We revisit Mandel's notion that the degree of coherence equals the degree of indistinguishability by performing Hong-Ou-Mandel- (HOM-)type interferometry with single photons elastically scattered by a cw resonantly driven excitonic transition of an InAs/GaAs epitaxial quantum dot. We present a comprehensive study of the temporal profile of the photon coalescence phenomenon which shows that photon indistinguishability can be tuned by the excitation laser source, in the same way as their coherence time. A new figure of merit, the coalescence time window, is introduced to quantify the delay below which two photons are indistinguishable. This criterion sheds new light on the interpretation of HOM experiments under cw excitation, particularly when photon coherence times are longer than the temporal resolution of the detectors. The photon indistinguishability is extended over unprecedented time scales beyond the detectors' response time, thus opening new perspectives to conducting quantum optics with single photons and conventional detectors.
We revisit Mandel's notion that the degree of coherence equals the degree of indistinguishability by performing Hong-Ou-Mandel- (HOM-)type interferometry with single photons elastically scattered by a cw resonantly driven excitonic transition of an InAs/GaAs epitaxial quantum dot. We present a comprehensive study of the temporal profile of the photon coalescence phenomenon which shows that photon indistinguishability can be tuned by the excitation laser source, in the same way as their coherence time. A new figure of merit, the coalescence time window, is introduced to quantify the delay below which two photons are indistinguishable. This criterion sheds new light on the interpretation of HOM experiments under cw excitation, particularly when photon coherence times are longer than the temporal resolution of the detectors. The photon indistinguishability is extended over unprecedented time scales beyond the detectors' response time, thus opening new perspectives to conducting quantum optics with single photons and conventional detectors.
We revisit Mandel's notion that the degree of coherence equals the degree of indistinguishability by performing Hong-Ou-Mandel-(HOM-)type interferometry with single photons elastically scattered by a cw resonantly driven excitonic transition of an InAs/GaAs epitaxial quantum dot. We present a comprehensive study of the temporal profile of the photon coalescence phenomenon which shows that photon indistinguishability can be tuned by the excitation laser source, in the same way as their coherence time. A new figure of merit, the coa-lescence time window, is introduced to quantify the delay below which two photons are indistinguishable. This criterion sheds new light on the interpretation of HOM experiments under cw excitation, particularly when pho-ton coherence times are longer than the temporal resolution of the detectors. The photon indistinguishability is extended over unprecedented time scales beyond the detectors' response time, thus opening new perspectives to conducting quantum optics with single photons and conventional detectors. Indistinguishable photons are one of the keys for the implementation of scalable quantum information systems [1, 2]. Indistinguishability is investigated using the coalescence phenomenon: two photons with similar spectral, spatial and polarization properties will bunch when arriving simultaneously on two opposite sides of a beam splitter. One of the pioneers of photon coalescence, Mandel, stated in 1991 that the degree of coherence equals the degree of indistinguishability [3, 4] by investigating theoretically the interference of two light sources, thus underlining the fundamental link of the wave-particle duality of light. In a two-photon interference Hong-Ou-Mandel (HOM) experiment [5], the photons from two sources are combined at the two inputs of a beam splitter and the coalescence will be detected through a drop of the coincidence rate at the outputs—the HOM dip. Under pulsed excitation, perfect temporal matching between the arrival times of the photons at the beam splitter will allow for the observation of the HOM dip. When working with a two-level system, its coherence time T 2 and its lifetime T 1 are tightly linked to the photon indistin-guishability. For example, perfect coalescence giving rise to a zero value in the HOM dip is observed only if the radiative limit T 2 = 2T 1 is reached. The figure of merit under pulsed excitation is thus given by the ratio T 2 /2T 1 which constitutes a fundamental limit to the coalescence efficiency [6]. Under continuous wave (cw) excitation, with two ideal ultrafast detectors , the coincidence rate always vanishes at zero time delay , even for deviations in the properties of the photons [7]. In the case of real detectors, the indistinguishability is thus properly resolved only if the temporal resolution of the detectors T R is shorter than the coherence time of the photons [8]. If T R ∼ T 1 , T 2 , the HOM dip is strongly affected and will disappear completely in the limit of very slow detectors. With a cw source, the value at zero delay of the coincidence rate is thus very sensitive to T R and does not accurately characterize the intrinsic properties of the source with regard to photon indis-tinguishability. A new figure of merit has to be considered. Single semiconductor quantum dots (QD) [9], along with other systems under extensive study including atoms [7, 10], molecules [11–13], trapped ions [14, 15], and colored centers in diamond [16], are promising candidates for sources of single indistinguishable photons. In the case of semiconductor QDs, photon indistinguishability is either limited by the QD dynamics under pulsed excitation [6], or by the detec-tors' temporal resolution under cw excitation [17, 18]. Recent experimental studies focused on the regime of resonant Rayleigh scattering (RRS) under low power cw excitation, where the incoming photons are elastically scattered. This is a well-known phenomenon described by the two-level system resonance fluorescence theory [23], which has been observed with QDs [24–28]. As predicted by theory and shown by ho-modyne and heterodyne detection experiments [26–28], the scattered photons inherit the coherence time of the excitation laser T L , which can be much longer than T 2 and T R , while still exhibiting sub-Poissonian statistics [24, 25]. The resulting QD emission spectrum can then be much narrower than the natural linewidth imposed by the radiative limit, even if the percentage of elastically scattered photons remains limited to T 2 /2T 1 [Fig. 1(b)]. Considering that under such conditions the inherited coherence time surpasses T R , along with Man-del's notion that coherence equals indistinguishability [3], the RRS regime constitutes the ideal ground for the generation of highly indistinguishable photons.
