Photon-pair states, whether spectrally correlated or separable, can all be very useful in quantum technology applications. For example, the former are used for improving the security of quantum key distribution, whilst the latter are the backbone in heralded single photon sources. It has been shown that the amount of spectral correlations is well-described by the shape of the Joint Spectral Amplitude function (JSA), which mostly depends on the relative group velocity relation between the pump, signal and idler photons within the source medium [1].
Photon-pair states, whether spectrally correlated or separable, can all be very useful in quantum technology applications. For example, the former are used for improving the security of quantum key distribution, whilst the latter are the backbone in heralded single photon sources. It has been shown that the amount of spectral correlations is well-described by the shape of the Joint Spectral Amplitude function (JSA), which mostly depends on the relative group velocity relation between the pump, signal and idler photons within the source medium [1].
Control over the joint spectral amplitude of a photon pair has proved highly desirable for many quantum applications, since it contains the spectral quantum correlations, and has crucial effects on the indistinguishability of photons, as well as promising emerging applications involving complex quantum functions and frequency encoding of qudits. Until today, this has been achieved by engineering a single degree of freedom, either by custom poling nonlinear crystal or by shaping the pump pulse. We present a combined approach where two degrees of freedom, the phase-matching function, and the pump spectrum, are controlled. This approach enables the two-dimensional control of the joint spectral amplitude, generating a variety of spectrally encoded quantum states - including frequency uncorrelated states, frequency-bin Bell states, and biphoton qudit states. In addition, the joint spectral amplitude is controlled by photon bunching and anti-bunching, reflecting the symmetry of the phase-matching function.
Two-photon absorption (TPA) is a nonlinear optical process with wide applications in fluorescence microscopy and spectroscopy of organic molecules and compounds, as it enables atoms or molecules to transition into states that may otherwise be inaccessible by a single photon, either because of selection rules or energy conservation. Despite its common use, TPA is a rather inefficient process, often requiring very large photon numbers to produce significant results. It has been demonstrated and analytically described [1,2], that using frequency entangled pairs of photons can in some cases enhance the efficiency of TPA. For this to occur, the joint spectral amplitude (JSA) of the photon-pair state, which describes the spectral entanglement between the pair, must be engineered according to the spectral properties of the TPA response-function of the specific system in question. In this work, we consider different cases for the spectral functionality of TPA and propose that the control of the group indices of the modes involved in the pair-generation process is a key property in the design of photon-pair sources for optimized TPA.
One 01 the main objectives of quantum optiCS is to prepare quantum light sources 'Nith the characteristics required lor various quantum optica ppllcallons. Pure single photons and entangled paired photons are two of the most 'Nidely used types of quantum tight. Single photons In a pure, well ellned quantum state may prove to be the building blocks lor future quantum technologies. These technologies promise enormous improvements ove heir ctasslcal counterparts In terms of speed or security. For eICample, in quantum inlormation processing, single photons may be used in quanturT ogic gales, playing the role of electrons in current electric circuits. Although light is all around us In all possible colors, polarizations and intensities, it I ICtremely difficult to get a single photon In a pure quantum state. On the other hand, 11 is relallvely easy to produce pairs of photons, and pure singl horons can be obtained from a two-photon source in a heralded way. Thus, generatlng paired photons with desired photonic properties becomes o'nE pf the cruciattasks in the research area 01 quantum optics and related applications.
rrhe process of spontaneous parametric down-conversion (SPDC) is one 01 the most convenient ways to produce pairs 01 photons. In SPDC, a strons ump laser beam Is shone on a nonlinear crystal. Occasionally, a pump photon disappears and two new photons with lower energy are create imultaneously. The production of photon paIrs In the nonlinear crystal is probabilistic and the fact that the two photons are produced simultaneously I n advantage. The two photons can be taken apart and one 01 them can be used as a trigger 10 indicate (herald) the presence of the olher, thereb elllng us when a photon is ready to be used. These pairs of photons have special types 01 correlation In their color (frequency), in theIr spatial shape ndIor In Iheir polarization. For many applications, such as quantum cryptography, these types of correlation may be useful, but at the moment 0 enerating pure Single photons they are detrimental since they diminish the purity of the single photon.
