The blinking statistics of quantum emitters and their corresponding Markov models play an important role in high-resolution microscopy of biological samples as well as in nano-optoelectronics and many other fields of science and engineering. Current methods for analyzing the blinking statistics like the full counting statistics and the Viterbi algorithm break down for low photon rates. We present an evaluation scheme that eliminates the need for both a minimum photon flux and the usual binning of photon events which limits the measurement bandwidth. Our approach is based on higher-order spectra of the measurement record which we model within the recently introduced method of quantum polyspectra from the theory of continuous quantum measurements. By virtue of this approach we can determine on- and off-switching rates of a semiconductor quantum dot at light levels 1000 times lower than in a standard experiment and 20 times lower those than achieved with a scheme from full counting statistics. Thus, a very powerful high-bandwidth approach to the parameter-learning task of single-photon hidden Markov models is established with applications in many fields of science.
The blinking statistics of quantum emitters and their corresponding Markov models play an important role in high-resolution microscopy of biological samples as well as in nano-optoelectronics and many other fields of science and engineering. Current methods for analyzing the blinking statistics like the full counting statistics and the Viterbi algorithm break down for low photon rates. We present an evaluation scheme that eliminates the need for both a minimum photon flux and the usual binning of photon events which limits the measurement bandwidth. Our approach is based on higher-order spectra of the measurement record which we model within the recently introduced method of quantum polyspectra from the theory of continuous quantum measurements. By virtue of this approach we can determine on- and off-switching rates of a semiconductor quantum dot at light levels 1000 times lower than in a standard experiment and 20 times lower those than achieved with a scheme from full counting statistics. Thus, a very powerful high-bandwidth approach to the parameter-learning task of single-photon hidden Markov models is established with applications in many fields of science.
Quantum polyspectra of up to fourth order are introduced for modeling and evaluating quantum transport measurements offering a powerful alternative to methods of the traditional full counting statistics. Experimental time traces of the occupation dynamics of a single quantum dot are evaluated via simultaneously fitting their second-, third-, and fourth-order spectra. The scheme recovers the same electron tunneling and spin relaxation rates as previously obtained from an analysis of the same data in terms of factorial cumulants of the full counting statistics and waiting-time distributions. Moreover, the evaluation of time traces via quantum polyspectra is demonstrated to be feasible also in the weak measurement regime even when quantum jumps can no longer be identified from time traces and methods related to the full counting statistics cease to be applicable. A numerical study of a double dot system shows strongly changing features in the quantum polyspectra for the transition from the weak measurement regime to the Zeno regime where coherent tunneling dynamics is suppressed. Quantum polyspectra thus constitute a general unifying approach to the strong and weak regime of quantum measurements with possible applications in diverse fields as nanoelectronics, circuit quantum electrodynamics, spin noise spectroscopy, or quantum optics.
Abstract Single quantum light emitters are valuable resources for engineered quantum systems. They can function as robust single-photon generators, allow optical control of single spins, provide readout capabilities for atomic-scale sensors, and provide interfaces between stationary and flying qubits. Environmental factors can lead to single emitters exhibiting ‘blinking’, whereby the fluorescence level switches between on and off states. Detailed characterisation of this blinking behaviour including determining the switching rates is often a powerful way to gain understanding about the underlying physical mechanisms. While simple thresholds can be used to identify the on and off intervals and thus extract the rates from the time-series of counts for bright emitters with low background noise, such approaches become difficult for emitters fluorescing at low levels, high noise, or switching at fast rates. We develop a Bayesian approach capable of inferring switching rates directly from the time-series. This is able to deal with high levels of noise and fast switching in fluorescence traces. Moreover, the Bayesian inference also yields a robust picture of the parameter uncertainties, providing a benefit also for bright emitters in low-noise settings. The technique can be adapted to identify the underlying states as well as extracting the rates of switching. Finally, our method is applicable to a broad range of systems that show behaviour analogous to a blinking emitter.
