Jeffrey Perkins
A closed form solution is derived for the biphoton k-vector spectrum for an arbitrary pump spatial mode. The resulting mode coefficients for the pump input that maximize the probability of biphoton detection in the far field are found. It is thus possible to include the effect of arbitrary crystal poling strucures, and optimize the resulting biphoton flux.
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We report on controlling the bi-photon orbital angular momentum (OAM) eigenmodes in the spontaneous parametric down conversion process by simply adjusting the asymmetry of the pump vortex beam. Adjusting the optic axis of the spiral phase plate (SPP) of phase winding corresponding to OAM mode, l, with respect to the beam propagation axis, we have transformed a Gaussian beam into an asymmetric vortex beam with OAM modes, l, l-1, l-2, 0 with different weightages. Pumping the nonlinear crystal with such asymmetric vortices and controlling their asymmetry we have tailored the spiral spectrum of th…
We study the generation of paired photons due to the effect of four-wave mixing in an ensemble of pumped two-level systems that decay via an intermediate metastable state. The slow population relaxation of the metastable state to the ground state is utilized to create long-lived coherent population oscillation, leading to narrowband nonlinear response of the medium. The biphotons have a narrow bandwidth, long coherence time and length, which can be controlled by the pump field. In addition, the biphotons are antibunched, with antibunching period determined by the dephasing time. During this pe…
Beyond critical coupling: optimal design considerations for spontaneous four-wave mixing in microring resonators
针对微环谐振器中的自发四波混频双光子产生问题，提出涵盖多结构、多耦合条件、多泵浦模式的解析模型，明确不同泵浦条件下最大化光子提取效率的耦合方案及相关权衡，为集成光子源设计提供支撑。
In this work we study the spatio-temporal correlations of photons produced by spontaneous parametric down conversion. In particular, we study how the waists of the detection and pump beams impact on the spectral bandwidth of the photons. Our results indicate that this parameter is greatly affected by the spatial properties of the detection beam, while not as much by the pump beam. This allows for a simple experimental implementation to control the bandwidth of the biphoton spectra, which only entails modifying the optical configuration to collect the photons. Moreover, we have performed Hong-O…
A double-Gaussian model and the Schmidt modes are found for the biphoton wave function characterizing spontaneous parametric down-conversion with the degenerate collinear phase-matching of the type I and with a pulsed pump. The obtained results are valid for all durations of the pump pulses, short, long and intermediately long.
Spontaneous parametric down-conversion (SPDC) is a widely used source for photonic entanglement. Years of focused research have led to a solid understanding of the process, but a cohesive analytical description of the paraxial biphoton state has yet to be achieved. We derive a general expression for the spatio-temporal biphoton state that applies universally across common experimental settings and correctly describes the non-separability of spatial and spectral modes. We formulate a criterion on how to decrease the coupling of the spatial from the spectral degree of freedom by taking into acco…
Algebraic Characterization of Biphoton Spatial-Mode Entanglement in Higher-Order Laguerre--Gaussian-Pumped SPDC
本文通过将LG泵浦SPDC分解为分束器变换与空间双模压缩，建立代数框架，推导施密特数解析式，统一描述高阶LG泵浦SPDC的模式结构、守恒律与纠缠维度。
Biphoton State Reconstruction via Phase Retrieval Methods
本研究提出通过空间分辨单光子探测和二阶相关性分析，分离并观察自发参量下转换中泵浦与相位匹配的模及自由空间传播，结合最大似然或遗传算法恢复相位结构，实现无需源控制的双光子波函数完整重建。
In this work we present a simple method to reconstruct the complex spectral wavefunction of a biphoton, and hence gain complete information about the spectral and temporal properties of a photon pair. The technique, which relies on quantum interference, is applicable to biphoton states produced with a monochromatic pump when a shift of the pump frequency produces a shift in the relative frequencies contributing to the biphoton. We demonstrate an example of such a situation in type-II parametric down-conversion (SPDC) allowing arbitrary paraxial spatial pump and detection modes. Moreover, our t…
In spontaneous parametric down-conversion photons are known to be created coherently and with equal probability over the entire length of the crystal. Then, there is no particular position in the crystal where a photon pair is created. We make the seemingly contradictory observation that we can control the time delay with the crystal position along the propagation direction. We resolve this contradiction by showing that the spatio-temporal correlations critically affect the temporal properties of the pair of photons, when using a finite detector size. We expect this to have important implicati…
We study two-photon excitation using biphotons generated via the process of spontaneous parametric down-conversion in a nonlinear crystal. We show that the focusing of these biphotons yields an excitation distribution that is essentially the same as the distribution of one-photon excitation at the pump wavelength. We also demonstrate that biphoton excitation in the image region yields a distribution whose axial width is approximately that of the crystal thickness and whose transverse width is that of the pump at the input to the crystal.