Abstract We report a set of experiments designed to test the quantum indistinguishability of single photons emitted by a resonantly pumped InAs/GaAs quantum dot, embedded in a microcavity. We first performed high resolution interferometric measurements on the source to infer its coherence time. By comparison with the exciton lifetime, obtained by time‐resolved spectroscopy, we found that some quantum dots were emitting almost transform‐limited photons. The measured ratio of the coherence time to the pulse duration gives a lower bound on the dephasing time which agrees well with previous studies. We then directly measured the mean overlap between wave packets of consecutive photons emitted 2 ns apart, through a Hong–Ou–Mandel type two‐photon interference experiment. For the best dot, an overlap as high as 0.81 was inferred. This result suggests that quantum dots could be a practical single photon source to perform quantum information processing experiments. We stress the importance of the microcavity for identical photon generation.
To characterize the statistics and indistinguishability of a source, it is common to measure the correlation functions of the emitted field using various interferometers. Here, we present a theoretical framework for the computation of the correlation functions of a two-level system that is resonantly driven by a realistic noisy cw excitation laser. Analytic expressions of the first- and second-order autocorrelation functions are obtained where the various contributions of the noisy excitation source are correctly taken into account. We predict that, even in the low power regime, the noise source has a strong influence on the two-level system dynamics, which is not anticipated by simpler models. The characterization of photon indistinguishability in the pulsed excitation regime is usually done by measuring the value of the zero-delay intensity correlation obtained with a Hong-Ou-Mandel interferometer. We show that this figure is irrelevant in the cw excitation regime and we introduce the coalescence time window, a figure of merit based on a probabilistic interpretation of the notion of photon indistinguishability. We finally use the coalescence time window to quantify how noisy cw excitation influences photon indistinguishability.
We report on two-photon interference of highly indistinguishable single photons emitted by a quantum dot. Strictly resonant excitation with picosecond laser pulses has been used to prepare coherent states with a significantly increased coherence time $({T}_{2}\ensuremath{\sim}1\text{ns})$ and reduced lifetime $({T}_{1}\ensuremath{\sim}650\text{ps})$, as compared to a nonresonant excitation scheme. Indistinguishable photons, with visibilities greater than 70%, have been observed by measuring the Hong-Ou-Mandel dip without postselection of the interfering photons. Near-unity indistinguishable photons should be achievable by preventing fluctuations in the electrostatic environment in the vicinity of the dots, considered as an important source of decoherence.
In the fields of quantum communications and quantum computing, the transmission of information using single photons guarantees the security of the communication and enables calculations that would be impossible with our "classical" computers. One of the key elements in implementing such protocols is the photon source. It must emit, on demand, one and only one photon with specific quantum properties.The aim of this project is to characterise a source of single and indistinguishable photons, designed and manufactured at CEA-Grenoble, and consisting of an indium arsenide (InAs) semiconductor quantum dot integrated into a gallium arsenide (GaAs) nanocavity. With its low quality factor, the nanocavity enables photons to be extracted efficiently over a wide range of wavelengths (30nm). In addition, thanks to its small mode volume, the spontaneous emission of quantum dots within it can be accelerated by Purcell effect (Purcell factor up to 6).In this manuscript, we first detail the implementation and the optimisation of the experimental setups used to characterise the photons emitted by our sample : microphotoluminescence, radiative lifetime measurement, Hanbury-Brown and Twiss (HBT) experiment and Hong-Ou-Mandel (HOM) experiment. Then, we present the experimental results obtained for photons emitted by two distinct quantum dots : One containing neutral exciton states, and the second, containing a charged exciton state. In order to photo-create these exciton states in the quantum dots, two pulsed optical excitation schemes were implemented: the two-photon resonant excitation of the neutral biexciton, and the phonon-assisted quasi-resonant excitation of the neutral and charged excitons. We present the measurement of the three figures of merit of a single photon source for these two quantum dots : the brightness, the single-photon purity and the indistinguishability of the emitted photons. In a second phase, we will focus on the charged exciton state and measure the profile of its emission line and its autocorrelation function under continuous resonant excitation. These results, achieved within the nano-photonics group of the University of Basel, constitute the first demonstration of continuous excitation on these nanostructures, which is a good surprise given their small size.Finally, we will look at the effects of the application of mechanical stress on the energy separation of the two neutral exciton states, known as the "fine structure splitting" (FSS). During the radiative cascade of the neutral biexciton state, the two photons emitted are entangled in polarisation, and the fidelity of the entanglement depends in particular on the FSS. Here, we will consider a second sample, where the InAs quantum dots are embedded in a GaAs photonic nanowire. By bending the nanowire, mechanical stresses are applied to the quantum dots, which will modify the energy of the exciton states. We will present an experimental study aimed at observing a possible effect on the fine structure splitting.In conclusion, we have developed and optimised various experimental setups for characterising photon sources for applications in the fields of quantum communications and quantum computing. For a first version of these photonic nanostructures, the brightness, the single-photon purity and the indistinguishability of the photons emitted by our quantum dots integrated into nanocavities are very encouraging for the future. The next objectives are to improve the nanocavities and to characterise the decoherence phenomena and the mechanical coupling between the quantum dots and these nanostructures.
Single photons produced by fundamentally dissimilar physical processes will in general not be indistinguishable. We show how photons produced from a quantum dot and by parametric down-conversion in a nonlinear crystal can be manipulated to be indistinguishable. The measured two-photon coalescence probability is 16%, and is limited by quantum-dot decoherence. Temporal filtering to the quantum-dot coherence time and accounting for detector time response increases this to 61% while retaining 25% of the events. This technique can connect different elements in a scalable quantum network.