Quantum Trajectories for Realistic Detection

Quantum trajectories describe the stochastic evolution of an open quantum system conditioned on continuous monitoring of its output, such as by an ideal photodetector. Here we derive (non-Markovian) quantum trajectories for realistic photodetection, including the effects of efficiency, dead time, bandwidth, electronic noise, and dark counts. We apply our theory to a realistic cavity QED scenario and investigate the impact of such detector imperfections on the conditional evolution of the system state. A practical theory of quantum trajectories with realistic detection will be essential for experimental and technological applications of quantum feedback in many areas.Comment: 5 pages, 4 figures (3 .eps included, 1 jpeg as an additional file). To be published in Phys. Rev.

Dynamical parameter estimation using realistic photodetection

We investigate the effect of imperfections in realistic detectors upon the problem of quantum state and parameter estimation by continuous monitoring of an open quantum system. Specifically, we have reexamined the system of a two-level atom with an unknown Rabi frequency introduced by Gambetta and Wiseman [Phys. Rev. A 64, 042105 (2001)]. We consider only direct photodetection and use the realistic quantum trajectory theory reported by Warszawski, Wiseman, and Mabuchi [Phys. Rev. A 65, 023802 (2002)]. The most significant effect comes from a finite bandwidth, corresponding to an uncertainty in the response time of the photodiode. Unless the bandwidth is significantly greater than the Rabi frequency, the observer's ability to obtain information about the unknown Rabi frequency, and about the state of the atom, is severely compromised. This result has implications for quantum control in the presence of unknown parameters for realistic detectors, and even for ideal detectors, as it implies that most of the information in the measurement record is contained in the precise timing of the detections.Comment: 8 pages, 6 figure

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

The effect of realistic equations of state and general relativity on the "snowplow" model for pulsar glitches

Many pulsars are observed to "glitch", i.e. show sudden jumps in their rotational frequency $\nu$, some of which can be as large as $\Delta \nu/\nu\approx 10^{-6}-10^{-5}$ in a subset of pulsars known as giant glitchers. Recently Pizzochero (2011) has shown that an analytic model based on realistic values for the pinning forces in the crust and for the angular momentum transfer in the star can describe the average properties of giant glitches, such as the inter-glitch waiting time, the step in frequency and that in frequency derivative. In this paper we extend the model (originally developed in Newtonian gravity and for a polytropic equation of state) to realistic backgrounds obtained by integrating the relativistic equations of stellar structure and using physically motivated equations of state to describe matter in the neutron star. We find that this more detailed treatment still reproduces the main features of giant glitches in the Vela pulsar and allows us to set constraints on the equation of state. In particular we find that stiffer equations of state are favoured and that it is unlikely that the Vela pulsar has a high mass (larger than $M\approx 1.5 M_\odot$).Comment: 15 pages, 8 figures, submitted to MNRA