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arXiv:1901.03237 · Physical Review A

Scalability of parametric down-conversion for generating higher-order Fock states

Johannes Tiedau, Tim J. Bartley, Georg Harder, Adriana E. Lita, Sae Woo Nam, Thomas Gerrits, Christine Silberhorn

Published Oct 18, 2019• 50 citations
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Abstract

Spontaneous parametric down-conversion (SPDC) is the most widely used method to generate higher-order Fock states ($n\ensuremath{\ge}2$). Yet, a consistent performance analysis from fundamental principles is missing. Here, we address this problem by introducing a framework for state fidelity and generation probability under the consideration of losses and multimode emission. With this analysis we show the fundamental limitations of this process as well as a trade-off between state fidelity and generation rate intrinsic to the probabilistic nature of the process. This identifies the parameter space for which SPDC is useful when generating higher-order Fock states for quantum applications. We experimentally investigate the multiphoton regime of SPDC and demonstrate heralded Fock states up to $|n\ensuremath{\rangle}=4$.

DOI
10.1103/physreva.100.041802

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Spontaneous parametric down-conversion (SPDC) is the most widely used method to generate higher-order Fock states (n\ensuremath≥2n\ensuremath{\ge}2n\ensuremath≥2). Yet, a consistent performance analysis from fundamental principles is missing. Here, we address this problem by introducing a framework for state fidelity and generation probability under the consideration of losses and multimode emission. With this analysis we show the fundamental limitations of this process as well as a trade-off between state fidelity and generation rate intrinsic to the probabilistic nature of the process. This identifies the parameter space for which SPDC is useful when generating higher-order Fock states for quantum applications. We experimentally investigate the multiphoton regime of SPDC and demonstrate heralded Fock states up to ∣n\ensuremath⟩=4|n\ensuremath{\rangle}=4∣n\ensuremath⟩=4.
Parametric down-conversion (PDC) is one of the most widely used methods to create pure single-photon states for quantum information applications. However, little attention has been paid to higher-order photon components in the PDC process, yet these ultimately limit the prospects of generating single photons of high quality. In this paper we investigate the impact of higher-order photon components and multiple frequency modes on the heralding rates and single-photon fidelities. This enables us to determine the limits of PDC sources for single-photon generation. Our results show that a perfectly single-mode PDC source in conjunction with a photon-number-resolving detector is ultimately capable of creating single-photon Fock states with unit fidelity and a maximal state creation probability of 25%. Hence, an array of 17 switched sources is required to build a deterministic ($>999999%$ emission probability) pure single-photon source.
Spontaneous parametric down-conversion (SPDC) has been one of the foremost tools in quantum optics for over five decades. Over that time, it has been used to demonstrate some of the curious features that arise from quantum mechanics. Despite the success of SPDC, its higher-order analogs have never been observed, even though it has been suggested that they generate far more unique and exotic states than SPDC. An example of this is the emergence of non-Gaussian states without the need for postselection. Here we calculate the expected rate of emission for nthn\mathrm{th}nth-order SPDC with and without external stimulation (seeding). Focusing primarily on third-order parametric down-conversion, we estimate the photon detection rates in a rutile crystal for both the unseeded and seeded regimes.
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This thesis presents experimental progress towards highly efficient generation of cavity- enhanced, narrow-band multiphotons using spontaneous parametric downconversion. It also suggests theoretical proposals for new applications of multiphoton sources in quantum information technology. Photons prepared in Fock states, with a well-defined number of particles, are the essence of the quantum nature of light, and their unique nonclassical properties help us to develop quantum information technology. The generation of Fock states has been most commonly achieved by using spontaneous parametric down-conversion (SPDC) through the χ(2) nonlinearity in bulk crystals. During the SPDC process the nonlinear crystal emits photon-number correlated modes, and a photon-number- resolving measurement in one mode heralds the preparation of the other mode in a Fock state. The fidelity and the success rate of Fock state generation is limited by the multimode nature of SPDC emission. In this thesis, I will investigate the use of cavity-enhanced SPDC modes for higher fidelity photon pair generation, in which the well defined mode of the cavity is enhanced and results in the narrow-band source of the heralded single-photons with up to 80% heralding efficiency. The heralding efficiency is defined as the ratio between number of coincidences and single events on the heralding mode. The photon-number-resolving ability of high-quantum-efficiency transition edge sensors is used for the heralding and detection. We further discuss the feasibility of Fock state generation with higher photon numbers upon improving the data acquisition and analysis techniques. We also demonstrate and implement an interferometry scheme that exploit the phase of the photon and is capable of reading boundless bits of digital information using a single photon. This thesis also introduces new theoretical proposals for using Fock states to obtain quantum advantages for various quantum information applications, here to increase the efficiency in reading out information stored in a classical digital memory and to discriminate optical phases with lower error rates than is feasible with classical protocols.
The multiphoton states generated by high-gain spontaneous parametric down-conversion (SPDC) in the presence of large losses are investigated theoretically and experimentally. The explicit form for the two-photon output state has been found to exhibit a Werner structure very resilient to losses for any value of the nonlinear gain parameter ggg. The theoretical results are found to be in agreement with experimental data obtained by ``entanglement witness'' methods and by the quantum tomography of the state generated by a high-ggg SPDC.
Abstract Entangled photon sources are desirable and key elements for photonic quantum information processing. The spontaneous parametric down‐conversion (SPDC) process is a convenient way to produce entangled photon pairs. It has been widely used and has already made great contributions to quantum information science. SPDC sources have been thoroughly studied, and a detailed review, previously lacking, is now appropriate. In this article, different types of SPDC sources suitable for multiphoton experiments are reviewed. A comparison of their respective performances is presented, focusing on the parameters of indistinguishability, collection efficiency, and brightness, from which it is possible to see how the spatial and spectral properties of the SPDC process can be tailored, step by step, to achieve near‐perfect photon pairs. Recent progress on multiplexed heralded single‐photon sources, which effectively mitigate the nondeterministic nature of the SPDC process, is also described.