Second-order Intensity Research Articles

Second-order quasi-likelihood for spatial point processes.

Applications of spatial point processes for large and complex data sets with inhomogeneities as encountered, example, in tropical rain forest ecology call for estimation methods that are both statistically and computationally efficient. We propose a novel second-order quasi-likelihood procedure to estimate the parameters for a second-order intensity reweighted stationary spatial point process. Our approach is to derive first- and second-order estimating functions and then combine them linearly using appropriate weight functions. In the stationary case, we argue that the asymptotically optimal weight functions are respectively a constant and a function of lags between distinct locations in the observation window. This leads to a considerable gain in computational efficiency. We further exploit this simplification in the nonstationary case. Simulations show that, when compared with several existing approaches, our method can achieve significant gains in statistical efficiency. An application to a tropical rain forest data set further illustrates the advantages of our procedure.

Second-order nonlinear optical switching with a record-high contrast for a photochromic and thermochromic bistable crystal.

Nonlinear optical (NLO) switchable materials are important for photonic and optoelectronic technologies. One important issue for NLO photoswitching, the most studied physical switching approach, is how to improve the switching contrast of second harmonic generation (SHG) in crystals, because the known values are generally below 3 times. Thermoswitching, as another approach, has shown impressive high SHG-switching contrasts (4-∞ times), but the fast decay of thermally induced states demands constant heat sources to maintain specific SHG intensities. We have synthesized a photochromic and thermochromic bistable acentric compound, β-[(MQ)ZnCl3] (MQ+ = N-methyl-4,4'-bipyridinium), which represents the first crystalline compound with both photo- and heat-induced SHG-switching behavior and the first example of a thermoswitchable NLO crystal that can maintain its expected second-order NLO intensity without any heat source. The SHG-switching contrast can reach about 8 times after laser irradiation or 2 times after thermal annealing. The former value is the highest recorded for photoswitchable NLO crystals. This work also indicates that higher SHG-switching contrasts may be obtained through increasing electron-transfer efficiency, variation of permanent dipole moment, and self-absorption.

Dynamic hysteresis in a coherent high-β nanolaser

The quest for an integrated light source that promises high energy efficiency and a fast modulation for high-performance photonic circuits has led to the development of room-temperature telecom-wavelength nanoscale lasers with a high spontaneous emission factor β. The coherence characterization of this type of laser using the conventional measurement of output light intensity versus input pump intensity is inherently difficult due to the diminishing kink in the measurement curve. We demonstrate that the transition from incoherent to coherent emission of a high-β pulse-pump metallo-dielectric nanolaser can be determined by examining the width of a second-order intensity correlation peak that shrinks below and broadens above the threshold. Our photon fluctuation study, the first ever reported for this type of nanolaser, confirms the validity of this measurement technique. Additionally, we show that the width variation above the threshold results from the delayed threshold phenomenon, providing the first observation of dynamical hysteresis in a nanolaser.

Correlation functions in resonance fluorescence with spectral resolution: Signal-processing approach

In the framework of the signal processing approach to single-atom resonance fluorescence with spectral resolution, we diagrammatically derive an analytical formula for arbitrary-order spectral correlation functions of the scattered fields that pass through Fabry-Perot interferometers. Our general expression is then applied to study correlation signals in the limit of well separated spectral lines of the resonance fluorescence spectrum. In particular, we study the normalized second-order temporal intensity correlation functions in the case of the interferometers tuned to the components of the spectrum and obtain interferential corrections to the approximate results derived in the secular limit. In addition, we explore purely spectral correlations and show that they can fully be understood in terms of the two-photon cascades down the dressed state ladder.

Fourier-Transform Ghost Imaging with Hard X Rays.

Knowledge gained through x-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. However, it is only applied to crystalline structures and cannot resolve noncrystalline materials. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudothermal hard x rays that extends x-ray crystallography to noncrystalline samples. By measuring the second-order intensity correlation function of the light, Fourier-transform diffraction pattern of a complex amplitude sample is achieved at the Fresnel region in our experiment and the amplitude and phase distributions of the sample in the spatial domain are retrieved successfully. For the first time, ghost imaging is experimentally realized with x rays. Since a highly coherent x-ray source is not required, the method can be implemented with laboratory x-ray sources and it also provides a potential solution for lensless diffraction imaging with fermions, such as neutrons and electrons where intensive coherent sources usually are not available.