In this thesis, we are interested in the frequency properties 01 SPDC pairs of photons. and our main goal Is 10 demonstrate new methods 10 contre hese properties. The frequency properties ollhe photon pairs are described by its joint spectrum, which contains the information of the bandwidth, th wavalorm and the type of frequency correlation possessed by the two photons.
n the first part of our work, two new toolklts are added to the current toolbox to manipulate the joint spectrum of photon pairs. One tool is called pulse ronHill' technique. This technique is based on the appropriate Introduction of angular dispersion into the interacting waves. The feasibitity of thi method is demonstrated by observing a sevenfold increase of the band;dth of photon pairs. The corresponding experiment has been accomplished b dding angular dispersion into a coItinear SPDC geometry, where the interacting waves propagate at the same direction. Also, we discuss Ih mplicalion 01 this method lor the generation 01 narrow temporal Fourier transform limited btphotons, and paired photons 'Nith high degree 0 ntangtement. The second tool is called spatial-to·spectral' mapping technique. This technique takes eHec! in a noncoUinear geomelry, in which caSE he pump beam and the down-<:onverted paired photons propagate at different directions. With this situatton, the spatial features of the pump beam 'Nil ~ Imprinted inlo the lrequency distribution 01 the new created photon pairs. We eICperimenlalty prove this method by shaping the waveform, and tunin he types ollrequency correlation 01 the dO'M'l-converted two photons.
n addition, we propose a new scheme to fully control the Joint spectrum ollhe pholon pairs by combining the above two discussed techniques. In thi proposal, angular dispersion is introduced into a noncollinear SPDC geometry. This opens a new way to obtain pure single photons 'Nith tunabl band'Nidth.
Another topic discussed in this thesis is the exploration of more compact quantum light sources 'Nith versatile characteristics. We describe an SPDC !WO-photon source by using Brag9 reflection wavegulde (BAW) in AI .Gah. As material as down-converting material. Here, the nonlinear proces happens between a pump beam in 8 Bragg refleclion wavegulde mode, and down-converted photon pairs in total internal rellection (TtA) mode. Th ~aveguide dispersion properties can be largely modified by implementing different ridge sizes. and this allows the described monolithic source 10 oHe Ignificant control over the process band'Nidth. We numerically demonstrate the possibility 01 tuning the bandwidth 01 the photon pairs between 1 n~ nd 450 nm with the same waler structure. The results presented in this part have been obtained as a result 01 the collaboration ;th Prol. Amr S.
Helmy and his PhD student Payam Abolghasem from University of Toronto. In particular, the programs used lor the presented simulations have bee developed by the University of Toronto leam.
o summarize, In this thesis, we add new elements to the current ways 01 engineering quantum light sources. Two readily be used methods to enginee he spectrum of the photon pairs are presented. Particularly, new routes are provided to get pure heralded single photons and narrow tempora biphoton. In addil!on, a compact monolithic two-photon source ;th tunable bandwidth control Is Investigated, which could be very promIsing for furthe pOrlormance of various quantum applications towards reality.
