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arXiv:1609.00257 · Physical Review A

Characterization and shaping of the time-frequency Schmidt mode spectrum of bright twin beams generated in gas-filled hollow-core photonic crystal fibers

Martin A. Finger, Nicolas Y. Joly, Philip St.J. Russell, Maria V. Chekhova

Published May 4, 2017• 34 citations
arXivHTMLPDF

Abstract

We vary the time-frequency mode structure of ultrafast pulse-pumped modulational instability (MI) twin beams in an argon-filled hollow-core kagome-style photonic crystal fiber by adjusting the pressure, pump pulse chirp, fiber length, and parametric gain. Compared to solid-core systems, the pressure-dependent dispersion landscape brings increased flexibility to the tailoring of frequency correlations, and we demonstrate that the pump pulse chirp can be used to tune the joint spectrum of femtosecond-pumped ${\ensuremath{\chi}}^{(3)}$ sources. We also characterize the resulting mode content, not only by measuring the multimode second-order correlation function ${g}^{(2)}$, but also by directly reconstructing the shapes and weights of time-frequency Schmidt (TFS) modes. We show that the number of modes directly influences the shot-to-shot pulse-energy and spectral-shape fluctuations in MI. Using this approach we control and monitor the number of TFS modes within the range from 1.3 to 4 using only a single fiber.

DOI
10.1103/physreva.95.053814

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arXiv:1703.04543•Physical Review A•Jan 12, 2018•25 citations
We vary the time-frequency mode structure of ultrafast pulse-pumped modulational instability (MI) twin beams in an argon-filled hollow-core kagome-style photonic crystal fiber by adjusting the pressure, pump pulse chirp, fiber length, and parametric gain. Compared to solid-core systems, the pressure-dependent dispersion landscape brings increased flexibility to the tailoring of frequency correlations, and we demonstrate that the pump pulse chirp can be used to tune the joint spectrum of femtosecond-pumped \ensuremathχ(3){\ensuremath{\chi}}^{(3)}\ensuremathχ(3) sources. We also characterize the resulting mode content, not only by measuring the multimode second-order correlation function g(2){g}^{(2)}g(2), but also by directly reconstructing the shapes and weights of time-frequency Schmidt (TFS) modes. We show that the number of modes directly influences the shot-to-shot pulse-energy and spectral-shape fluctuations in MI. Using this approach we control and monitor the number of TFS modes within the range from 1.3 to 4 using only a single fiber.
We report a novel source of twin beams based on modulational instability in high-pressure argon-filled hollow-core kagome-style photonic-crystal fiber. The source is Raman-free and manifests strong photon-number correlations for femtosecond pulses of squeezed vacuum with a record brightness of ∼2500 photons per mode. The ultra-broadband (∼50 THz) twin beams are frequency tunable and contain one spatial and less than 5 frequency modes. The presented source outperforms all previously reported squeezed-vacuum twin-beam sources in terms of brightness and low mode content.
It has been shown that noble-gas filled hollow-core photonic crystal fibres (HC-PCFs) are suitable for Raman-free generation of entangled sidebands, both in the low-gain regime for the generation of biphoton states and for bright states in the high-gain regime [1] , [2] . The frequency correlations of the bipartite system and its entanglement properties are often described in terms of time-frequency Schmidt (TFS) modes, which can be extracted from the joint spectral amplitude (JSA). It is however experimentally easier to measure the joint spectral intensity (JSI = |JSA| 2 ), which can also yield valuable information about the source [1] . The major difference between twin beam or biphoton generation in a crystal and in a fibre is that in fibre the propagation dynamics of pump, signal and idler play a bigger role due to the much longer path-lengths.
Non-classical correlated twin beams can be generated through the modulational instability in a hollow-core photonic crystal fibre filled with a noble gas. Since the gain is provided by a monatomic gas, the influence of Raman effect, which is typical for fibre-based sources of entangled photons, is avoided. Additionally, the gas pressure together with the frequency chirp of the input pump pulse allow continuous tuning of the number of frequency modes of the twin beams. We combine spectral interferometry and single-shot measurement to retrieve the phase of the noise-driven generated sidebands.
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.
We present the results of an experimental and numerical investigation into temporally nonlocal coherent interactions between ultrashort pulses, mediated by Raman coherence, in a gas-filled kagome-style hollow-core photonic-crystal fiber. A pump pulse first sets up the Raman coherence, creating a refractive index spatiotemporal grating in the gas that travels at the group velocity of the pump pulse. Varying the arrival time of a second, probe, pulse allows a high degree of control over its evolution as it propagates along the fiber through the grating. Of particular interest are soliton-driven effects such as self-compression and dispersive wave (DW) emission. In the experiments reported, a DW is emitted at $\ensuremath{\sim}300\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ and exhibits a wiggling effect, with its central frequency oscillating periodically with pump-probe delay. The results demonstrate that a strong Raman coherence, created in a broadband guiding gas-filled kagome photonic-crystal fiber, can be used to control the nonlinear dynamics of ultrashort probe pulses, even in difficult-to-access spectral regions such as the deep and vacuum ultraviolet.