325 research outputs found
Universally Valid Error-Disturbance Relations in Continuous Measurements
In quantum physics, measurement error and disturbance were first naively
thought to be simply constrained by the Heisenberg uncertainty relation. Later,
more rigorous analysis showed that the error and disturbance satisfy more
subtle inequalities. Several versions of universally valid error-disturbance
relations (EDR) have already been obtained and experimentally verified in the
regimes where naive applications of the Heisenberg uncertainty relation failed.
However, these EDRs were formulated for discrete measurements. In this paper,
we consider continuous measurement processes and obtain new EDR inequalities in
the Fourier space: in terms of the power spectra of the system and probe
variables. By applying our EDRs to a linear optomechanical system, we confirm
that a tradeoff relation between error and disturbance leads to the existence
of an optimal strength of the disturbance in a joint measurement.
Interestingly, even with this optimal case, the inequality of the new EDR is
not saturated because of doublely existing standard quantum limits in the
inequality.Comment: 11 pages, 2 figure
Quantum interactions between a laser interferometer and gravitational waves
LIGO's detection of gravitational waves marks a first step in measurable
effects of general relativity on quantum matter. In its current operation,
laser interferometer gravitational-wave detectors are already quantum limited
at high frequencies, and planned upgrades aim to decrease the noise floor to
the quantum level over a wider bandwidth. This raises the interesting idea of
what a gravitational-wave detector, or an optomechanical system more generally,
may reveal about gravity beyond detecting gravitational waves from highly
energetic astrophysical events, such as its quantum versus classical nature. In
this paper we develop a quantum treatment of gravitational waves and its
interactions with the detector. We show that the treatment recovers known
equations of motion in the classical limit for gravity, and we apply our
formulation to study the system dynamics, with a particular focus on the
implications of gravity quantization. Our framework can also be extended to
study alternate theories of gravity and the ways in which their features
manifest themselves in a quantum optomechanical system
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
Hybrid method for understanding black-hole mergers: Inspiralling case
We adapt a method of matching post-Newtonian and black-hole-perturbation theories on a timelike surface (which proved useful for understanding head-on black-hole-binary collisions) to treat equal-mass, inspiralling black-hole binaries. We first introduce a radiation-reaction potential into this method, and we show that it leads to a self-consistent set of equations that describe the simultaneous evolution of the waveform and of the timelike matching surface. This allows us to produce a full inspiral-merger-ringdown waveform of the l=2, m=±2 modes of the gravitational waveform of an equal-mass black-hole-binary inspiral. These modes match those of numerical-relativity simulations well in phase, though less well in amplitude for the inspiral. As a second application of this method, we study a merger of black holes with spins antialigned in the orbital plane (the superkick configuration). During the ringdown of the superkick, the phases of the mass- and current-quadrupole radiation become locked together, because they evolve at the same quasinormal-mode frequencies. We argue that this locking begins during the merger, and we show that if the spins of the black holes evolve via geodetic precession in the perturbed black-hole spacetime of our model, then the spins precess at the orbital frequency during the merger. In turn, this gives rise to the correct behavior of the radiation, and produces a kick similar to that observed in numerical simulations
The AEI 10 m prototype interferometer
A 10 m prototype interferometer facility is currently being set up at the AEI in Hannover, Germany. The prototype interferometer will be housed inside a 100 m^3 ultra-high vacuum envelope. Seismically isolated optical tables inside the vacuum system will be interferometrically interconnected via a suspension platform interferometer. Advanced isolation techniques will be used, such as inverted pendulums and geometrical anti-spring filters in combination with multiple-cascaded pendulum suspensions, containing an all-silica monolithic last stage. The light source is a 35 W Nd:YAG laser, geometrically filtered by passing it through a photonic crystal fibre and a rigid pre-modecleaner cavity. Laser frequency stabilisation will be achieved with the aid of a high finesse suspended reference cavity in conjunction with a molecular iodine reference. Coating thermal noise will be reduced by the use of Khalili cavities as compound end mirrors. Data acquisition and control of the experiments is based on the AdvLIGO digital control and data system. The aim of the project is to test advanced techniques for GEO 600 as well as to conduct experiments in macroscopic quantum mechanics. Reaching standard quantum-limit sensitivity for an interferometer with 100 g mirrors and subsequently breaching this limit, features most prominently among these experiments. In this paper we present the layout and current status of the AEI 10 m Prototype Interferometer project
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
Mathematical framework for simulation of quantum fields in complex interferometers using the two-photon formalism
We present a mathematical framework for simulation of optical fields in
complex gravitational-wave interferometers. The simulation framework uses the
two-photon formalism for optical fields and includes radiation pressure
effects, an important addition required for simulating signal and noise fields
in next-generation interferometers with high circulating power. We present a
comparison of results from the simulation with analytical calculation and show
that accurate agreement is achieved
Detection template families for gravitational waves from the final stages of binary--black-hole inspirals: Nonspinning case
We investigate the problem of detecting gravitational waves from binaries of
nonspinning black holes with masses m = 5--20 Msun, moving on quasicircular
orbits, which are arguably the most promising sources for first-generation
ground-based detectors. We analyze and compare all the currently available
post--Newtonian approximations for the relativistic two-body dynamics; for
these binaries, different approximations predict different waveforms. We then
construct examples of detection template families that embed all the
approximate models, and that could be used to detect the true
gravitational-wave signal (but not to characterize accurately its physical
parameters). We estimate that the fitting factor for our detection families is
>~0.95 (corresponding to an event-rate loss <~15%) and we estimate that the
discretization of the template family, for ~10^4 templates, increases the loss
to <~20%.Comment: 58 pages, 38 EPS figures, final PRD version; small corrections to GW
flux terms as per Blanchet et al., PRD 71, 129902(E)-129904(E) (2005
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