Second-order Correlation Function Research Articles

(Invited) Correlation Measurements for Carbon Nanotubes with Quantum Defects

Single-photon sources are one of the essential building blocks for the development of photonic quantum technology. In terms of potential practical application, an on-demand electrically driven quantum-light emitter on a chip is notably crucial for integrating photonic integrated circuits. Here, we propose functionalized single-walled carbon nanotube field-effect transistors as a promising solid-state quantum-light source by demonstrating photon antibunching behavior via electrical excitation. The sp3 quantum defects were formed on the surface of (7, 5) carbon nanotubes by 3,5-dichlorophenyl functionalization, and individual carbon nanotubes were wired to graphene electrode pairs. Filtered electroluminescent defect-state emission at 77 K was coupled into a Hanbury Brown and Twiss experiment setup, and single-photon emission was observed by performing second-order correlation function measurements. We discuss the dependence of the intensity correlation measurement on excitation power and emission wavelength highlighting the challenges of performing such measurements while simultaneously analyzing acquired data. Our results indicate a route toward room-temperature electrically-triggered single-photon emission.

Advanced analysis of single-molecule spectroscopic data

We present Full SMS, a multipurpose graphical user interface (GUI)-based software package for analyzing single-molecule spectroscopy (SMS) data. SMS typically delivers multiparameter data—such as fluorescence brightness, lifetime, and spectra—of molecular- or nanometer-scale particles such as single dye molecules, quantum dots, or fluorescently labeled biological macromolecules. Full SMS allows an unbiased statistical analysis of fluorescence brightness through level resolution and clustering, analysis of fluorescence lifetimes through decay fitting, as well as the calculation of second-order correlation functions and the display of fluorescence spectra and raster-scan images. Additional features include extensive data filtering options, a custom HDF5-based file format, and flexible data export options. The software is open source and written in Python but GUI based so it may be used without any programming knowledge. A multiprocess architecture was employed for computational efficiency. The software is also designed to be easily extendable to include additional import data types and analysis capabilities.

Realization of nonreciprocal photon statistics by manipulating the quantum nonlinearity of cold atoms in an asymmetric cavity

In a strongly coupled cavity quantum electrodynamics (QED) system, the second-order correlation function g(2)(τ) of the transmitted probe light from the cavity is determined by the nonlinearity of the atom in the cavity. Therefore, the system provides a platform for controlling the photon statistics by manipulating nonlinearity. In this paper, we experimentally demonstrate nonreciprocal quantum statistics in a cavity QED system with several atoms strongly coupled to an asymmetric optical cavity, which is composed of two mirrors with different transmittivities. When the direction of the probe light is reversed, the intracavity light field alternates to a different level. Distinct photon statistics are then observed due to the quantum nonlinearity associated with strongly coupled atoms. Sub-Poissonian photon-number statistics for forward light and a Poissonian distribution for backward light are then realized. Our work provides an effective approach for realizing nonreciprocal quantum devices, which have potential applications in the unidirectional generation of nonclassical light fields and quantum sensing.

Estimation of photon number distribution and derivative characteristics of photon-pair sources

The evaluation of a photon-pair source employs characteristic metrics like the photon-pair generation rate, heralding efficiency, and second-order correlation function, all of which are determined by the photon number distribution of the source. The photon number distribution, however, can be altered due to spectral or spatial filtering and optical losses, leading to changes in the above characteristics. This paper theoretically describes the effects of different filterings, losses, and noise counts on the photon number distribution and related characteristics. From the theoretical description, an analytic expression for the effective mode number of the joint spectral density is also derived. Compared with previous methods for estimating the photon number distribution and characteristics, an improved methodology is introduced along with a suitable metric of accuracy for estimating the photon number distribution, focusing on photon-pair sources. We discuss the accuracy of the calculated characteristics from the estimated (or reconstructed) photon number distribution through repeated simulations and bootstrapped experimental data.

