Towards the Design of Gravitational-Wave Detectors for Probing Neutron-Star Physics

The gravitational waveform of merging binary neutron stars encodes information about extreme states of matter. Probing these gravitational emissions requires the gravitational-wave detectors to have high sensitivity above 1 kHz. Fortunately for current advanced detectors, there is a sizeable gap between the quantum-limited sensitivity and the classical noise at high frequencies. Here we propose a detector design that closes such a gap by reducing the high-frequency quantum noise with an active optomechanical filter, frequency-dependent squeezing, and high optical power. The resulting noise level from 1 kHz to 4 kHz approaches the current facility limit and is a factor of 20 to 30 below the design of existing advanced detectors. This will allow for precision measurements of (i) the post-merger signal of the binary neutron star, (ii) late-time inspiral, merger, and ringdown of low-mass black hole-neutron star systems, and possible detection of (iii) high-frequency modes during supernovae explosions. This design tries to maximize the science return of current facilities by achieving a sensitive frequency band that is complementary to the longer-baseline third-generation detectors: the10 km Einstein Telescope, and 40 km Cosmic Explorer. We have highlighted the main technical challenges towards realizing the design, which requires dedicated research programs. If demonstrated in current facilities, the techniques can be transferred to new facilities with longer baselines.Comment: 14 pages, 15 figures, published versio

Non-adiabatic elimination of auxiliary modes in continuous quantum measurements

When measuring a complex quantum system, we are often interested in only a few degrees of freedom-the plant, while the rest of them are collected as auxiliary modes-the bath. The bath can have finite memory (non-Markovian), and simply ignoring its dynamics, i.e., adiabatically eliminating it, will prevent us from predicting the true quantum behavior of the plant. We generalize the technique introduced by Strunz et. al. [Phys. Rev. Lett 82, 1801 (1999)], and develop a formalism that allows us to eliminate the bath non-adiabatically in continuous quantum measurements, and obtain a non-Markovian stochastic master equation for the plant which we focus on. We apply this formalism to three interesting examples relevant to current experiments.Comment: a revised versio

Universal quantum entanglement between an oscillator and continuous fields

Quantum entanglement has been actively sought in optomechanical and electromechanical systems. The simplest system is a mechanical oscillator interacting with a coherent optical field, while the oscillator also suffers from thermal decoherence. With a rigorous functional analysis, we develop a mathematical framework for treating quantum entanglement that involves infinite degrees of freedom. We show that the quantum entanglement is always present between the oscillator and continuous optical field—even when the environmental temperature is high and the oscillator is highly classical. Such a universal entanglement is also shown to be able to survive more than one mechanical oscillation period if the characteristic frequency of the optomechanical interaction is larger than that of the thermal noise. In addition, we introduce effective optical modes that are ordered by the entanglement strength to better understand the entanglement structure, analogously to the energy spectrum of an atomic system. In particular, we derive the optical mode that is maximally entangled with the mechanical oscillator, which will be useful for future quantum computing and encoding information into mechanical degrees of freedom

General quantum constraints on detector noise in continuous linear measurements

In quantum sensing and metrology, an important class of measurement is the continuous linear measurement, in which the detector is coupled to the system of interest linearly and continuously in time. One key aspect involved is the quantum noise of the detector, arising from quantum fluctuations in the detector input and output. It determines how fast we acquire information about the system and also influences the system evolution in terms of measurement backaction. We therefore often categorize it as the so-called imprecision noise and quantum backaction noise. There is a general Heisenberg-like uncertainty relation that constrains the magnitude of and the correlation between these two types of quantum noise. The main result of this paper is to show that, when the detector becomes ideal, i.e., at the quantum limit with minimum uncertainty, not only does the uncertainty relation takes the equal sign as expected, but also there are two new equalities. This general result is illustrated by using the typical cavity QED setup with the system being either a qubit or a mechanical oscillator. Particularly, the dispersive readout of a qubit state, and the measurement of mechanical motional sideband asymmetry are considered.Comment: journal accepted versio

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

Sensitivity of intracavity filtering schemes for detecting gravitational waves

We consider enhancing the sensitivity of future gravitational-wave detectors by adding optical filters inside the signal-recycling cavity -- an intracavity filtering scheme, which coherently feeds the sideband signal back to the interferometer with a proper frequency-dependent phase. We study three cases of such a scheme with different motivations: (i) the case of backaction noise evasion, trying to cancel radiation-pressure noise with only one filter cavity for a signal-recycled interferometer; (ii) the speed-meter case, similar to the speed-meter scheme proposed by Purdue and Chen [Phys. Rev. D 66, 122004 (2002)] but without the resonant-sideband-extraction mirror, and also relieves the optical requirement on the sloshing mirror; (iii) the broadband detection case with squeezed-light input, numerically optimized for a broadband sensitivity.Comment: 10 pages, 10 figure

Signatures of the quantum nature of gravity in the differential motion of two masses

We show that a signature of the quantum nature of gravity is the quantum mechanical squeezing of the differential motion of two identical masses with respect to their common mode. This is because the gravitational interaction depends solely on the relative position of the two masses. In principle, this squeezing is equivalent to quantum entanglement between the masses. In practice, detecting the squeezing is more feasible than detecting the entanglement. To that end, we propose an optical interferometric scheme to falsify hypothetical models of gravity.Comment: 5 pages, 1 figure. Comments welcome