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Optics Letters

Arbitrary shaping of biphoton correlations using near-field frequency-to-time mapping

Hsuan‐Hao Lu, Ogaga D. Odele, Daniel E. Leaird, Andrew M. Weiner

Published Feb 6, 2018• 7 citations
Publisher

Abstract

Frequency-to-time mapping (FTM) is a technique used to mirror the spectral shape of an optical waveform in the time domain. The regular approach, based on the far-field condition, requires large amounts of dispersion for successful mapping. However, when the far-field condition is insurmountable for achieving a desired temporal profile, another technique, termed near-field FTM, can be employed to assist with the mapping. For the first time, we demonstrate a shaper-assisted near-field FTM using entangled photon pairs. By pre-modifying the two-photon spectral amplitude and phase before propagating the photon pairs through dispersion, we can achieve arbitrary temporal correlations in the near-field region.

DOI
10.1364/ol.43.000743

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Frequency-to-time mapping (FTM) is a technique used to mirror the spectral shape of an optical waveform in the time domain. The regular approach, based on the far-field condition, requires large amounts of dispersion for successful mapping. However, when the far-field condition is insurmountable for achieving a desired temporal profile, another technique, termed near-field FTM, can be employed to assist with the mapping. For the first time, we demonstrate a shaper-assisted near-field FTM using entangled photon pairs. By pre-modifying the two-photon spectral amplitude and phase before propagating the photon pairs through dispersion, we can achieve arbitrary temporal correlations in the near-field region.
Time-frequency entangled photons ("biphotons") exhibit joint spectral and temporal correlations that are unattainable with classical light. Besides being deployed for tests of quantum nonlocality, these photonic states are desirable for a unique range of applications that can significantly impact communications and computation. In this dissertation, we describe novel schemes based on spectral and temporal domain processing for manipulating and characterizing broadband biphotons. Implementing frequency-dependent filters, first, we present and demonstrate a technique for controlling the relative delay between a pair of entangled photons, relying on pump frequency tuning and the quantum concept of nonlocal dispersion cancellation. Next, we demonstrate near-field frequency-to-time mapping, a technique adopted from classical photonics, for arbitrary control of biphoton temporal correlations. Subsequently, we generate temporal correlation trains by creating biphoton frequency combs through programmable spectral amplitude shaping and demonstrate the temporal Talbot effect with entangled photons for the first time. Moreover, in the absence of fast single-photon detectors, we show how electro-optic phase modulation (originally a time-dependent operation) can be used to examine the coherence of biphoton frequency combs. Lastly, we introduce a scheme based on electro-optic intensity modulation, another time-domain operation, for improving the resolution in biphoton temporal correlation measurements. Overall, our body of work could provide additional insight into the manipulation and characterization of biphoton states, as well as contribute towards the improvement of quantum technologies.
The miniaturization of optical systems via integrated photonics is critical to the ultimate scalability and performance of photonic quantum processors, yet many longstanding optical signal processing capabilities—such as Fourier-transform pulse shaping—remain unrealized on chip. In this work, we demonstrate on-chip spectral shaping of entangled photons using a multichannel microring-resonator-based silicon photonic pulse shaper. Achieving line-by-line phase control on a 3 GHz grid for two frequency-bin-entangled qudits, the pulse shaper's fine spectral resolution enables control of nanosecond-scale temporal features, which are observed by direct coincidence detection of biphoton correlation functions that show excellent agreement with theory. This work marks a demonstration of biphoton pulse shaping using an integrated spectral shaper and holds significant promise for applications in photonic quantum information processing.
We demonstrate the generation of two-photon correlation trains based on spectral filtering of broadband biphotons. Programmable amplitude filtering is employed to create biphoton frequency combs, which when coupled with optical dispersion allows us to experimentally verify the temporal Talbot effect for entangled photons. Additionally, an alternative spectral phase-filtering approach is shown to significantly improve the overall efficiency of the generation process when a comb-like spectrum is not required. Our technique is ideal for the creation of tunable and high-repetition-rate biphoton states.
The entangled photon pairs (biphotons) produced from parametric down-conversion (PDC) in a χ(2)crystal are the key element for several quantum information and communication schemes. Recent theoretical investigations [1–2] have revealed the peculiar structure of the biphotonic correlation characterizing the entanglement of twin beams in the space-time domain. The biphotonic correlation in type I PDC is characterized in the near field by a X-shaped geometry, which turns out to be non-factorable in space and time, offering thus the relevant possibility of manipulating the temporal bandwidth of biphoton entanglement by acting on their spatial degrees of freedom. The name “X-entanglement” was coined to describe this geometry [1]. An other key feature which emerged is the extreme spatial and temporal localization of the biphotonic correlation, on the micrometer and femtosecond range, respectively.
We experimentally demonstrate amplitude and phase modulation of a time-energy entangled two-photon wave function. The entangled photons are produced by spontaneous parametric down-conversion, spectrally dispersed in an prism compressor, modulated in amplitude and/or phase, and detected in coincidence by sum-frequency generation. First, we present a Fourier optical analysis of the optical setup yielding an analytic expression for the resulting field distribution at the exit plane of the shaping apparatus. We then introduce amplitude and/or phase shaping and present results which can only be obtained through a combination of the two. Specifically, we use a shaper-based interferometer to measure the two-photon interference of an almost bandwidth-limited two-photon wave function.