Phase retrieval in incoherent diffractive imaging using higher-order photon correlation functions

To obtain spatial information about an arbitrary atomic distribution in x-ray structure analysis, e.g. in molecules or proteins, the standard method is to measure the intensity in the far field, i.e. the first-order photon correlation function of the coherently scattered x-ray photons (coherent diffractive imaging). Recently, it was suggested to record alternatively the incoherently scattered photons and measure the second-order photon correlation function to reconstruct the geometry of the unknown atomic distribution (incoherent diffractive imaging). Yet, besides various advantages of the latter method, both techniques suffer from the so-called phase retrieval problem. Lately, an ab-initio phase retrieval algorithm to reconstruct the phase of the so-called structure factor of the scattering objects based on the third-order photon correlation function was reported. The algorithm makes use of the closure phase, which contains important, yet incomplete phase information, well-known from triple correlations and their bispectrum in speckle masking and astronomy applications. Here, we provide a detailed analysis of the underlying scheme and quantities in the context of x-ray structure analysis. In particular, we explicitly calculate for the first time the third-order photon correlation function for single photon emitters in a full quantum mechanical treatment and discuss the uniqueness of the closure phase equations constructed from. In this context, we recapitulate the sign problem of the closure phase and how it can be lifted using redundant information. We further show how the algorithm can be improved using even higher-order photon correlation functions produced by single photon emitters, e.g. the fourth-order correlation function, delivering new phase relations appearing in the four-point correlations.

Observation of amplitude squeezing in a constant-current-driven distributed feedback quantum dot laser with optical feedback

We illustrate the generation of single-mode amplitude squeezing in a distributed feedback quantum dot laser driven by a constant-current pump. Achieving broadband amplitude squeezing of 1.7 dB over a 10 GHz range at room temperature is realized by suppressing carrier noise and implementing optical feedback. The noise-corrected squeezing level reached 5.1 dB. Furthermore, the examination of the zero-delay second-order correlation function demonstrates the robust feedback stability of the amplitude-squeezed state in the quantum dot laser compared to a reference quantum well laser. This investigation lays the groundwork for future advancements in integrated optical quantum chips.

Multimode heralded single photons based on the DLCZ.

High-quality single-photon sources are crucial for the development of simple quantum devices. Quantum communication stands at the forefront of cutting-edge technologies, promising unprecedented levels of security and efficiency. A cornerstone of this revolutionary field is the development of high-speed single-photon sources, which play a pivotal role in quantum key distribution and other quantum communication protocols. In this context, the concept of space multimode emerges as a promising avenue to propel the capabilities of single-photon sources to new heights. We have spatial multiplexing technology to develop single-photon sources that deliver high-speed heralded single photons in the Duan-Lukin-Cirac-Zoller (DLCZ) scheme. We propose a spatial multiplexing single-photon source scheme based on the DLCZ. Compared to a single spatial mode, by adding six spatial modes through spatial multiplexing, the single-photon generation rate increases 4.3 times. And the second-order correlation function of single photons is less than 0.5. We show that expanding the spatial degrees of freedom of the quantum storage scheme based on DLCZ does not affect the single-photon properties. The generation rate of the single photon can be significantly increased through spatial multiplexing with a feedback circuit. Our approach offers a promising path to creating a high-speed photon source based on a spatial multimode scheme.

Correlation Measurements for Carbon Nanotubes with Quantum Defects.

Single-photon sources are essential building blocks for the development of photonic quantum technology. Regarding potential practical application, an on-demand electrically driven quantum-light emitter on a chip is notably crucial for photonic integrated circuits. Here, we propose functionalized single-walled carbon nanotube field-effect transistors as a promising solid-state quantum-light source by demonstrating photon antibunching behavior via electrical excitation. The sp3 quantum defects were formed on the surface of (7, 5) carbon nanotubes by 3,5-dichlorophenyl functionalization, and individual carbon nanotubes were wired to graphene electrode pairs. Filtered electroluminescent defect-state emission at 77 K was coupled into a Hanbury Brown and Twiss experiment setup, and single-photon emission was observed by performing second-order correlation function measurements. We discuss the dependence of the intensity correlation measurement on electrical power and emission wavelength, highlighting the challenges of performing such measurements while simultaneously analyzing acquired data. Our results indicate a route toward room-temperature electrically triggered single-photon emission.

Adopting molecular tagging velocimetry for high-resolution measurements of oscillating grid turbulence

