Quantum-jumps and photon-statistic in fluorescent systems coupled to classically fluctuating reservoirs

A double quantum dot coupled to an optical cavity is a prototypical example of a non-trivial open quantum system. Recent experimental and theoretical studies show that this system is a candidate for single-photon detection in the microwave domain. This motivates studies that go beyond just the average current, and also take into account the full counting statistics of photon and electron detections. With this in mind, here we provide a detailed analysis of the waiting time st...

We derive an extension to the quantum regression theorem which facilitates the calculation of two-time correlation functions and emission spectra for systems undergoing non-Markovian evolution. The derivation exploits projection operator techniques, with which we obtain explicit equations of motion for the correlation functions, making only a second order expansion in the system--environment coupling strength, and invoking the Born approximation at a fixed initial time. The r...

Fundamental properties of light unavoidably impose features on images collected using fluorescence microscopes. Modeling these features is ever more important in quantitatively interpreting microscopy images collected at scales on par or smaller than light's wavelength. Here we review the optics responsible for generating fluorescent images, fluorophore properties, microscopy modalities leveraging properties of both light and fluorophores, in addition to the necessarily proba...

We investigate the continuous quantum measurement of a superconducting qubit undergoing fluorescence. The fluorescence of the qubit is detected via a phase-preserving heterodyne measurement, giving the fluorescence quadrature signals as two continuous qubit readout results. By using the stochastic path integral approach to the measurement physics, we derive most likely paths between boundary conditions on the state, and compute approximate time correlation functions between a...

In this paper, one of the major shortcomings of the conventional numerical approaches is alleviated by introducing the probabilistic nature of molecular transitions into the framework of classical computational electrodynamics. The main aim is to develop a numerical method, which is capable of capturing the statistical attributes caused by the interactions between a group of spontaneous as well as stimulated emitters and the surrounding electromagnetic field. The electromagne...

Based on the system-reservoir description we propose a simple solvable microscopic model for a nonequilibrium bath. This captures the essential features of a nonstationary quantum Markov process. We establish an appropriate generalization of the fluctuation-dissipation relation pertaining to this process and explore the essential modifications of the Bloch equations to reveal the nonexponential decay of the Bloch vector components and transient spectral broadening in resonanc...

In order to discern aggregation in solutions, we present a quantum mechanical analog of the photon statistics from fluorescent molecules diffusing through a focused beam. A generating functional is developed to fully describe the experimental physical system as well as the statistics. Histograms of the measured time delay between photon counts are fit by an analytical solution describing the static as well as diffusing regimes. To determine empirical fitting parameters, fluor...

Small quantum systems can now be continuously monitored experimentally which allows for the reconstruction of quantum trajectories. A peculiar feature of these trajectories is the emergence of jumps between the eigenstates of the observable which is measured. Using the Stochastic Master Equation (SME) formalism for continuous quantum measurements, we show that the density matrix of a system indeed shows a jumpy behavior when it is subjected to a tight measurement (even if the...

Using a real-time path integral approach we develop an algorithm to calculate multi-time correlation functions of open few-level quantum systems that is applicable to highly nonequilibrium dynamics. The calculational scheme fully keeps the non-Markovian memory introduced by the pure-dephasing type coupling to a continuum of oscillators. Furthermore, we discuss how to deal consistently with the simultaneous presence of non-Markovian and Markovian system reservoir interactions....

We describe a method to probe the spectral fluctuations of a transition over broad ranges of frequencies and timescales with the high spectral resolution of Fourier spectroscopy, and a temporal resolution as high as the excited state lifetime, even in the limit of very low photocounting rates. The method derives from a simple relation between the fluorescence spectral dynamics of a single radiating dipole and its fluorescence intensity correlations at the outputs of a continu...