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Optics Express

Generation of two-temporal-mode photon states by vector four-wave mixing

Colin J. McKinstrie, Jesper B. Christensen, Karsten K. Rottwitt, M. G. Raymer

Published Aug 18, 2017• 5 citations
Publisher

Abstract

Photon pair states and multiple-photon squeezed states have many applications in quantum information science. In this paper, Green functions are derived for spontaneous four-wave mixing in the low- and high-gain regimes. Nondegenerate four-wave mixing in a strongly-birefringent medium generates signal and idler photons that are associated with only one pair of temporal (Schmidt) modes, for a wide range of pump powers and arbitrary pump shapes. The Schmidt coefficients (expected photon numbers) depend sensitively on the pump powers, and the Schmidt functions (shapes of the photon wavepackets) depend sensitively on the pump powers and shapes, which can be controlled.

DOI
10.1364/oe.25.020877

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Photon pair states and multiple-photon squeezed states have many applications in quantum information science. In this paper, Green functions are derived for spontaneous four-wave mixing in the low- and high-gain regimes. Nondegenerate four-wave mixing in a strongly-birefringent medium generates signal and idler photons that are associated with only one pair of temporal (Schmidt) modes, for a wide range of pump powers and arbitrary pump shapes. The Schmidt coefficients (expected photon numbers) depend sensitively on the pump powers, and the Schmidt functions (shapes of the photon wavepackets) depend sensitively on the pump powers and shapes, which can be controlled.
This thesis deals with applications of nonlinear four-wave mixing in the context of optical quantum information science. By enabling diverse functionalities such as single-photon generation, temporal shaping, and frequency conversion, four-wave mixing is a highly versatile tool for processing optical quantum information. The first part addresses the use of spontaneous four-wave mixing for generating entangled photon pairs with the particular property that the photons are uncorrelated in time and frequency. Two schemes are proposed to achieve this. The first proposal relies on a gradually varying interaction between two orthogonally polarized pump pulses in a birefringent waveguide. It is shown that, if the two pump pulses undergo a complete walk-through, the two generated photons emerge in orthogonal polarizations with uncorrelated- and tailorable time-frequency distributions. The second proposal deals with photon-pair generation in a microring resonator. In this setting, it is shown that a dual-pulse configuration can be used to excite- and subsequently de-excite the resonator on a sub-lifetime timescale. This turns out to strongly diminish time-frequency correlations. The second part considers the four-wave-mixing process Bragg scattering, which is known to enable noise-free frequency conversion. The Bragg-scattering process treated here, which occurs in a birefringent waveguide, is shown to allow for shape-preserving and strongly uni-directional conversion with a large acceptance bandwidth.
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.
If the idler photon flux is continuously measured in a photon-counting detector and the photocurrent fluctuations are fed back to control the pump intensity, the output signal state will be an amplitude-squeezed state (near-number state) at low frequencies and high feedback loop gain. Electromagnetic field in number-phase minimum-uncertainty states (amplitude- squeezed states), and its limit (photon-number states) have potential applications in optical communication, precision measurement, and atomic spectroscopy, and gravitational wave detection. These states have been the focus of considerable attention.