AbstractSingle-component molecular tagging velocimetry (1c-MTV) experiments are conducted in an oscillating grid turbulence facility to systematically clarify the trade-offs between maximizing measurement dynamic range and minimizing measurement uncertainty. The primary aim is to obtain reliable turbulence data with the maximum possible vector resolution ($$\varDelta {x}_{1}$$ Δ x 1 ). Four optical magnifications ($$M{_{0}}$$ M 0 =0.11, 0.22, 0.45, 1.11) with four interframe time delay ($$\varDelta {t}$$ Δ t ) values, for each optical magnification case, ranging from 3 to 10 ms, are investigated. The grid oscillates with a frequency (f) of 3.2 and 4.1 Hz, and a single fixed stroke length (S) of 55 mm. The measurement quality is quantified using three important turbulence descriptors — the second-order transverse velocity correlation function $$(\langle {g(r)}\rangle )$$ ( ⟨ g ( r ) ⟩ ) , the second-order transverse velocity structure function $$([\Delta {_{g}u}]^2)$$ ( [ Δ g u ] 2 ) , and the turbulence energy dissipation rate ($$\langle \epsilon \rangle$$ ⟨ ϵ ⟩ ). Other descriptors such as the longitudinal integral length scale (l) and the longitudinal Taylor microscale ($${\lambda }$$ λ ) are also used to compare with reference values reported in literature. The degree of agreement with the reference values from literature, and insensitivity of the descriptor estimates to different MTV design parameters are used to determine the most robust means of obtaining high-resolution turbulence data from 1c-MTV. The experimental design parameters are contextualized using the Kolmogorov length ($${\eta }$$ η ), time ($${\tau _{\eta }}$$ τ η ), and velocity ($${u_{\eta }}$$ u η ) scales that are based on the most reliable $$\langle {\epsilon }\rangle$$ ⟨ ϵ ⟩ estimates from the current experiments. The pixel-displacement corresponding to $${u_{\eta }}$$ u η $$({\varDelta {x}{_{2}}{_{\eta }}})$$ ( Δ x 2 η ) describes the interdependencies between $${M_{0}}$$ M 0 and $$\varDelta {t}$$ Δ t . The data set with $${M_{0}}=0.45$$ M 0 = 0.45 ($${\eta =}18{\varDelta {x}_{1}}$$ η = 18 Δ x 1 for f=3.2 Hz, and $${\eta =}13{\varDelta {x}_{1}}$$ η = 13 Δ x 1 for f=4.1 Hz) represents the most reliable and the highest resolution case. This conclusion was deduced by taking the performance of all the turbulence descriptors into account. As far as the interframe time delay is concerned, $$\varDelta {t} \ge$$ Δ t ≥ 4 ms ($${\varDelta {x}{_{2}}{_{\eta }}}\ge 0.5 \text {pixels}$$ Δ x 2 η ≥ 0.5 pixels ) works well for all $${{M}_{0}}$$ M 0 . To the authors’ knowledge, the present study documents the first instance of a series of 1c-MTV experiments conducted for a systematic clarification of the nature of balancing the available dynamic range and the measurement uncertainty. Additionally, since the study involves turbulent flow with negligible mean-flow, it serves as an adequate representation of 1c-MTV performance in a three-dimensional flow.

Properties of new even and odd nonlinear coherent states with different parameters

We construct a class of nonlinear coherent states (NLCSs) by introducing a more general nonlinear function and study their nonclassical properties, specifically the second-order correlation function [Formula: see text], Mandel parameter Q, squeezing, amplitude-squared squeezing and Wigner function of the optical field. The results indicate that the nonclassical properties of the new types of even and odd NLCSs crucially depend on the nonlinear functions. More concretely, we find that the new even NLCSs could exhibit the photon-bunching effect, whereas the new odd NLCSs could show the photon-antibunching effect. The degree of squeezing is also significantly affected by the parameter selection of these NLCSs. By employing various forms of nonlinear functions, it becomes possible to construct the NLCSs with diverse properties, thereby providing a theoretical foundation for the corresponding experimental investigations.

Enhanced magnon blockade in a magnomechanical system

Magnon blockade is one of the effective methods for realizing single magnon sources which have great potential application in quantum information processing and quantum computing. To enhance single-magnon blockade effect, we introduce a two-magnon driving to the magnomechanical system, which is used to form the multipath destructive interference. Our result shows that both the conventional magnon blockade (CMB) and unconventional magnon blockade (UMB) can be achieved due to nonlinear term of the magnon-mechanical oscillator and magnetic parametric amplification term(MPA) induced by two-magnon driving. By setting certain parameters of MPA, we combine the effect of CMB and UMB. As a result, the single-magnon blockade effect is enhanced, and the disadvantage of rapid oscillations of the time-delay second-order correlation function g (2)(τ) with UMB is overcome, which makes high time resolution not necessary in the detection of second-order correlation function.