We prepare qudits based on angular multimode biphoton states by modulating the pump angular spectrum. The modes are prepared in the Schmidt basis and their intensity distributions do not overlap in space. This allows one to get rid of filtering losses while addressing single modes and to realize a single-shot qudit readout.
Spectral and temporal coincidence and single-particle photon wave packets are described and their widths and durations are found. The degree of entanglement is characterized by the experimentally measurable parameter R defined as the ratio of the coincidence and single-particle spectral widths. In the frequency representation, this parameter is found as a function of the pump-pulse duration. This function is shown to have a minimum and even in the minimum, at rather natural conditions, the parameter R is found to be very high (R=73>>1). The Schmidt number K is found for both short and long pum…
Nonclassical photon sources of high brightness are key components of quantum communication technologies. We here demonstrate the generation of narrowband, nonclassical photon pairs by employing spontaneous four-wave mixing in an optically-dense ensemble of cold atoms within a hollow-core fiber. The brightness of our source approaches the limit of achievable generated spectral brightness at which successive photon pairs start to overlap in time. For a generated spectral brightness per pump power of up to $2\times 10^{9} \ \textrm{pairs/(s MHz mW)}$ we observe nonclassical correlations at pump p…
We report interferometric schemes to prepare arbitrary states of four-dimensional qudits (ququarts) based on biphoton states of ultrafast-pumped frequency-nondegenerate spontaneous parametric down-conversion. Preparation and tomographic characterization of a few examples of general single-ququart states, a pure state, a completely mixed state, and a partially-mixed state, are experimentally demonstrated.
We propose a quantum ghost imaging scheme based on biphotons, that, by using a collimated pump beam of the right size for biphoton generation, obviates the need for lenses to achieve imaging. The scheme is found to be analogous to the classical pinhole camera, where we show that the equivalent to the classical pinhole size depends mainly on the width of the pump beam, but also on the thickness of the nonlinear crystal and the wavelengths of the biphoton.
Two-dimensional Control of a Biphoton Joint Spectrum
本文提出一种组合方法，同时控制相位匹配函数和泵浦光谱两个自由度，实现对双光子联合光谱振幅的二维控制，生成多种光谱编码量子态，并利用光子聚束与反聚束反映相位匹配对称性。
Self-induced manipulation of biphoton entanglement in topologically distinct modes
本文提出通过波导非线性与晶格结构结合，利用泵浦功率自诱导调控缺陷态拓扑性质，在拓扑平凡模式上生成双光子纠缠态，并给出实验方案及其在SSH模型和容错量子信息处理中的应用。
Quantum Gouy phase singularities in a propagating biphoton state
该研究揭示量子古伊相位会在纠缠光子对的纵向传播空间产生非局域相位奇点，明确其拓扑荷、位置及符号的决定因素，确立传播距离为纠缠光子对拓扑结构的坐标空间。
Photon modes have an important role in characterizing the quantum sources of light. Proper coupling of various photon modes obtained in spontaneous parametric down conversion (SPDC) process in optical fibers is essential to generate an effective source of entangled photons. The two main pre-detection factors affecting the biphoton mode coupling in SPDC are the pump beam focusing parameter and the crystal thickness. We present the numerical and experimental results on the effect of pump focusing on conditional down-converted photon modes for a Type-I BBO crystal. We experimentally verify that b…
Nowadays fiber biphoton sources are nearly as popular as crystal-based ones. They offer a single spatial mode and easy integrability into optical networks. However, fiber sources lack the broad tunability of crystals, which do not require a tunable pump. Here, we report a broadly tunable biphoton source based on a suspended core fiber. This is achieved by introducing pressurized gas into the fibers hollow channels, changing the step index. The mechanism circumvents the need for a tunable pump laser, making this a broadly tunable fiber biphoton source with a convenient tuning mechanism, compara…
We provide a toolbox for continuous variables quantum state engineering and characterization of biphoton states produced by spontaneous parametric down conversion in a transverse pump configuration. We show that the control of the pump beam's incidence spot and angle corresponds to phase space displacements of conjugate collective continuous variables of the biphoton. In particular, we illustrate with numerical simulations on a semiconductor device how this technique can be used to engineer and characterize arbitrary states of the frequency and time degrees of freedom.