Uoc I data Barcelona, 2009·11-16 Signature
Temporal modes (TM) of light are a promising resource for quantum information as they span a discrete infinite dimensional encoding basis [1]. Additionally, TM are compatible with standard fibered communication as they share the same polarization, carrier frequency and transverse spatial mode properties. Single photons in specific TM can be obtained by Spontaneous Parametric Down Conversion (SPDC) and Spontaneous Four-Wave-Mixing (SFWM) sources. The Joint Spectral Amplitude (JSA), derived from energy and momentum conservation constraints describes the two-photon state and the signal and idler spectral distribution. The Schmidt decomposition of the JSA function : F = n √ λ n S n (ω s)I n (ω i) where the ({S n }) and ({I n }) are the TM basis of the signal and idler photons is sometimes reduced to one non zero term [2] where both signal and idler photons are generated in a single TM, giving rise to a fac-torable state of the pair. This can be achieved if a group velocity matching condition is satisfied (either β 1 (ω p) = β 1 (ω s) or β 1 (ω p) = β 1 (ω i) or 2 β 1 (ω p) = β 1 (ω s) + β 1 (ω i) in the case of SFWM with β 1 the inverse group velocity). Such single TM states are very useful for scalable heralded photon sources [3]. On the contrary, having several non-zero terms in the Schmidt decomposition depicts spectral correlations between the signal and idler which can also be required for others applications. Here we show experimentally in a stimulated regime how the shape of the JSA can be changed for photon pairs produced by FWM in a gas-filled inhibited-coupling (IC) fiber. IC fibers exhibit a discontinuous multiband dispersion where the position of the discontinuities are dictated by the strut thickness [4]. Such exotic dispersion opens new possibilities for the FWM phase matching fulfillment, and thus for tailoring the JSA. With the ability to have the pump and the generated signal and idler photons lying in different dispersion band, group-velocity matching can be easily obtained. We use stimulated emission tomography, which consists in seeding the FWM process with a tunable continuous wave laser, to reconstruct the 2D JSI (= |JSA| 2) as a function of signal and idler wavelengths. With a femtosecond pulsed pump at 1030 nm and a seed laser at telecom wavelength, Figure 1: Simulated JSI for different configurations of length, gas pressure and pump wavelength. Starting from the conditions of (a) P =3bar λp =1085 nm L = 1m, (b-d) correspond to the change of one parameter (b) L = 30 cm (c) P = 2.6 bar (d) λp =985 nm we chose two optimized fibers denoted A and B with struts thickness t=600 nm and inner-diameter d=40 µm and t=1250 nm; d=49 µm (Fig 2). These two fiber designs allow a multi-band FWM. Indeed the signal (fiber A), or both the signal and idler (fiber B) are generated in a different band from the pump. Xenon gas has been chosen because i) no Raman-Scattering can take place in a noble gas, which eliminates the usual main source of noise in fibered photon-pair generation and ii) it exhibits high non-linearity (in the order of 10 −21 m 2 /W at 10 bar). For a given fiber design, pump wavelength, gas pressure and fiber length are three adjustable parameters that can be tuned to access various JSA shapes as can be seen on the simulations in Fig.1. Both single TM or, opposingly, multi-TM can be obtained. Changing the gas pressure impacts the medium dispersion, which results in shifting the JSA and modifying its shape (Fig 1). As a first experimental demonstration in such gas-filled IC fibers, we experimentally reconstruct the JSI for two different fibers (Fig 2) with signal and idler wavelength respectively in the 771 nm and 1550 nm ranges. showing that two very different Schmidt decompositions can be obtained: a quasi factorable state and a correlated state. Figure 2: Fiber cross-section, experimental JSI and corresponding Schmidt decomposition for a 8 tubes IC-fiber and a kagome-IC fiber denoted A and B. In JSI of A the red dashed-lines define the measurement range. The pixelated structure of the JSI of B is due to an insufficient number of measures and will be improved. We have made a new proposal of using multi-dispersion band medium in order to engineer photon-pair time-frequency correlations. For the first time to our knowledge, we implement this technique using gas-filled inhibited-coupling fiber. More configurations are currently being investigated in order to demonstrate the real time tuning possibility in such a medium.
In spontaneous parametric down-conversion, the spectral correlations between the signal and the idler are expressed by the joint spectral amplitude (JSA) function. However, in the standard coincidence measurements, the phase information of the JSA is lost, and only the square of the absolute value of the JSA is recorded, thus preventing full characterization of the biphoton state. Here, we present an experimental technique to investigate the interference of biphoton joint spectral amplitudes, unlocking new avenues in quantum photonics research. Our method explores phase-dependent phenomena within entangled biphoton spectra. This is achieved by simultaneously pumping two structured nonlinear photonic crystals and observing their interference, which reveals previously inaccessible effects with direct intensity measurements. We demonstrate the versatility of our technique by analyzing two types of joint spectra: one exhibiting a two-lobe shape and the other a three-lobe shape. Additionally, we reconstruct the joint spectral amplitudes for both scenarios and observe good agreement with theoretical predictions. These results pave the way for developing advanced quantum communication and information processing technologies using biphoton spectra.