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arXiv:1111.4095 · Physical Review A

Limits on the deterministic creation of pure single-photon states using parametric down-conversion

Andreas Christ, Christine Silberhorn

Published Feb 22, 2012• 127 citations
arXivHTMLPDF

Abstract

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 ($>$99$%$ emission probability) pure single-photon source.

DOI
10.1103/physreva.85.023829

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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2017•0 citations
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 (>>>99% emission probability) pure single-photon source.
Parametric down-conversion (PDC) offers the possibility to control the fabrication of non-Gaussian states such as Fock states. However, in conventional PDC sources energy and momentum conservation introduce strict frequency and photon number correlations, which impact the fidelity of the prepared state. In our work we optimize the preparation of single-photon Fock states from the emission of waveguided PDC via spectral filtering. We study the effect of correlations via photon number resolving detection and quantum interference. Our measurements show how the reduction of mixedness due to filtering can be evaluated. Interfering the prepared photon with a coherent state we establish an experimentally measured fidelity of the produced target state of 78%. (C) 2009 Optical Society of America
Parametric down-conversion (PDC) offers the possibility to control the fabrication of non-Gaussian states such as Fock states. However, in conventional PDC sources energy and momentum conservation introduce strict frequency and photon number correlations, which impact the fidelity of the prepared state. In our work we optimize the preparation of single-photon Fock states from the emission of waveguided PDC via spectral filtering. We study the effect of correlations via photon number resolving detection and quantum interference. Our measurements show how the reduction of mixedness due to filtering can be evaluated. Interfering the prepared photon with a coherent state we establish an experimentally measured fidelity of the produced target state of 78%.
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 $|n\ensuremath{\rangle}=4$.
We analyze the generation rates and preparation fidelities of photon triplet states in pulsed cascaded parametric down-conversion (PDC) under realistic experimental circumstances. As a model system, we assume a monolithically integrated device with negligible interface loss between the two consecutive PDC stages. We model the secondary down-conversion process in terms of a lossy channel and provide a detailed analysis of noise contributions. Taking variable pump powers into account, we estimate the impact of higher-order photon contributions and conversion processes on the achievable coincidence probabilities. At mean photon numbers of ⟨m⟩∼0.25\langle m\rangle\sim0.25⟨m⟩∼0.25 photons per pulse behind the first PDC stage, we expect around 4.04.04.0 genuine photon triplets per hour. Additionally, we discuss fundamental limitations of our model system as well as feasible improvements to the detectable photon triplet rate.
Single-photon sources that emit only one photon at a time with high yield are important for security and efficiency in quantum communication and computation, respectively. One method to develop the desired single-photon source is through entangled single-photon pairs from spontaneous parametric down-conversion (SPDC) crystals where detection of idler photons “heralds” the presence of signal photons. If the SPDC crystal is pumped with weak intensity laser, high purity heralded single photons can be produced at the cost of low yield. Increasing the yield by using stronger laser intensity inevitably decreases the purity due to the presence of multiple photons. Here, we propose a conceptual method to overcome this trade-off between single-photon purity and single-photon yield. Our setup consists of a weakly pumped SPDC crystal seeded with strong coherent states (CS) at the idler mode. Clicks on a click detector at the idler mode conditionally prepare a superposition state of zero-, one-, and two-photon Fock states (FS) at the signal mode. By employing repeated processes of infinitesimal displacement (ID) and two-photon elimination (PE), we can obtain a final state of one-photon FS. Based on the heralding probability (single-photon yield) and single-photon fidelity (single-photon purity), we found that our method transforms the initial state with high heralding probability but low single-photon fidelity (near minimum) to a final state with high heralding probability and high single-photon fidelity (maximum). Furthermore, we discussed the conditions required for the experimental implementations of the processes. Thus, our work paves the way to producing heralded single photons with high purity and yield in SPDC sources.
Summary form only given. Parametric downconversion (PDC) allows the generation of highly coherent, spectrally pure single photons for quantum photonics. In a typical heralded PDC source, the signal photon emerges in a spectrally mixed state due to strong (anti)correlation in the joint spectrum of PDC photon pairs.One method for reducing spectral correlations is spectral filtering, but this compromises the heralding efficiency and the brightness of the source. A more sophisticated method for increasing the heralded photon purity is group-velocity matching, which works by erasing part of the timing information between the pump and PDC photons. What group-velocity matching cannot address, however, are the remaining correlations in the joint spectrum that come from the sinc-shaped phase-matching function (PMF) typical to standard PDC crystals. Further source engineering is therefore required to remove these correlations. Several studies have introduced domain-engineering techniques for shaping the phase matching function (PMF) in periodically poled crystals to improve single photon purities [1-4]. We present a new technique for tailoring crystal nonlinearities which combines the advantages of a deterministic method for domain engineering [4] and an annealing method developed for classical applications in higher-harmonic generation [5]. In our method, we first choose each domain orientation such that the generated field amplitude along the crystal matches the target field amplitude obtained by integrating the desired nonlinearity profile. Using a one-block structure instead of a two-blocks structure (as in [4]) results in a higher flexibility of the algorithm in tracking the target function and yields to more accurate results. We then use an annealing algorithm to slightly vary the width of each domain, further improving the effective PMF. Our technique outperforms its predecessors, particularly for short crystals, leading to high single photon purities, as shown in Fig.1. We experimentally characterise our method through a high-precision measurement of multiphoton interference between two heralded photons generated by two independent sources.We also notice that by considering a complex target field amplitude function it is possible to generalise the algorithm in [5] to any constant domain width (not necessarily equal to the coherence length), leading to a better approximation of the desired phase matching function, especially in the very short crystal regime. Moreover, tracking both the real and imaginary components of the target function allows us to approximate more exotic cases such as chirped nonlinearity profiles. Since scalable quantum photonics will require integrated architectures in which nonlinear processes are typically employed for single-photon generation, it will be interesting to explore new techniques similar to in-fibre Bragg grating structures which might yield quasi-periodic four-wave mixing and apply our algorithm to these new platforms.