Suppression of single-cesium-atom heating in a microscopic optical dipole trap for demonstration of an 852-nm triggered single-photon source

We investigate single cesium (Cs) atom heating owing to the momentum accumulation process induced by the resonant pulsed excitation in a microscopic optical dipole trap formed by a strongly focused 1064 nm laser beam. The heating depends on the trap frequency which restricts the maximum repetition rate of pulsed excitation. We experimentally verify the heating of a single atom and then demonstrate how to suppress it with an optimized pulsed excitation/cooling method. The typical trap lifetime of single Cs atom is extended from 108 +/- 6 us to 2536 +/- 31 ms, and the corresponding number of excitation increases from ~ 108 to ~ 360000. In applying this faster cooling method, we use the trapped single Cs atom as a triggered single-photon source at an excitation repetition rate of 10 MHz. The second-order intensity correlations of the emitted single photons are characterized by implementing Hanbury Brown and Twiss setup, and clear anti-bunching effect has been observed.

Retrieving the covariance matrix of an unknown two-mode Gaussian state by means of a reference twin beam

A method for revealing the covariance matrix of an unknown two-mode Gaussian state is given based on the interference with a reference twin beam whose covariance matrix is known. In the method, first- and second-order cross-correlation intensity moments are determined varying the overall phase of the reference twin beam.

Spatiotemporal soliton solution to generalized nonlinear Schrödinger equation with a parabolic potential in Kerr media

A class of new spatiotemporal solitary solution to nonlinear Schrödinger equation with a parabolic potential is investigated analytically and numerically using the F-expansion method and homogeneous balance principle. The propagation characteristics of soliton wave solutions are analyzed with/without spatial-temporal chirp. It is noteworthy that, by calculating spatial and temporal second-order intensity moment, several novel features of optical beam propagations are obtained, such as stable, oscillating, decaying and blowing up. Additionally, controllability of these solutions with the modulation depth of the parabolic potential is demonstrated.

Radiation emission from an asymmetric quantum dot coupled to a plasmonic nanostructure

We propose a scheme for controlling the absorption and RFS of a quantum dot (QD) with broken inversion symmetry interacting with a plasmonic nanostructure. The QD is described as a two-level atom-like system with a permanent dipole moment in the excited state. A linearly polarized laser field drives the optical transition of the QD and produces localized surface plasmons in the MNP. The influence of plasmonic effects between the nanoparticle and the dot is analyzed using the Green tensor method. We found terahertz (THz) emission in the resonance fluorescence spectrum when the laser frequency lies above the transition frequency. The position and strength of the THz peaks is controlled by means of the dot-nanoparticle separation. The quantum nature of the emitted THz photons is analyzed by evaluating the second-order fluorescence intensity correlation function. We found a periodic alternation of photon bunching and anti-bunching with a period that depends on the polarization of the driving field.

852-nm triggered single-photon source based on trapping and manipulation of a single cesium atom confined in a microscopic optical dipole trap

Single-atom-based single-photon source has several advantages, such as narrow bandwidth, wavelength matching with the absorption line of the same atomic ensemble, and insensitivity to the environment disturbing, and it is very important not only for basic researches in quantum optic field but also for applications in quantum information processing. In this paper, we report the generation of a 10-MHz-repetition-rate triggered single-photon source at 852 nm based on a trapped single cesium atom in a far-off-resonance microscopic optical dipole trap (FORT). To generate an optical dipole trap, a far-red-detuned 1064 nm laser beam is tightly focused by using a high numerical aperture lens, a typical trap depth is 2 mK and trap waist is 2.3 m. To obtain a maximum probability of pulsed excitation, the frequency of the pulsed laser should be resonant with the atomic energy levels and the trapped single atom must be excited with a -pulse. However, the interaction between the FORT laser and the atoms causes AC Stark shifts of the atomic energy levels. Thus, in order to demonstrate the resonant pulsed excitation, it is important to calculate and measure the shift of 6S1/2|Fg=4,mF=+4-6P3/2|Fe=5,mF=+5 cyclical transition in the FORT. For a two-level system, the probability of pulsed excitation can be described by Rabi oscillations with a characteristic Rabi frequency . With an optimized time sequence, we experimentally demonstrate the Rabi oscillation between the ground state and the excited state, and the peak power of -pulse laser is about 1.25 mW. We also measure the temporal envelope of single photons after a -pulse excitation. A gated pulsed excitation and cooling technique are used to reduce the possibility that atoms are heated by -pulse laser. The typical trapping lifetime of single cesium atom is extended from~108 ups to~2536 ms. The corresponding number of excitations is improved from 108 to 360000. The second-order intensity correlations of the emitted single-photon are characterized by implementing Hanbury Brown-Twiss setup. The statistics shows a strong anti-bunching with a value of 0.09 for the second-order correlation at zero delay. In the future, we will perform a Hong-Ou-Mandel two-photon interference experiment to analyze the indistinguishability of the single photons. We will also trap single atoms in a magic-wavelength optical dipole trap where the ground and the excited states have the same shift.