Topological bias: how haloes trace structural patterns in the cosmic web

ABSTRACT We trace the connectivity of the cosmic web as defined by haloes in the Planck-Millennium simulation using a persistence and Betti curve analysis. We normalize clustering up to the second-order correlation function and use our systematic topological analysis to correlate local information and properties of haloes with their multiscale geometrical environment of the cosmic web (elongated filamentary bridges and sheetlike walls). We capture the multiscale topology traced by the halo distribution through filtrations of the corresponding Delaunay tessellation. The resulting nested alpha shapes are sensitive to the local density, perfectly outline the local geometry, and contain the complete information on the multiscale topology. We find a remarkable linear relationship between halo masses and topology: haloes of different mass trace environments with different topological signature. This is a topological bias, an environmental structure bias independent of the halo clustering bias associated with the two-point correlation function. This mass-dependent linear scaling relation allows us to take clustering into account and determine the overall connectivity from a limited sample of galaxies. The presence of topological bias has major implications for the study of voids and filaments in the observed distribution of galaxies. The (infra)structure and shape of these key cosmic web components will strongly depend on the underlying galaxy sample. Their use as cosmological probes, with their properties influenced by cosmological parameters, will have to account for the subtleties of topological bias. This is of particular relevance with the large upcoming galaxy surveys such as DESI, Euclid, and the Vera Rubin telescope surveys.

Improving the Resolution of Correlation Imaging via the Fluctuation Characteristics

The resolution is an important factor in evaluating image quality. In general, the resolution of correlation imaging is taken to the full width at half maximum (FWHM) of the point spread function (PSF) produced by the second-order correlation function. In this paper, we show that the resolution of correlation imaging can be improved by the fluctuation characteristic of the second-order correlation function. It is demonstrated both experimentally and theoretically that the resolution of the system can be drastically improved. We also prove that the FWHM of the PSF can be narrowed by 2n by extracting the n-order fluctuation information of the second-order correlation function.

Nonclassicality in a dispersive atom–cavity field interaction in the presence of an external driving field

We investigate nonclassical properties of a state generated by the interaction of a three-level atom with a quantized cavity field and an external classical driving field. In this study, the fields being degenerate in frequency are highly detuned from the atom. The atom interacts with the quantized field in a dispersive manner. The experimental setup involves a three-level atom passing through a cavity and interacting dispersively with the cavity field mode. Simultaneously, the atom interacts with an external classical field that is in resonance with the cavity field. The three-level atom can enter the cavity in one of the bare states [Formula: see text], [Formula: see text] or [Formula: see text] or in a superposition of two of these states. In this paper, we consider superposition of [Formula: see text] and [Formula: see text]. In our analysis, we focus on the statistical properties of the cavity field after interacting with the atom. The state vector [Formula: see text] describes the entire atom–field system but we analyze the properties of the cavity field independently neglecting the atomic component of the system. For this the atom part is traced out from [Formula: see text] to acquire the cavity field state only, denoted by [Formula: see text]. We evaluate different nonclassical measures including photon number distribution, Mandel’s [Formula: see text] parameter, squeezing properties [Formula: see text] and [Formula: see text], Wigner distribution, [Formula: see text] function, second-order correlation function [Formula: see text], etc. for the obtained cavity field state.

Generation and characterization of polarization-entangled states using quantum dot single-photon sources

Single-photon sources based on semiconductor quantum dots find several applications in quantum information processing due to their high single-photon indistinguishability, on-demand generation, and low multiphoton emission. In this context, the generation of entangled photons represents a challenging task with a possible solution relying on the interference in probabilistic gates of identical photons emitted at different pulses from the same source. In this work, we implement this approach via a simple and compact design that generates entangled photon pairs in the polarization degree of freedom. We operate the proposed platform with single photons produced through two different pumping schemes, the resonant excited one and the longitudinal-acoustic phonon-assisted configuration. We then characterize the produced entangled two-photon states by developing a complete model taking into account relevant experimental parameters, such as the second-order correlation function, Hong–Ou–Mandel visibility, multiphoton emission and pump laser filtering. Our source shows long-term stability and high quality of the generated entangled states, thus constituting a reliable building block for optical quantum technologies.

Allotropic Ga2Se3/GaSe nanostructures grown by van der Waals epitaxy: narrow exciton lines and single-photon emission.