The fundamental understanding of biological pathways requires minimally invasive nanoscopic optical resolution imaging. Many approaches to high-resolution imaging rely on localization of single emitters, such as fluorescent molecules or quantum dots. Additionally, the exact determination of the number of such emitters in an imaging volume is essential for a number of applications; however, in standard intensity-based microscopy it is not possible to determine the number of individual emitters within a diffraction limited spot without initial knowledge of system parameters. Here we explore how quantum measurements of the emitted photons using photon number resolving detectors can be used to address this challenging task. In the proposed new approach, the problem of counting emitters reduces to the task of determining differences between the emitted photon distribution and the Poisson limit. We show that quantum measurements of the number of photons emitted from an ensemble of emitters enable the determination of both the number of emitters and the probability of emission. This method can be applied for any type of single-photon emitters. The scaling laws of this new approach are presented by the Cramer-Rao Lower Bounds, and this technique has great potential in quantum optical imaging with nanoscopic resolution.
The classical optical diffraction limit can be overcome by exploiting the quantum properties of light in several theoretical studies; however, they mostly rely on an entangled light source. Recent experiments have demonstrated that quantum properties are preserved in many fluorophores, which makes it possible to add a new dimension of information for super-resolution fluorescence imaging. Here, we developed a statistical quantum coherence model for fluorescence emitters and proposed a new super-resolution method using fluorescence quantum coherence in fluorescence microscopy. In this study, by exploiting a single-photon avalanche detector (SPAD) array with a time-correlated single-photon-counting technique to perform spatial-temporal photon statistics of fluorescence coherence, the subdiffraction-limited spatial separation of emitters is obtained from the determined coherence. We numerically demonstrate an example of two-photon interference from two common fluorophores using an achievable experimental procedure. Our model provides a bridge between the macroscopic partial coherence theory and the microscopic dephasing and spectral diffusion mechanics of emitters. By fully taking advantage of the spatial-temporal fluctuations of the emitted photons as well as coherence, our quantum-enhanced imaging method has the significant potential to improve the resolution of fluorescence microscopy even when the detected signals are weak.
This thesis intends to familiarize the reader with the concepts of photon statistics and correlations in quantum optics. Developing light sources that emit quantum states is central for the realization of quantum technologies. One important step in characterizing these sources is the measurement of field fluctuations and correlations, by coincidence measurements. The expectation value of a coincidence measurement, a simultaneous measurement of two intensities (or, more general, four fields), is represented by the fourth-order correlation function. The value of the correlation function, at zero delay between the detection of two photons, reveals important properties of the state to which they belonged, for example the fluctuations of the photon number. Since predictability is important for many applications, light sources emitting single photons are also characterized by the indistinguishability of consecutively emitted photons, or of two photons from separate emitters. In paper I we investigate blinking behaviour in quantum emitters, and its effect on the interference pattern and photon statistics with photons from two separate emitters. Blinking refers to an emitters transition into a non-emitting state, and subsequent transition back to an emitting state. We show that blinking can not be treated as linear loss, when measuring the fourth-order correlation function for two emitters in a Hong-Ou-Mandel setup. In general, a measurement of the fourth-order correlation function is robust to loss, which makes it a very practical tool. However, the relation between recorded coincidence counts and the correlation function is only direct in the limit of zero detection efficiency, and depends on the detection system. In paper II, we show that by adding a variable attenuation in the beam path, we can trace back to the ''true'' value of the correlation function at zero quantum efficiency. This method improves accuracy in correlation measurements by decreasing a systematic error at the expense of an increased statistical error, which is easier to handle, extending the use of coincidence methods to classical and non-classical multi-photon states.
Random-time sampling of a quantum system is introduced as a new approach to continuous quantum measurements with prospects for ultra-low-perturbation measurements. Random sampling is, e.g., naturally realized in an optical spin noise experiment when weak probe-laser light exhibits random single-photon events in the detector. We show that a direct evaluation of these detector time-traces yields power spectra that are equivalent to those of the usual continuous measurement regime. Surprisingly, this holds true even for average sampling rates much lower than the typical frequency range of the measured quantum dynamics. The third-order quantum polyspectrum (bispectrum) also contains the same information as its continuous counterpart. Many applications of random-time sampling are envisioned for high-resolution spectroscopy, circuit quantum electrodynamics, quantum sensing, and quantum measurements in general.