Tomography of an optomechanical oscillator via parametrically amplified position measurement

We propose a protocol for quantum state tomography of nonclassical states in optomechanical systems. Using a parametric drive, the procedure overcomes the challenges of weak optomechanical coupling, poor detection efficiency, and thermal noise to enable high efficiency homodyne measurement. Our analysis is based on the analytic description of the generalized measurement that is performed when optomechanical position measurement competes with thermal noise and a parametric drive. The proposed experimental procedure is numerically simulated in realistic parameter regimes, which allows us to show that tomographic reconstruction of otherwise unverifiable nonclassical states is made possible.Comment: 37 pages, 5 figures, comments welcome. Published versio

Gravitational-wave bursts and stochastic background from superfluid vortex avalanches during pulsar glitches

The current-quadrupole gravitational-wave signal emitted during the spin-up phase of a pulsar glitch is calculated from first principles by modeling the vortex dynamics observed in recent Gross-Pitaevskii simulations of pinned, decelerating quantum condensates. Homogeneous and inhomogeneous unpinning geometries, representing creep- and avalanche-like glitches, provide lower and upper bounds on the gravitational wave signal strength respectively. The signal arising from homogeneous glitches is found to scale with the square root of glitch size, whereas the signal from inhomogeneous glitches scales proportional to glitch size. The signal is also computed as a function of vortex travel distance and stellar angular velocity. Convenient amplitude scalings are derived as functions of these parameters. For the typical astrophysical situation, where the glitch duration (in units of the spin period) is large compared to the vortex travel distance (in units of the stellar radius), an individual glitch from an object $1\,\rm{kpc}$ from Earth generates a wave strain of $10^{-24} [(\Delta\omega/\omega) / 10^{-7}] (\omega/10^2 \rm{rad s}^{-1})^3 (\Delta r / 10^{-2} \rm{m})^{-1}$, where $\Delta r$ is the average distance travelled by a vortex during a glitch, $\Delta\omega/\omega$ is the fractional glitch size, and $\omega$ is the pulsar angular velocity. The non-detection of a signal from the 2006 Vela glitch in data from the fifth science run conducted by the Laser Interferometer Gravitational-Wave Observatory implies that the glitch duration exceeds $\sim 10^{-4}\,\rm{ms}$. This represents the first observational lower bound on glitch duration to be obtained.Comment: Accepted for publication in MNRA

Engineering Quantum Jump Superoperators for Single Photon Detectors

We study the back-action of a single photon detector on the electromagnetic field upon a photodetection by considering a microscopic model in which the detector is constituted of a sensor and an amplification mechanism. Using the quantum trajectories approach we determine the Quantum Jump Superoperator (QJS) that describes the action of the detector on the field state immediately after the photocount. The resulting QJS consists of two parts: the bright counts term, representing the real photoabsorptions, and the dark counts term, representing the amplification of intrinsic excitations inside the detector. First we compare our results for the counting rates to experimental data, showing a good agreement. Then we point out that by modifying the field frequency one can engineer the form of QJS, obtaining the QJS's proposed previously in an ad hoc manner

Stochastic simulations of conditional states of partially observed systems, quantum and classical

In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional state will be given by a state matrix $\rho_r(t)$ and if classical the conditional state will be given by a probability distribution $P_r(x,t)$ where $r$ is the result of the measurement. Thus to determine the evolution of this conditional state under continuous-in-time monitoring requires an expensive numerical calculation. In this paper we demonstrating a numerical technique based on linear measurement theory that allows us to determine the conditional state using only pure states. That is, our technique reduces the problem size by a factor of $N$, the number of basis states for the system. Furthermore we show that our method can be applied to joint classical and quantum systems as arises in modeling realistic measurement.Comment: 16 pages, 11 figure

Quantum trajectories for the realistic measurement of a solid-state charge qubit

We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by embedding the detector in an equivalent circuit for measurement. Our aim is to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit. We achieve this by generalizing a recently developed quantum trajectory theory for realistic photodetectors [P. Warszawski, H. M. Wiseman and H. Mabuchi, Phys. Rev. A_65_ 023802 (2002)] to treat solid-state detectors. This yields stochastic equations whose (numerical) solutions are the ``realistic quantum trajectories'' of the conditioned qubit state. We derive our general theory in the context of a low transparency quantum point contact. Areas of application for our theory and its relation to previous work are discussed.Comment: 7 pages, 2 figures. Shorter, significantly modified, updated versio

