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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Dispersion sensitivity of amplitude and phase modulated time-energy entangled photons

Christof Bernhard, Bänz Bessire, André Stefanov, Thomas Feurer

Published May 1, 2013• 0 citations
Publisher

Abstract

We demonstrate spectral amplitude and phase modulation of time-energy entangled photon pairs by means of a spatial light modulator (SLM) [1]. Coincidences are detected by sum frequency generation in a nonlinear crystal which has been applied in several experiments as an ultrafast coincidence detection method to temporally resolve entangled photons on a timescale of fs [2,3]. By taking into account the properties of the detection crystal, we derive an expression for the up-converted frequency signal in the form of a second-order correlation function G(1)[3]. This detection scheme is in contrast to a perfect coincidence detection described by the fourth-order correlation function G(2). However, in former two photon shaping experiments [1,2] the detected signal was compared to simulations based on G(2). We investigate here under which conditions the G(2)ceases to provide an accurate description of the measurements.

DOI
10.1109/cleoe-iqec.2013.6801672

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We demonstrate spectral amplitude and phase modulation of time-energy entangled photon pairs by means of a spatial light modulator (SLM) [1]. Coincidences are detected by sum frequency generation in a nonlinear crystal which has been applied in several experiments as an ultrafast coincidence detection method to temporally resolve entangled photons on a timescale of fs [2,3]. By taking into account the properties of the detection crystal, we derive an expression for the up-converted frequency signal in the form of a second-order correlation function G(1)[3]. This detection scheme is in contrast to a perfect coincidence detection described by the fourth-order correlation function G(2). However, in former two photon shaping experiments [1,2] the detected signal was compared to simulations based on G(2). We investigate here under which conditions the G(2)ceases to provide an accurate description of the measurements.
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.
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.
We experimentally demonstrate shaping of the two-photon wave function of entangled-photon pairs, utilizing coherent pulse-shaping techniques. By performing spectral-phase manipulations we tailor the second-order correlation function of the photons exactly like a coherent ultrashort pulse. To observe the shaping we perform sum-frequency generation with an ultrahigh flux of entangled photons. At the appropriate conditions, sum-frequency generation performs as a coincidence detector with an ultrashort response time (approximately 100 fs), enabling a direct observation of the two-photon wave function. This property also enables us to demonstrate background-free, high-visibility two-photon interference oscillations.
Nonlinear optics has had extensive application into a vast array of scientific fields. One such nonlinear process, two-photon absorption (TPA), has had a wildly successful \nadoption into the field of biological imaging and microscopy. As far and as fast as this field is progressing, limitations stemming from the use of ultrafast lasers are starting to appear. \nIn this work, an alternative nonclassical light source will be motivated for the application \nof low photon-flux two-photon microscopy. The origin and properties of the chosen \nnonclassical source, spontaneous parametric downconversion (SPDC), will be discussed along with the spatial and spectral properties modelled. Nonlinear processes such as TPA and sum frequency generation (SFG) will be viewed as "ultrafast coincidence measurements" of two photons arriving at a molecule within the time window of excitation. These ultrafast coincidence measurements will be viewed in an alternative manner: in terms of the second-order coherence from a light source. This degree of second-order coherence can be subdivided into two categories arising from different combinations of correlations within and between entangled photon pairs. Of interest, the energy-time correlations within the photon pair allow for enhancements in ultrafast coincidence rates over coherent light sources. The makings of an experimental setup to demonstrate enhanced rates from ultrafast two-photon coincidences taking place in SFG in a nonlinear crystal will be discussed.
Single photons provide a natural platform for quantum communication and quantum networking, as they can be entangled in many degrees of freedom and maintain coherence over long-distance links. However, while their minimal interactions with the environment isolate them from detrimental noise, it can make them difficult to measure and manipulate. In particular, manipulation on the ultrafast timescale is necessary to fully exploit the energy-time (or spectral) photonic degree of freedom. Full control over the spectral properties of single photons is key to many quantum technologies and opens the door to natural high-dimensional quantum encodings. \n \nIn this thesis, we theoretically and experimentally examine the use of nonlinear optical processes mediated by strong laser pulses as a method to control the spectral properties of ultrafast single photons. By mixing single-photon pulses with strong escort pulses that have been shaped through dispersion in a nonlinear crystal, the shape of the escort is imprinted on the photon, resulting in a custom-tailored upconverted pulse. We theoretically examine this process for quadratic spectral phases and show that it has the potential to be simultaneously effective and efficient for the customization of single-photon spectral waveforms, and can be performed in an entanglement-conserving manner. \n \nWe then experimentally demonstrate the range of this technique through three applications. First, we show that sum-frequency generation with shaped pulses can be used to coherently measure time-bin encoded photons with bin separations on the order of picoseconds, well below the timing resolution of our detectors. Secondly, we show that this technique can be adapted to convert a train of pulses to a frequency comb, which can be read out in a straightforward manner using diffraction-based spectrometry. We also show here that this process can be performed in a polarization-maintaining fashion, and demonstrate that entanglement with a partner photon is conserved with high fidelity. Finally, we show that this process can be viewed as a time lens, which modulates a temporal waveform in an analogous fashion to a lens focusing a beam of light. We apply the time lens to a photon from an energy-time entangled pair, and show negative magnification of the joint spectrum through a reversal of the spectral correlations. Such processes could find application in quantum state engineering and high-speed single-photon measurement.
Energy-time entangled photon pairs remain tightly correlated in time when the photons are passed through equal magnitude, but opposite in sign, dispersion. A recent experimental demonstration has observed this effect on ultrafast time scales using second-harmonic generation of the photon pairs. However, the experimental signature of this effect does not require energy-time entanglement. Here, we demonstrate a direct analogue to this effect in narrow-band second-harmonic generation of a pair of classical laser pulses under similar conditions. Perfect cancellation is observed for fs pulses with dispersion as large as 850 fs2{}^{2}2, comparable to the quantum result, but with an 1013{10}^{13}1013-fold improvement in signal brightness.