We analyze spontaneous parametric down-conversion in various experimentally feasible 1D quadratic nonlinear waveguide arrays, with emphasis on the relationship between the lattice's topological invariants and the biphoton correlations. Nontrivial topology results in a nontrivial "winding" of the array's Bloch waves, which introduces additional selection rules for the generation of biphotons. These selection rules are in addition to, and independent of existing control using the pump beam's spatial profile and phase matching conditions. In finite lattices, nontrivial topology produces single ph…
We report the generation of biphotons, with a temporal full width at the half maximum (FWHM) of 13.4$\pm$0.3 $μ$s and a spectral FWHM of 50$\pm$1 kHz, via the process of spontaneous four-wave mixing. The temporal width is the longest, and the spectral linewidth is the narrowest up to date. This is also the first biphoton result that obtains a linewidth below 100 kHz, reaching a new milestone. The very long biphoton wave packet has a signal-to-background ratio of 3.4, which violates the Cauchy-Schwarz inequality for classical light by 4.8 folds. Furthermore, we demonstrated a highly-tunable-lin…
We draw an intuitive picture of the spatio-temporal properties of the entangled state of twin photons, where they are described as classical wave-packets. This picture predicts a precise relation between their temporal and transverse spatial separations at the crystal output. The space-time coupling described by classical arguments turns out to determine in a precise way the spatio-temporal structure of the quantum entanglement, analysed by means of the biphotonic correlation and of the Schmidt dimensionality of the entanglement.
We investigate spontaneous four wave mixing (SFWM) in a single-channel side-coupled integrated spaced sequence of resonators (SCISSOR). Analytic expressions for the number of photon pairs generated, as well as the biphoton wave function (joint spectral amplitude) describing the pairs, are derived and numerically computed for different pump pulse durations and numbers of ring resonators. In the limit of a long input pump pulse, we show a strong analogy between super-linear scaling of generation efficiency with respect to the number of rings in the structure and Dicke superradiance. More general…
A detailed theoretical analysis of the spatiotemporal mode of a single photon prepared via conditional measurements on a photon pair generated in the process of parametric down-conversion is presented. The maximum efficiency of coupling the photon into a transform-limited classical optical mode is calculated and ways for its optimization are determined. An experimentally feasible technique of generating the optimally matching classical mode is proposed. The theory is applied to a recent experiment on pulsed homodyne tomography of the single-photon Fock state (A. I. Lvovsky et al., Phys Rev. Le…
The spectral-temporal correlation and the correlation time of a biphoton wavepacket generated in the process of parametric down-conversion (PDC), is of great importance for a broad range of quantum experiments. We utilise an integrated PDC source to generate biphotons with different types of spectral-temporal correlations and probe their respective correlation times. The outcomes confirms that the correlation time is independent of the coherence time of the pump light, and it is only determined by the waveguide length and its dispersion properties. Furthermore, we investigate the properties of…
Does entanglement enhance single-molecule pulsed biphoton spectroscopy?
本研究探究纠缠对单分子脉冲双光子光谱学的增强作用，明确了光谱信息的贡献构成，证实时频纠缠可提升弱泵浦PDC探针的性能，且非纠缠测量能捕获大部分信息，为量子光谱应用提供依据。
Time-resolved Hanbury Brown-Twiss interferometry of on-chip biphoton frequency combs using Vernier phase modulation
针对探测器抖动限制BFC时间相关函数测量精度的问题，提出基于游标电光相位调制的时间分辨HBT干涉方法，在集成微环上实现最高3×3维双qutrit的精细时间特征表征，与理论高度一致。
Spatio-spectral properties of twin beams at their transition from low to high intensities are analyzed in parametric and paraxial approximations using the decomposition into paired spatial and spectral modes. Intensity auto- and cross-correlation functions are determined and compared in the spectral and temporal domains as well as the transverse wave-vector and crystal output planes. Whereas the spectral, temporal and transverse wave-vector coherence increases with the increasing pump intensity, coherence in the crystal output plane is practically independent on the pump intensity owing to the…
Intense spatio-spectral twin beams generated in the regime with pump depletion are analyzed applying a suggested quantum model that treats the signal, idler and pump fields in the same way. The model assumes the signal and idler fields in the form of the generalized superposition of signal and noise and reveals nonzero signal coherent components in both fields, contrary to the models developed earlier. The influence of coherent components on the properties of intense twin beams is elucidated. The interference pattern formed in the process of sum-frequency generation and that of the Hong-Ou-Man…
Using the model of parametric interaction based on the spatio-spectral Schmidt modes and generalized parametric approximation, we analyze coherence and mode structure of ultra-intense twin beams generated in the regime with pump depletion. We show that the increase of spatial and spectral coherence with the increasing pump power observed for moderate powers is replaced by the decrease for the pump powers at which pump depletion occurs. This behavior of coherence is opposed to that exhibited by the number of spatio-spectral modes effectively constituting the twin beam. The conditions for maxima…
Twin-beam coherence properties are analyzed both in the spatial and spectral domains at high-gain regime including pump depletion. The increase of the size of intensity auto- and cross-correlation areas at increasing pump power is replaced by a decrease in the pump depletion regime. This effect is interpreted as a progressive loss in the mode selection occurring at high-gain amplification. The experimental determination of the number of spatio-spectral modes from $g^{(2)} $-function measurements confirms this explanation.