The ability to emit narrow exciton lines, preferably with a clearly defined polarization, is one of the key conditions for the use of nanostructures based on III-VI monochalcogenides and other layered crystals in quantum technology to create non-classical light. Currently, the main method of their formation is exfoliation followed by strain and defect engineering. A factor limiting the use of epitaxy is the presence of different phases in the grown films. In this work, we show that control over their formation makes it possible to create structures with the desired properties. We propose Ga2Se3/GaSe nanostructures grown by van der Waals epitaxy with a high VI/III flux ratio as a source of narrow exciton lines. Actually, these nanostructures are a combination of allotropes: GaSe and Ga2Se3, consisting of the same atoms in different arrangements. The energy positions of the narrow lines are determined by the quantum confinement in Ga2Se3 inclusions of different sizes in the GaSe matrix, similar to quantum dots, and their linear polarization is due to the ordering of Ga vacancies in a certain crystalline direction in Ga2Se3. Such nanostructures exhibit single-photon emission with second-order correlation function g(2)(0) ∼ 0.10 at 10 K that makes them promising for quantum technologies.

General Theory of Quantum Holography Based on Two Photon Interference

As a kind of quantum phenomenon, Hong-Ou-Mandel (HOM) interference is more robust against phase noise. Due to this feature, robust quantum holography emerges, through which wave function of interested photon can be retrieved according to HOM interference pattern. For better understanding and developing this method, we derive a theoretical framework of robust HOM holography. In quantum holography scheme, test state and reference state interfere at beam splitter (BS). Then, degree of freedom (DOF) resolved detections (such as spatial resolved detection, temporal resolved detection or spectrum resolved detection) are applied at the BS output ports, respectively. Based on the single photon detection results, the DOF resolved coincidence counts are postselected, producing interference patterns. The information of the test states is retrieved from the patterns. According to different test states and reference states, four combinations are analysed, including measuring the wave function of single photon state using standard single photon state or coherent state and measuring the wave function of coherent state using standard single photon state or coherent state. In all cases, information of the test states is reflected in normalized second-order correlation function or interference patterns in similar forms. Specially, the wave function of test states can be directly retrieved from the interference patterns, with no complex algorithm required. Besides, phase noise from environment has no influence on this kind quantum holography. Comparison between traditional holography and quantum holography is analysed.

Photostability of colloidal single photon emitter in near-infrared regime at room temperature

The photostability of a colloidal single photon emitter in near-infrared regime at room temperature is investigated. The fluorescence lifetime, blinking phenomenon, and anti-bunching effect of a single CdTeSe/ZnS quantum dot with an emission wavelength of 800 nm at room temperature are studied. The second-order correlation function at zero delay time is much smaller than 0.1, which proves that the emission from single quantum dots at 800 nm is a highly pure single-photon source. The effects of the irradiation duration on the fluorescence from single quantum dots are analyzed. The experimental results can be explained by a recombination model including a multi-nonradiative recombination center model and a multi-charged model.

Phase-Controlled Tunable Unconventional Photon Blockade in a Single-Atom-Cavity System.

In the past few years, cavity optomechanical systems have received extensive attention and research and have achieved rapid development both theoretically and experimentally. The systems play an important role in many fields, such as quantum information processing, optomechanical storage, high-precision measurement, macroscopic entanglement, ultrasensitive sensors and so on. Photon manipulation has always been one of the key tasks in quantum information science and technology. Photon blockade is an important way to realize single photon sources and plays an important role in the field of quantum information. Due to the nonlinear coupling of the optical force system, the energy level is not harmonic, resulting in a photon blockade effect. In this paper, we study the phase-controlled tunable unconventional photon blockade in a single-atom-cavity system, and the second-order nonlinear crystals are attached to the cavity. The cavity interacts with squeezed light, which results in a nonlinear process. The system is driven by a complex pulsed laser, and the strength of the coherent driving contains the phase. We want to study the effect of squeezed light and phase. We use the second-order correlation function to numerically and theoretically analyze the photon blockade effect. We show that quantum interference of two-photon excitation between three different transition pathways can cause a photon blockade effect. When there is no squeezed light, the interference pathways becomes two, but there are still photon blockade effects. We explore the influence of the tunable phase and second-order nonlinear strength on the photon blockade effect. We calculate the correlation function and compare the numerical results with the analytical results under certain parameters and find that the agreement is better.

Unconventional photon blockade in the two-photon Jaynes–Cummings model with two-frequency cavity drivings and atom driving

In a two-frequency cavity driving and atom driving atom-cavity system, we find the photon blockade effect. In a truncated eigenstates space, we calculate the zero-delay second-order correlation function of the cavity mode analytically and obtain an optimal condition for the photon blockade. By including three transition pathways, we find that higher excitations of the cavity mode can be further suppressed and the zero-delay second-order correlation function can be reduced additionally. Based on the master equation, we simulate the system evolution and find that the analytical solutions match well with the numerical results. Our scheme is robust with small fluctuations of parameters and may be used as a new type of single photon source.