Time-delayed intensity–interferometry of the emission from ultracold atoms in a steady-state magneto-optical trap

Time-delayed intensity–interferometry (TDII) measurements of the fluorescent emission from an ultracold ensemble of thermal 87Rb atoms in a steady-state magneto-optical trap are presented, which reveal the underlying coherent and incoherent dynamics of the atoms. Measurements carried out with a 5 ns time resolution yielded a second-order intensity correlation function with the theoretically predicted value of 2 at zero delay. In addition coherent Rabi oscillations were seen for up to five full periods—much longer than the spontaneous emission lifetime of the excited state of Rb. The oscillations were damped out by ∼150 ns, and thereafter an exponential decay observed, from which the mean velocity of atoms and thus, the temperature of the ensemble was estimated. The values so obtained compare well with those determined by standard techniques. It is seen that TDII permits a quantitative study of the coherent and incoherent processes, even in a large ensemble of independent atomic emitters in random thermal motion. This measurement of second-order correlation powerful technique can reveal hidden periodicities such as coherent Rabi oscillations that are not directly seen in the emission from a large collection of atoms. In addition it can also reveal information about the mean velocity of the thermal ensemble of emitters, even though the Doppler broadening of emission due to the motion of atoms is smaller than the natural linewidth and is not directly measureable.

Few-photon transport in many-body photonic systems: A scattering approach

We study the quantum transport of multi-photon Fock states in one-dimensional Bose-Hubbard lattices implemented in QED cavity arrays (QCAs). We propose an optical scheme to probe the underlying many-body states of the system by analyzing the properties of the transmitted light using scattering theory. To this end, we employ the Lippmann-Schwinger formalism within which an analytical form of the scattering matrix can be found. The latter is evaluated explicitly for the two particle/photon-two site case using which we study the resonance properties of two-photon scattering, as well as the scattering probabilities and the second-order intensity correlations of the transmitted light. The results indicate that the underlying structure of the many-body states of the model in question can be directly inferred from the physical properties of the transported photons in its QCA realization. We find that a fully-resonant two-photon scattering scenario allows a faithful characterization of the underlying many-body states, unlike in the coherent driving scenario usually employed in quantum Master equation treatments. The effects of losses in the cavities, as well as the incoming photons' pulse shapes and initial correlations are studied and analyzed. Our method is general and can be applied to probe the structure of any many-body bosonic models amenable to a QCA implementation including the Jaynes-Cummings-Hubbard, the extended Bose-Hubbard as well as a whole range of spin models.

Study on propagation characteristics of temporal soliton in Scarff II PT-symmetric potential based on intensity moments

When a temporal soliton propagates in the inhomogeneous nonlinear medium with Scarff II parity-time (PT)-symmetric potential, we investigate the propagation characteristics of a temporal soliton based on intensity moments. Under the condition of Scarff II PT-symmetric potential, the propagation characteristics of a temporal soliton are affected by the dispersion coefficient, nonlinear coefficient and chirp. After a detailed analysis of the intensity evolution and the second-order intensity moment parameter, we find that the intensity and pulse width (PW) of a chirped-free temporal soliton are invariant during nonlinear propagation when the dispersion coefficients are the constant, exponential decreasing function and periodic modulated function, respectively. The intensity and PW of a chirped temporal soliton vary periodically when the dispersion coefficient is a periodic modulated function. So the chirp has no effect on propagation behavior of a temporal soliton. When the dispersion coefficients are the constant or exponential decreasing function, the intensity of a chirped temporal soliton is gradually increased, while the PW of a chirped temporal soliton is gradually decreased. Thus the temporal soliton is compressed and the chirp has a great effect on the propagation behavior of a temporal soliton. The results will be helpful to manipulation of nonlinear propagation of the laser pulses.

Architecture dependence of photon antibunching in cavity quantum electrodynamics

We investigate numerically the architecture dependence of the characteristics of antibunched photons generated in cavity quantum electrodynamic systems. We show that the quality of antibunching [the smallness of the second-order intensity correlation function at zero time ${g}^{(2)}(0)$] and the generation efficiency significantly depend on the configurations: the arrangements of single-mode optical cavities and waveguides. We found that for certain class of architecture, when the Jaynes-Cummings system (the atom-cavity system) couples to two terminated waveguides, there exists a fundamental tradeoff between high transmission and low ${g}^{(2)}(0)$, and is sensitive to dissipation. We further show that optimal antibunching can be achieved in two alternative cavity quantum electrodynamic configurations operating in the dissipatively weak coupling regime such that the two-photon transmission can be two orders of magnitude higher for the same ${g}^{(2)}(0)$.

