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Optics Letters

Scalable and efficient source of entangled frequency bins

Marco Liscidini, John E. Sipe

Published May 15, 2019• 25 citations
Publisher

Abstract

We present a scalable and efficient approach for the generation of frequency-bin encoded qudit states in photonic integrated devices. We exploit a series of coherently pumped resonators, each generating photon pairs in specific frequency bins via spontaneous four-wave mixing. The generated state can be described as a coherent superposition of the states that would describe the pairs generated in each ring separately. As the frequency bin separation is not fixed by the resonator free spectral range, small resonators having large finesse and pair generation rates can be used.

DOI
10.1364/ol.44.002625

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We present a scalable and efficient approach for the generation of frequency-bin encoded qudit states in photonic integrated devices. We exploit a series of coherently pumped resonators, each generating photon pairs in specific frequency bins via spontaneous four-wave mixing. The generated state can be described as a coherent superposition of the states that would describe the pairs generated in each ring separately. As the frequency bin separation is not fixed by the resonator free spectral range, small resonators having large finesse and pair generation rates can be used.
Quantum optical microcombs in integrated ring resonators generate entangled photon pairs over many spectral modes, and allow the preparation of high-dimensional qudit states. Ideally, those sources should be programmable and have a high generation rate, with comb lines tightly spaced for the implementation of efficient qudit gates based on electro-optic frequency mixing. While these requirements cannot all be satisfied by a single resonator device, for which there is a trade-off between the high generation rate and tight bin spacing, a promising strategy is the use of multiple resonators, each generating photon pairs in specific frequency bins via spontaneous four-wave mixing. Based on this approach we present a programmable silicon photonics device for the generation of frequency-bin-entangled qudits, in which bin spacing, qudit dimension, and the bipartite quantum state can be reconfigured on chip. Using resonators with a radius of $22\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$, we achieve a high brightness [about MHz/(mW)2\mathrm{MHz}/(\mathrm{mW}{)}^{2}MHz/(mW)2] per comb line with a bin spacing of 15 GHz, and fidelities above 85% with maximally entangled Bell states up to a Hilbert space dimension of 16. By individually addressing each spectral mode, we realize states that cannot be generated on chip using a single resonator. We measure the correlation matrices of maximally entangled two-qubit and two-qutrit states on a set of mutually unbiased bases, finding fidelities exceeding 98%, and indicating that the source can find application in high-dimensional secure communication protocols.
Quantum optical microcombs in integrated ring resonators generate entangled photon pairs over many spectral modes, and allow the preparation of high dimensional qudit states. Ideally, those sources should be programmable and have a high generation rate, with comb lines tightly spaced for the implementation of efficient qudit gates based on electro-optic frequency mixing. While these requirements cannot all be satisfied by a single resonator device, for which there is a trade-off between high generation rate and tight bin spacing, a promising strategy is the use of multiple resonators, each generating photon pairs in specific frequency bins via spontaneous four-wave mixing. Based on this approach we present a programmable silicon photonics device for the generation of frequency bin entangled qudits, in which bin spacing, qudit dimension, and bipartite quantum state can be reconfigured on-chip. Using resonators with a radius of 22 microns, we achieve a high brightness (MHz/(mW)^2) per comb line with a bin spacing of 15 GHz, and fidelities above 85% with maximally entangled Bell states up to a Hilbert space dimension of sixteen. By individually addressing each spectral mode, we realize states that can not be generated on-chip using a single resonator. We measure the correlation matrices of maximally entangled two-qubit and two-qutrit states on a set of mutually unbiased bases, finding fidelities exceeding 98%, and indicating that the source can find application in high-dimensional secure communication protocols.
Frequency bin encoding is becoming of widespread use in photonic quantum applications due to its strong noise resilience, the large information content that can be encoded per photon, and the inherent parallelism through which gates can be applied over multiple frequency modes. Ideally, sources of frequency bin qubits and qudits should be programmable, have high brightness, and have tightly spaced spectral modes to be useful for quantum algorithms. Here we present an integrated photonic device that simultaneously met all these requirement. We exploit the coherent generation of photon pairs over multiple ring resonators to overcome the trade-offs that hurdle single resonators. Harnessing the dense integration and phase stability of silicon photonics, we demonstrate a photon pair source of frequency bin qudits and qudits with simultaneously high brightness, fidelity, and purity.
We present a system capable of generating programmable polarization and frequency-bin hyperentangled photon pairs in an integrated photonic device. The structure is composed of ring resonators, each generating photon pairs with the same polarization in two pairs of frequency bins via spontaneous four-wave mixing. By combining several rings and controlling the amplitude and phase of the pump field, one can construct several hyperentangled states in a piece-by-piece fashion. For example, we consider a system composed of four rings and show that the density operator of the generated state describes a polarization and frequency-bin hyperentangled state. Finally, we calculate the expected generation rate and discuss the device efficiency.
Harnessing the frequency dimension in integrated photonics offers key advantages in terms of scalability, noise resilience, parallelization, and compatibility with telecom multiplexing techniques. Integrated ring resonators have been used to generate frequency-entangled states through spontaneous four-wave mixing. However, state-of-the-art integrated resonators are limited by trade-offs among size, spectral separation, and efficient photon pair generation. We have developed silicon ring resonators with a footprint below 0.05 mm2 providing more than 70 frequency channels separated by 21 GHz. We exploit the narrow frequency separation to parallelize and independently control 34 single qubit-gates with a single set of three off-the-shelf electro-optic devices. We fully characterize 17 frequency-bin maximally entangled qubit pairs by performing quantum state tomography. We demonstrate for the first time, we believe, a fully connected five-user quantum network in the frequency domain. These results are a step towards a generation of quantum circuits implemented with scalable silicon photonics technology, for applications in quantum computing and secure communications.