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arXiv:1403.4397 · Physical Review A

Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion

Benjamin Brecht, A. Eckstein, Raimund Ricken, Viktor Quiring, H. Suche, Linda Sansoni, Christine Silberhorn

Published Sep 12, 2014• 114 citations
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Abstract

Time-frequency Schmidt (TFS) modes of ultrafast quantum states are naturally compatible with high-bit-rate integrated quantum communication networks. Thus they offer an attractive alternative for the realization of high-dimensional quantum optics. Here, we present a quantum pulse gate based on dispersion-engineered ultrafast frequency conversion in a nonlinear optical waveguide, which is a key element for harnessing the potential of TFS modes. We experimentally retrieve the modal spectral-temporal structure of our device and demonstrate a single-mode operation fidelity of 80%, which is limited by experimental shortcomings. In addition, we retrieve a conversion efficiency of 87.7% with a high signal-to-noise ratio of 8.8 when operating the quantum pulse gate at the single-photon level.

DOI
10.1103/physreva.90.030302

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•Jan 1, 2013•1 citation
Time-frequency Schmidt (TFS) modes of ultrafast quantum states are naturally compatible with high-bit-rate integrated quantum communication networks. Thus they offer an attractive alternative for the realization of high-dimensional quantum optics. Here, we present a quantum pulse gate based on dispersion-engineered ultrafast frequency conversion in a nonlinear optical waveguide, which is a key element for harnessing the potential of TFS modes. We experimentally retrieve the modal spectral-temporal structure of our device and demonstrate a single-mode operation fidelity of 80%, which is limited by experimental shortcomings. In addition, we retrieve a conversion efficiency of 87.7% with a high signal-to-noise ratio of 8.8 when operating the quantum pulse gate at the single-photon level.
Full control over the spatiotemporal structure of quantum states of light is an important goal in quantum optics, to generate, for instance, single-mode quantum pulses or to encode information on multiple modes, enhancing channel capacities. Quantum light pulses feature an inherent, rich spectral broadband-mode structure. In recent years, exploring the use of integrated optics as well as source engineering has led to a deep understanding of the pulse-mode structure of guided quantum states of light. In addition, several groups have started to investigate the manipulation of quantum states by means of single-photon frequency conversion. In this paper, we explore new routes towards complete control of the inherent pulse-modes of ultrafast pulsed quantum states by employing specifically designed nonlinear waveguides with adapted dispersion properties. Starting from our recently proposed quantum pulse gate (QPG), we further generalize the concept of spatiospectral engineering for arbitrary χ (2) -based quantum processes. We analyse the sum-frequency generation-based QPG and introduce the difference-frequency generation-based quantum pulse shaper (QPS). Together, these versatile and robust integrated optical devices allow for arbitrary manipulations of the pulse-mode structure of ultrafast pulsed quantum states. The QPG can be utilized to select an arbitrary pulse mode from a multimode input state, whereas the QPS enables the generation of specific pulse modes from an input wavepacket with a Gaussian-shaped spectrum.
The temporal-mode (TM) basis is a prime candidate to perform high-dimensional quantum encoding. Quantum frequency conversion has been employed as a tool to perform tomographic analysis and manipulation of ultrafast states of quantum light necessary to implement a TM-based encoding protocol. While demultiplexing of such states of light has been demonstrated in the quantum pulse gate (QPG), a multiplexing device is needed to complete an experimental framework for TM encoding. In this work we demonstrate the reverse process of the QPG. A dispersion-engineered difference frequency generation in nonlinear optical waveguides is employed to imprint the pulse shape of the pump pulse onto the output. We study experimentally the process by spectrally shaping the first five orders of Hermite-Gauss modes of various bandwidths. Finally, we establish and model the limits of practical, reliable spectral pulse shaping operation.
Quantum frequency conversion (FC) in nonlinear optical media is a powerful tool for temporal-mode selective manipulation of light. Recent attempts at achieving high mode selectivities and/or fidelities have had to resort to multi-dimensional optimization schemes to determine the system's natural Schmidt modes. Certain combinations of relative-group velocities between the relevant frequency bands, medium length, and temporal pulse widths have been known to achieve good selectivities (exceeding 80%) for temporal modes that are nearly identical to pump pulse shapes, even for high conversion efficiencies. Working in this parameter regime using an off-the-shelf, second-harmonic generation, MgO:PPLN waveguide, and with pulses on the order of 500 fs at wavelengths around 800 nm, we verify experimentally that model-predicted Schmidt modes provide the high temporal-mode selectivity expected. The good agreement between experiment and theory paves the way to the implementation of a proposed two-stage FC scheme that is predicted by the present theory to reach near-perfect (100%) selectivity.
A new, and thus far only, method to overcome a selectivity barrier in parametrically pumped quantum pulse gates is proposed and experimentally demonstrated for the first time, using frequency conversion of optical temporal modes in second-order nonlinear waveguides. Temporal modes and quantum pulse gates are defined and their utilities are explored. Pulsed operation of three-field and four-field, parametric, optical processes are modeled and numerically investigated. A maximum limit to achievable selectivity for quantum pulse gating in uniform media is discovered and theoretically explained. An interferometric means of overcoming said limit and asymptotically approaching unit selectivity is proposed. The principle is experimentally verified by double-passing specifically shaped optical pulses derived from an ultrafast Ti:sapphire laser through a periodically-poled lithium niobate waveguide phasematched for sum-frequency generation. Further improvements and future implications for quantum technologies are discussed.
Temporal modes (TM) are a new basis for storage and retrieval of quantum information in states of light. The full TM manipulation toolkit requires a practical quantum pulse gate (QPG), which is a device that unitarily maps any given TM component of the optical input field onto a different, easily separable subspace or degree of freedom. An ideal QPG must "separate" the selected TM component with unit efficiency, whilst avoiding crosstalk from orthogonal TMs. All attempts at implementing QPGs in pulsed-pump traveling-wave systems have been unable to satisfy both conditions simultaneously. This is due to a known selectivity limit in processes that rely on spatio-temporally local, nonlinear interactions between pulsed modes traveling at independent group velocities. This limit is a consequence of time ordering in the quantum dynamical evolution, which is predicted to be overcome by coherently cascading multiple stages of low-efficiency, but highly TM-discriminatory QPGs. Multi-stage interferometric quantum frequency conversion in nonlinear waveguides was first proposed for precisely this purpose. TM-nonselective cascaded frequency conversion, also called optical Ramsey interferometry, has recently been demonstrated with continuous-wave (CW) fields. Here, we present the first experimental demonstration of TM-selective optical Ramsey interferometry and show a significant enhancement in TM selectivity over single-stage schemes.
We implemented a single-mode Quantum Pulse Gate (QPG), which singles out specific ultrafast time-frequency (TF) modes from multi-mode quantum pulses by transferring them to another wavelength. We directly measured the TF mode structure of our QPG and demonstrate a high degree of control over these modes. In addition, we prove the single-mode operation by monitoring a sharp drop in the conversion efficiencies for orthogonal TF mode combinations. Our QPG constitutes an important building block for future multi-mode quantum communication and information applications.