Photons with sub-Planckian Energy Cannot Efficiently Probe Space-Time Foam

Extra-galactic sources of photons have been used to constrain space-time quantum fluctuations in the Universe. In these proposals, the fundamental "fuzziness" of distance caused by space-time quantum fluctuations has been directly identified with fluctuations in optical paths. Phase-front corrugations deduced from these optical-path fluctuations are then applied to light from extra-galactic point sources, and used to constrain various models of quantum gravity. However, when a photon propagates in three spatial dimensions, it does not follow a specific ray, but rather samples a finite, three-dimensional region around that ray --- thereby averaging over space-time quantum fluctuations all through that region. We use a simple, random-walk type model to demonstrate that, once the appropriate wave optics is applied, the averaging of neighboring space-time fluctuations will cause much less distortion to the phase front. In our model, the extra suppression factor due to diffraction is the wave length in units of the Planck length, which is at least $10^{29}$ for astronomical observations.Comment: This is a revised version of arXiv:gr-qc/060509

Enhancing the bandwidth of gravitational-wave detectors with unstable optomechanical filters

For gravitational-wave interferometric detectors, there is a tradeoff between the detector bandwidth and peak sensitivity when focusing on the shot noise level. This has to do with the frequency-dependent propagation phase lag (positive dispersion) of the signal. We consider embedding an active unstable filter---a cavity-assisted optomechanical device operating in the instability regime---inside the interferometer to compensate the phase, and using feedback control to stabilize the entire system. We show that this scheme in principle can enhance the bandwidth without sacrificing the peak sensitivity. However, there is one practical difficulty for implementing it due to the thermal fluctuation of the mechanical oscillator in the optomechanical filter, which puts a very stringent requirement on the environmental temperature and the mechanical quality factor.Comment: 5 pages and 6 figures. Comments are welcom

Quantum noise of white light cavity using double-pumped gain medium

Laser interferometric gravitational-wave detectors implement Fabry-Perot cavities to increase their peak sensitivity. However, this is at cost of reducing their detection bandwidth, which origins from the propagation phase delay of the light. The "white-light-cavity" idea, first proposed by Wicht et al. [Optics Communications 134, 431 (1997)], is to circumvent this limitation by introducing anomalous dispersion, using double-pumped gain medium, to compensate for such phase delay. In this article, starting from the Hamiltonian of atom-light interaction, we apply the input-output formalism to evaluate the quantum noise of the system. We find that apart from the additional noise associated with the parametric amplification process noticed by others, the stability condition for the entire system poses an additional constraint. Through surveying the parameter regimes where the gain medium remains stable (not lasing) and stationary, we find that there is no net enhancement of the shot-noise limited sensitivity. Therefore, other gain mediums or different parameter regimes shall be explored for realizing the white light cavity.Comment: 12 pages, 7 figure

Extraction of energy from gravitational waves by laser interferometer detectors

In this paper we discuss the energy interaction between gravitational waves and laser interferom- eter gravitational wave detectors. We show that the widely held view that the laser interferometer gravitational wave detector absorbs no energy from gravitational waves is only valid under the approximation of a frequency-independent optomechanical coupling strength and a pump laser without detuning with respect to the resonance of the interferometer. For a strongly detuned interferometer, the optical-damping dynamics dissipates gravitational wave energy through the interaction between the test masses and the optical field. For a non-detuned interferometer, the frequency-dependence of the optomechanical coupling strength causes a tiny energy dissipation, which is proved to be equivalent to the Doppler friction raised by Braginsky et.al.Comment: 20 pages, 7 figure

Towards the Fundamental Quantum Limit of Linear Measurements of Classical Signals

The quantum Cram\'er-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 which arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum non-demolition 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.Comment: revised version with supplemental materials adde

A Hybrid Rydberg Quantum Gate for Quantum Network

The high fidelity storage, distribution and processing of quantum information prefers qubits with different physical properties. Thus, hybrid quantum gates interfacing different types of qubits are essential for the realization of complex quantum network structures. A Rydberg-atom based physical quantum CZ gate is proposed to hybridly process the polarisation-encoded single-photon optical qubit and the "Schroedinger cat" microwave qubit. The degradation of the fidelity under the influence of various noise channels, such as microwave cavity loss, sponetanous emission of atom states, and non-adiabaticity effect, etc, has been analyised through detailed theoretical analysis by deriving input-output relation of qubit fields. The feasibility and the challenges of the protocol within current technology are also discussed by analysing the possible experimental parameter settings

Accretion-modified stellar-mass black hole distribution and milli-Hz gravitational wave backgrounds from galaxy centre

Gas accretion of embedded stellar-mass black holes\,(sBHs) or stars in the accretion disk of active galactic nuclei\,(AGNs) will modify the mass distribution of these sBHs and stars, which will also affect the migration of the sBHs/stars. With the introduction of the mass accretion effect, we simulate the evolution of the sBH/star distribution function in a consistent way by extending the Fokker-Planck equation of sBH/star distributions to the mass-varying scenario, and explore the mass distribution of sBHs in the nuclear region of the galaxy centre. We find that the sBHs can grow up to several tens solar mass and form heavier sBH binaries, which will be helpful for us to understand the black-hole mass distribution as observed by the current and future ground-based gravitational wave detectors\,(e.g., LIGO/VIRGO, ET and Cosmic Explorer). We further estimate the event rate of extreme mass-ratio inspirals\,(EMRI) for sBH surrounding the massive black hole and calculate the stochastic gravitational wave\,(GW) background of the EMRIs. We find that the background can be detected in future space-borne GW detectors after considering the sBHs embedded in the AGN disk, while the mass accretion has a slight effect on the GW background.Comment: 15 pages, 8 figures, Accepted by MNRA