Direct Schmidt number measurement of high-gain parametric down conversion

In this work we estimate the transverse Schmidt number for the bipartite high-gain parametric down conversion state by means of second-order intensity correlation function measurement. Assuming that the number of modes is equal in both beams we determine the Schmidt number considering only one of the subsystems. The obtained results demonstrate that this approach is equally efficient over the whole propagation of the state from the near field to the far field regions of its emitter.

Incoherent on-off keying with classical and non-classical light

We analyze the performance of on-off keying (OOK) and its restricted version pulse position modulation (PPM) over a lossy narrowband optical channel under the constraint of a low average photon number, when direct detection is used at the output. An analytical approximation for the maximum PPM transmission rate is derived, quantifying the effects of photon statistics on the communication efficiency in terms of the g((2)) second-order intensity correlation function of the light source. Enhancement attainable through the use of sub-Poissonian light is discussed.

An experimental and theoretical mechanistic study of biexciton quantum yield enhancement in single quantum dots near gold nanoparticles

In this work, we systematically investigated the plasmonic effect on blinking, photon antibunching behavior and biexciton emission of single CdSe/CdS core/shell quantum dots (QDs) near gold nanoparticles (NPs) with a silica shell (Au@SiO2). In order to obtain a strong interaction between the plasmons and excitons, the Au@SiO2 NPs and CdSe/CdS QDs of appropriate sizes were chosen so that the plasmon resonance overlaps with the absorption and emission of the QDs. We observed that in the regime of a low excitation power, the photon antibunching and blinking properties of single QDs were modified significantly when the QDs were on the Au@SiO2 substrates compared to those on glass. Most significantly, second-order photon intensity correlation data show that the presence of plasmons increases the ratio of the biexciton quantum yield over the exciton quantum yield (QYBX/QYX). An electrodynamics model was developed to quantify the effect of plasmons on the lifetime, quantum yield, and emission intensity of the biexcitons for the QDs. Good agreement was obtained between the experimentally measured and calculated changes in QYBX/QYX due to Au@SiO2 NPs, showing the validity of the developed model. The theoretical studies also indicated that the relative position of the QDs to the Au NPs and the orientation of the electric field are important factors that regulate the emission properties of the excitons and biexcitons of QDs. The study suggests that the multiexciton emission efficiency in QD systems can be manipulated by employing properly designed plasmonic structures.

Theory of high gain cavity-enhanced spontaneous parametric down-conversion

We compute the output of multimode cavity-enhanced spontaneous parametric down-conversion (SPDC) for sub-threshold, but otherwise arbitrary, gain. We find analytic Bogoliubov transformations that allow us to calculate arbitrary field correlation functions, including the second-order intensity correlation function $G^{(2)}(T)$. The results show evidence of increased coherence due to stimulated SPDC. We extend an earlier model [Lu and Ou, Phys. Rev. A, 62, 033804 (2000)] to arbitrary gain and finesse, and show the extension gives accurate results in most scenarios. The results will allow simple, analytic description of cavity-based nonclassical light sources for quantum networking, quantum-enhanced sensing of atoms and generation of highly non-classical field states

Intensity interferometry of single x-ray pulses from a synchrotron storage ring.

We report on measurements of second-order intensity correlations at the high-brilliance storage ring PETRA III using a prototype of the newly developed adaptive gain integrating pixel detector. The detector records individual synchrotron radiation pulses with an x-ray photon energy of 14.4keV and repetition rate of about 5MHz. The second-order intensity correlation function is measured simultaneously at different spatial separations, which allows us to determine the transverse coherence length at these x-ray energies. The measured values are in a good agreement with theoretical simulations based on the Gaussian Schell model.

A Multipulse Time-Resolved Fluorescence Method for Probing Second-Order Recombination Dynamics in Colloidal Quantum Dots

The ability to generate and utilize multiexcited electronic states in colloidal quantum dots (QDs) is key to a growing range of QD technologies, but the factors that control their radiative and nonradiative recombination dynamics are not yet fully resolved. A significant barrier toward a greater understanding of these species is the fact that their spectroscopic signatures are energetically close to dominant exciton transitions, making it difficult to separate their decay contributions in inhomogeneously broadened ensembles. Here we describe a multipulse technique wherein a controllable number of 80 MHz laser pulses are used to generate different excited state populations, which are then monitored using time-resolved fluorescence. By changing the number of pulses and using a general data analysis method we are able to separate second-order emission generated by absorption of two or more laser pulses from first-order contributions generated by just one pulse. Furthermore, we show that it is possible to determine the nature of the multiexcited state by comparing the second-order emission intensity to models of QD decay dynamics. We find that in our sample of CdSe/CdS core/shell QDs the second-order emission is dominated by emissive trion states rather than biexcitons. Our spectroscopic technique offers a powerful new way to study multiexcited QDs, and the insights that will be gained from this and future studies could be an important step toward harnessing multiexcitons and other multiexcited states in new QD technologies.