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

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.

Effect of frequency mismatched photons in quantum information processing

Many promising schemes for quantum information processing (QIP) rely on few-photon interference effects. In these proposals, the photons are treated as being indistinguishable particles. However, single photon sources are typically subject to variation from device to device. Thus the photons emitted from different sources will not be perfectly identical, and there will be some variation in their frequencies. Here, we analyse the effect of this frequency mismatch on QIP schemes. As examples, we consider the distributed QIP protocol proposed by Barrett and Kok, and Hong-Ou-Mandel interference which lies at the heart of many linear optical schemes for quantum computing. In the distributed QIP protocol, we find that the fidelity of entangled qubit states depends crucially on the time resolution of single photon detectors. In particular, there is no reduction in the fidelity when an ideal detector model is assumed, while reduced fidelities may be encountered when using realistic detectors with a finite response time. We obtain similar results in the case of Hong-Ou-Mandel interference -- with perfect detectors, a modified version of quantum interference is seen, and the visibility of the interference pattern is reduced as the detector time resolution is reduced. Our findings indicate that problems due to frequency mismatch can be overcome, provided sufficiently fast detectors are available.Comment: 14 pages, 8 figures. Comments welcome. v2: Minor changes. v3: Cleaned up 3 formatting error

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

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

The Impact of HI in Galaxies on 21-cm Intensity Fluctuations During the Reionisation Epoch

We investigate the impact of neutral hydrogen (HI) in galaxies on the statistics of 21-cm fluctuations using analytic and semi-numerical modelling. Following the reionisation of hydrogen the HI content of the Universe is dominated by damped absorption systems (DLAs), with a cosmic density in HI that is observed to be constant at a level equal to ~2% of the cosmic baryon density from z~1 to z~5. We show that extrapolation of this constant fraction into the reionisation epoch results in a reduction of 10-20% in the amplitude of 21-cm fluctuations over a range of spatial scales. The assumption of a different percentage during the reionisation era results in a proportional change in the 21-cm fluctuation amplitude. We find that consideration of HI in galaxies/DLAs reduces the prominence of the HII region induced shoulder in the 21-cm power spectrum (PS), and hence modifies the scale dependence of 21-cm fluctuations. We also estimate the 21cm-galaxy cross PS, and show that the cross PS changes sign on scales corresponding to the HII regions. From consideration of the sensitivity for forthcoming low-frequency arrays we find that the effects of HI in galaxies/DLAs on the statistics of 21-cm fluctuations will be significant with respect to the precision of a PS or cross PS measurement. In addition, since overdense regions are reionised first we demonstrate that the cross-correlation between galaxies and 21-cm emission changes sign at the end of the reionisation era, providing an alternative avenue to pinpoint the end of reionisation. The sum of our analysis indicates that the HI content of the galaxies that reionise the universe will need to be considered in detailed modelling of the 21-cm intensity PS in order to correctly interpret measurements from forthcoming low-frequency arrays.Comment: 11 pages, 6 figures. Submitted to MNRA