Observations of microglitches in HartRAO radio pulsars

A detailed observation of microglitch phenomenon in relatively slow radio pulsars is presented. Our analyses for these small amplitude jumps in pulse rotation frequency ($\nu$) and/or spin down rate ($\dot{\nu}$) combine the traditional manual detection method (which hinges on careful visual inspections of the residuals of pulse phase residuals) and a new, and perhaps more objective, automated search technique (which exploits the power of the computer, rather than the eyes, for resolving discrete events in pulsar spin parameters). The results of the analyses of a sample of 26 radio pulsars reveal that: (i) only 20 pulsars exhibit significant fluctuations in their arrival times to be considered suitable for meaningful microglitch analyses; (ii) a phenomenal 299 microglitch events were identified in $\nu$ and/or $\dot{\nu}$: 266 of these events were found to be simultaneously significant in $\nu$ and $\dot{\nu}$, while 19 and 14 were noticeable only in $\nu$ and $\dot{\nu}$, respectively; (iii) irrespective of sign, the microglitches have fractional sizes which cover about 3 orders of magnitude in $\nu$ and $\dot{\nu}$ ($10^{-11} < |\Delta{\nu}/\nu| < 2.0\times10^{-8}$ and $5.0\times10^{-5} < |\Delta{\dot{\nu}}/\dot{\nu}| < 2.0\times10^{-2}$) with median values as $0.78\times10^{-9}$ and $0.36\times10^{-3}$, respectively.Comment: 12 pages, 3 figures, 2 Tables. Accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journa

Superfluid vortex unpinning as a coherent noise process, and the scale invariance of pulsar glitches

The scale-invariant glitch statistics observed in individual pulsars (exponential waiting-time and power-law size distributions) are consistent with a critical self-organization process, wherein superfluid vortices pin metastably in macroscopic domains and unpin collectively via nearest-neighbor avalanches. Macroscopic inhomogeneity emerges naturally if pinning occurs at crustal faults. If, instead, pinning occurs at lattice sites and defects, which are macroscopically homogeneous, we show that an alternative, noncritical self-organization process operates, termed coherent noise, wherein the global Magnus force acts uniformly on vortices trapped in a range of pinning potentials and undergoing thermal creep. It is found that vortices again unpin collectively, but not via nearest-neighbor avalanches, and that, counterintuitively, the resulting glitch sizes are scale invariant, in accord with observational data. A mean-field analytic theory of the coherent noise process, supported by Monte-Carlo simulations, yields a power-law size distribution, between the smallest and largest glitch, with exponent $a$ in the range $-2\leq a \leq 0$. When the theory is fitted to data from the nine most active pulsars, including the two quasiperiodic glitchers PSR J0537$-$6910 and PSR J0835$-$4510, it directly constrains the distribution of pinning potentials in the star, leading to two conclusions: (i) the potentials are broadly distributed, with the mean comparable to the standard deviation; and (ii) the mean potential decreases with characteristic age. An observational test is proposed to discriminate between nearest-neighbor avalanches and coherent noise.Comment: 39 pages, 11 figures. Accepted for publication in Ap

An analysis of the timing irregularities for 366 pulsars

We provide an analysis of timing irregularities observed for 366 pulsars. Observations were obtained using the 76-m Lovell radio telescope at the Jodrell Bank Observatory over the past 36 years. These data sets have allowed us to carry out the first large-scale analysis of pulsar timing noise over time scales of > 10yr, with multiple observing frequencies and for a large sample of pulsars. Our sample includes both normal and recycled pulsars. The timing residuals for the pulsars with the smallest characteristic ages are shown to be dominated by the recovery from glitch events, whereas the timing irregularities seen for older pulsars are quasi-periodic. We emphasise that previous models that explained timing residuals as a low-frequency noise process are not consistent with observation.Comment: Accepted by MNRAS. High resolution images available from the article on AD