Quantum back-action-evading measurement of motion in a negative mass reference frame.

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.

Broadband quantum back action evading measurements of a resonant force

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.

Assuming a two-component, positive and negative mass, superfluid/supersolid for space (the Winterberg model), we model the Higgs field as a condensate made up of a positive and a negative mass, planckion pair. The connection is shown to be consistent (compatible) with the underlying field equations for each field, and the continuity equation is satisfied for both species of planckions, as well as for the Higgs field. An inherent length scale for space (the vacuum) emerges, which we estimate from previous work to be of the order of, l+ (0) = l- (0) = 5.032E-19 meters, for an undisturbed (unperturbed) vacuum. Thus we assume a lattice structure for space, made up of overlapping positive and negative mass wave functions, ψ+, and, ψ-, which together bind to form the Higgs field, giving it its rest mass of 125.35 Gev/c2 with a coherence length equal to its Compton wavelength. If the vacuum experiences an extreme disturbance, such as in a LHC pp collision, it is conjectured that severe dark energy results, on a localized level, with a partial disintegration of the Higgs force field in the surrounding space. The Higgs boson as a quantum excitation in this field results when the vacuum reestablishes itself, within 10-22 seconds, with positive and negative planckion mass number densities equalizing in the disturbed region. Using our fundamental equation relating the Higgs field, φ, to the planckion ψ+ and ψ- wave functions, we calculate the overall vacuum pressure (equal to vacuum energy density), as well as typical ψ+ and ψ- displacements from equilibrium within the vacuum.

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.

Based on Baumgarte–Shapiro–Shibata–Nakamura formalism and moving puncture method, we demonstrate the first numerical evolutions of the interaction between positive and negative mass objects. Using the causal property of general relativity, we set our computational domain around the positive mass black hole while excluding the region around the naked singularity introduced by the negative mass object. Besides the usual Sommerfeld numerical boundary condition, an approximate boundary condition is proposed for this nonasymptotically-flat computational domain. Careful checks show that either boundary condition introduces smaller error than the numerical truncation errors. This is consistent with the causal property of general relativity. Except for the numerical truncation error and round-off error, our method gives an exact solution to the full Einstein's equation for a portion of spacetime with two objects whose masses have opposite signs. So our method opens the door for numerical explorations with negative mass objects. Based on this method, we investigate the Newtonian limit of spacetime with two objects whose masses have opposite sign. Our result implies that this spacetime does have a Newtonian limit which corresponds to a negative mass particle chasing a positive mass particle. This result sheds some light on an interesting debate about the Newtonian limit of a spacetime with positive and negative point masses.

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.

Some experiments have indicated the possible existence of particles with a negative inertial mass. It is shown under which conditions Weber’s electrodynamics gives rise to this effect. Some specific experiments related to this aspect of Weber’s law are described. Two particles equally electrified with charges of the same sign would then move toward one another if they had negative effective inertial masses. A new concept for nuclear fusion is presented based on the possibility of creating a negative effective inertial mass for ions. It is then considered some properties of the inertial dipole, that is, a system composed by a pair of particles in which one particle has a positive effective inertial mass while the other particle has a negative effective inertial mass. The possible utilization of the inertial dipole as a propulsion system is briefly discussed.

Single particle mass spectral signatures from vehicle exhaust particles and the source apportionment of on-line PM2.5 by single particle aerosol mass spectrometry

The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the standard quantum limit that arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum nondemolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric 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.

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.

Measurement-induced back action, a direct consequence of the Heisenberg Uncertainty Principle, is the defining feature of quantum measurements. We use quantum measurement theory to analyze the recent experiment of Safavi-Naeini et al. [Phys. Rev. Lett. {\bf 108}, 033602 (2012)], and show that results of this experiment not only characterize the zero-point fluctuation of a near-ground-state nanomechanical oscillator, but also demonstrate the existence of quantum back-action noise --- through correlations that exist between sensing noise and back-action noise. These correlations arise from the quantum coherence between the mechanical oscillator and the measuring device, which build up during the measurement process, and are key to improving sensitivities beyond the Standard Quantum Limit.

The positive and negative ion mass spectra of three secondary metabolites of Aspergillus Wentii Wehmer, namely 15-acetoxyhexadecyl-, 15-oxohexadecyl- and 15-hydroxyhexadecylcitraconic anhydrides are reported and discussed. The positive ion mass spectra, which have been studied in detail by exact mass measurements and metastable ion detection using a defocusing method, show very weak molecular ions and complex fragmentation pathways, strongly influenced by the group on C-15. However, the negative ion mass spectra show very abundant molecular ions and little fragmentation, with the negative charge mainly retained by the anhydride moiety. The behavior of both positive and negative ions is in agreement with the charge localization concept, on the grounds of ionization energy and electron affinity considerations. positive and negative ion mass spectra are largely complementary, thus increasing their analytical value.