up to room temperature. We use the scale of the quantum correlations, which is determined by fundamental constants, to gauge the size of thermal motion, demonstrating a path toward absolute thermometry with quantum mechanically calibrated ticks.

Second-generation interferometric gravitational-wave detectors will be operating at the Standard Quantum Limit (SQL), a sensitivity limitation set by the trade off between measurement accuracy and quantum back action, which is governed by the Heisenberg Uncertainty Principle. We review several schemes that allows the quantum noise of interferometers to surpass the SQL significantly over a broad frequency band. Such schemes may be an important component of the design of third-generation detectors.

After a quick review of the basic theory of quantum optomechanical systems, based largely on linearized Heisenberg–Langevin equations, this chapter focuses on selected topics related to quantum measurement and quantum optomechanics. Included are: a comprehensive discussion of the quantum limit on the added noise of a continuous position detector, following the quantum linear response approach; a detailed discussion of the role of noise correlations, and how these can be achieved in an optomechanical cavity (by using squeezed input light, or by modifying the choice of measured output quadrature); and a discussion of back-action evading measurements of a mechanical quadrature, discussing how this can be achieved in a two-tone driven cavity system. The chapter ends with a quick introduction to the theory of conditional continuous quantum measurement, and a discussion on how a back-action evading measurement can be used to produce conditional mechanical squeezed states.

As quantum systems become more experimentally accessible, we are forced to reconsider the notions of control and work to fully account for quantum effects. To this end, we identify the work injected into a quantum system during a general quantum-mechanical driving protocol and quantify the relevant heat flows. The known results that are applicable in the limit of a classical drive are shown to emerge from our equations as a special case. Using the established framework, we show that the Bochkov-Kuzovlev identity for the exclusive work distribution is modified in a nontrivial way by the accumulation of system-drive correlations resulting from quantum back action. Our results accentuate the conceptual and discernible differences between a fully quantum-mechanical and classical driving protocols of quantum systems.

In this chapter, we describe how an observation of the quantum back-action is related to the gravitational-wave (GW) detectors and test of quantum mechanics in macroscopic domain. As for force measurements such as the GW detectors, in which the mechanical oscillator is used as a probe of external force, its sensitivity has almost been limited by the standard quantum limit (SQL). Also, theoretical analysis has proven to be a connection between reaching the SQL imposed on the free mass (so-called free-mas SQL) and the generation of entanglement states, even between massive mechanical oscillators, such as suspended mirrors. Because of the massiveness (and the long relaxation time of the oscillator), such states might have a key to solve the quantum measurement problem. Thus, optomechanics is not only useful as sensitive probes for the weak force, but also leads to possibilities of testing fundamental problems. Although there are some motivations for using optomechanical system in the field of quantum information, let us focus on the above two topics.

Quantum physics ultimately constrains how well sensors of position, speed and acceleration can perform. A hybrid quantum system that avoids these constraints could give rise to improved sensor technologies. See Letter p.191 The Heisenberg uncertainty principle imposes a fundamental limit on measurement precision and is intertwined with the effect of quantum back-action. This effect occurs when measuring the position of an object results in a small but certain random perturbation of its momentum. Eugene Polzik and colleagues demonstrate a way to evade quantum back-action by coupling the object under observation, a mechanical oscillator, to another oscillator. The mechanical oscillator is a millimetre-sized suspended membrane, which they couple to an ensemble of atomic spins. The trick is to measure the motion of the membrane in the reference frame of the atomic system, which is tuned to a regime of negative effective mass. This results in suppression of the quantum back-action on the membrane. This technique could be used for sensing force, motion and gravity beyond the limit imposed by the Heisenberg uncertainty principle.

The quantum radiation pressure and the quantum shot noise in laser-interferometric gravitational wave detectors constitute a macroscopic manifestation of the Heisenberg inequality. If quantum shot noise can be easily observed, the observation of quantum radiation pressure noise has been elusive, so far, due to the technical noise competing with quantum effects. Here, we discuss the evidence of quantum radiation pressure noise in the Advanced Virgo gravitational wave detector. In our experiment, we inject squeezed vacuum states of light into the interferometer in order to manipulate the quantum backaction on the 42kg mirrors and observe the corresponding quantum noise driven displacement at frequencies between 30 and 70Hz. The experimental data, obtained in various interferometer configurations, is tested against the Advanced Virgo detector quantum noise model which confirmed the measured magnitude of quantum radiation pressure noise.

In a nanomechanical resonator coupled to a quantum point contact, the back action of the electronic state on mechanical motion is studied. The quantum point contact conductance changing with subband index and the eigenfrequency of the resonator are found to correlate. A model is constructed explaining the frequency deviations by the variable ability of the quantum point contact to screen the piezoelectric charge induced by mechanical oscillations. The observed effects can be used to develop electromechanical methods for studying the density of states in quasi-one-dimensional systems.

Heisenberg’s back action and Robertson’s intrinsic uncertainty are presented. von Neumann’s analysis of quantum measurement is recounted. Advanced LIGO is used as an example of quantum measurement: giant Michelson interferometers achieve sensitivity to motion of 1 part in 1021. The discovery at LIGO of gravitational waves is outlined. Then the standard quantum limit is deduced. The use of cavities in the interferometer arms to increase the photon flux is described. The potential for improvement by squeezing the vacuum at the blank input port is discussed. Prospects for speed interferometry are outlined.

Static Stability Analysis Method for Fuzzy Rule-Chaining Real-Time Systems