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arXiv:1105.3956 · Physical Review A

Classical analog for dispersion cancellation of entangled photons with local detection

Robert Prevedel, K. M. Schreiter, Jonathan Lavoie, Kevin J. Resch

Published Nov 22, 2011• 14 citations
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Abstract

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 fs${}^{2}$, comparable to the quantum result, but with an ${10}^{13}$-fold improvement in signal brightness.

DOI
10.1103/physreva.84.051803

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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.
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 directly 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 fs2^22, comparable to the quantum result, but with an 101310^{13}1013-fold improvement in signal brightness.
Recently the engineering of the entanglement for photon pairs generated during the spontaneous parametric down conversion process (SPDC) can be achieved via manipulation of pump wavelength behind a \c{hi}(2)-based type II SPDC process [1]. Such effect is used in this paper for demonstration of non-classical dispersion cancellation phenomenon in both local and nonlocal detections, theoretically. The following results are analytically achieved: I) For local detection, if narrow pump laser (highly entangled photons) are used, the dispersive broadening cancelation is directly depends on the degree of entanglement. The higher entanglement degree, the more compensation occurs. The results indicate that by increasing the FWHM of the pump the impact of the entanglement degree is decreased in such a way that for a pump with FWHM=4 nm the entanglement has no effect on the broadening. Therefore, the dispersive broadening is only depends on the temporal walk-off between generated photon pairs and the pump. II) For nonlocal detection, it is also shown that entanglement cancels the dispersive broadening if and only if each of the generated paired photons propagate through dispersive material with identical length with opposite group velocity sign.
Energy-time entangled photons are critical in many quantum optical phenomena and have emerged as important elements in quantum information protocols. Entanglement in this degree of freedom often manifests itself on ultrafast time scales, making it very difficult to detect, whether one employs direct or interferometric techniques, as photon-counting detectors have insufficient time resolution. Here, we implement ultrafast photon counters based on nonlinear interactions and strong femtosecond laser pulses to probe energy-time entanglement in this important regime. Using this technique and single-photon spectrometers, we characterize all the spectral and temporal correlations of two entangled photons with femtosecond resolution. This enables the witnessing of energy-time entanglement using uncertainty relations and the direct observation of nonlocal dispersion cancellation on ultrafast time scales. These techniques are essential to understand and control the energy-time degree of freedom of light for ultrafast quantum optics.
We derive an inequality bounding the strength of temporal correlations for a pair of light beams prepared in a separable state and propagating through dispersive media with opposite signs of group-velocity dispersion. The presented inequality can be violated by entangled states of light, such as photon pairs produced in spontaneous parametric down-conversion. Because the class of separable states covers the entire category of classical fields as a particular case, this result provides an unambiguously quantum feature of nonlocal dispersion cancellation that cannot be reproduced within the classical theory of electromagnetic radiation.
We demonstrate dispersion cancellation of entangled photons for arbitrary spectral orders, generalizing Franson cancellation typically considered in second order alone. Employing ultrafast coincidence detection based on sum-frequency generation in a periodically poled lithium niobate waveguide with a record-high pair conversion efficiency of 10(-5), we verify cancellation of dispersion up to fifth order. Cancellation of odd-order phase is experimentally shown to require identical signal and idler dispersion coefficients, in contrast to even-order phase, which cancels with opposite signs. These results are especially important for future work on ultrabroadband biphotons.
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.