We theoretically investigate the generation of two entangled beams of light in the process of single-pass type-I noncollinear frequency degenerate parametric downconversion with an ultrashort pulsed pump. We find the spatio-temporal squeezing eigenmodes and the corresponding squeezing eigenvalues of the generated field both numerically and analytically. The analytical solution is obtained by modeling the joint spectral amplitude of the field by a Gaussian function in curvilinear coordinates. We show that this method is highly efficient and is in a good agreement with the numerical solution. We…
We study the nonlinear QED signature of x-ray vacuum diffraction in the head-on collision of optical high-intensity and x-ray free-electron laser pulses at finite spatio-temporal offsets between the laser foci. The high-intensity laser driven scattering of signal photons outside the forward cone of the x-ray probe constitutes a prospective experimental signature of quantum vacuum nonlinearity. Resorting to a simplified phenomenological ad-hoc model, it was recently argued that the angular distribution of the signal in the far-field is sensitive to the wavefront curvature of the probe beam in t…
We present an experimental and theoretical study of photon pairs generated by spontaneous four wave mixing (SFWM), based on birefringent phasematching, in a fiber which supports more than one transverse mode. We present SFWM spectra, obtained through single-channel and coincidence photon counting, which exhibit multiple peaks shown here to be the result of multiple SFWM processes associated with different combinations of transverse modes for the pump, signal, and idler waves.
Shift current---a photocurrent induced by light irradiating noncentrosymmetric materials in the absence of any bias voltage or built-in electric field---is one of the mechanisms of the so-called bulk photovoltaic effect. It has been traditionally described as a nonlinear optical response of periodic solids to continuous wave light using a perturbative formula, which is linear in the intensity of light and which involves Berry connection describing the shift in the center of mass position of the Wannier wave function associated with the transition between the valence and conduction bands. We an…
Single Spatio-Temporal Mode Bright Twin-Beam Source Across the Near- and Mid-Infrared
本文提出一种超快、明亮的纠缠双束源，通过在周期性波导铌酸锂中进行类型0参数下转换，实现可调Schmidt数K的连续调节，适用于量子增强计量、非线性干涉和中红外光谱传感。
In this work the Schmidt number of the two-photon state generated by parametric-down conversion (PDC) is evaluated in the framework of a fully spatio-temporal model for PDC. A comparison with the results obtained in either purely spatial or purely temporal models shows that the degree of entanglement of the PDC state cannot be trivially reduced to the product of the Schmidt numbers obtained in models with lower dimensionality, unless the detected bandwidth is very narrow. This result is a consequence of the non-factorability of the state in the spatial and temporal degrees of freedoms of twin …
Phase Diagram and dynamical phases of self organization of a Bose-Einstein condensate in a transversely pumped red-detuned cavity
研究了玻色-爱因斯坦凝聚体在横向泵浦红移腔中的相图和动态相，揭示了自组织现象中的稳定性、混沌轨迹和时空模式形成机制。
We experimentally demonstrate a mode-selective quantum frequency converter over a compound spatio-temporal Hilbert space. We show that our method can achieve high-extinction for high-dimensional quantum state tomography by selectively upconverting the signal modes with a modulated and delayed pump. By preparing the pump in optimized modes through adaptive feedback control, selective frequency conversion is demonstrated with up to 30 dB extinction. The simultaneous operations over high-dimensional degrees of freedom in both spatial and temporal domains can serve as a viable resource for photon-…
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