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Physical Review Letters

Nonlocal Pulse Shaping with Entangled Photon Pairs

Marco Bellini, Francesco Marin, Silvia Viciani, Alessandro Zavatta, F. T. Arecchi

Published Jan 31, 2003• 70 citations
Publisher

Abstract

Nonlocal shaping effects in the time or spectral profiles of an entangled photon pair emerging from a pulsed parametric down-converter are observed by spectrally or temporally filtering one of the twin beams. In particular, we demonstrate the appearance of fourth-order ("ghost") interference fringes in the spectrum of one beam conditioned by photodetection at the output of an unbalanced Michelson interferometer placed in the path of the other beam. The coherence time of the pump is the limiting factor for the sharpness of the details in the shaped biphoton spectrum.

DOI
10.1103/physrevlett.90.043602

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Nonlocal shaping effects in the time or spectral profiles of an entangled photon pair emerging from a pulsed parametric down-converter are observed by spectrally or temporally filtering one of the twin beams. In particular, we demonstrate the appearance of fourth-order ("ghost") interference fringes in the spectrum of one beam conditioned by photodetection at the output of an unbalanced Michelson interferometer placed in the path of the other beam. The coherence time of the pump is the limiting factor for the sharpness of the details in the shaped biphoton spectrum.
We present an experimental and theoretical analysis of the energy-time entanglement properties of a two-photon state generated by pulsed spontaneous parametric down-conversion. Different methods of spectral or temporal shaping of one of the two photons have allowed the observation of nonlocal modulations in the autocorrelation or in the spectrum of the other, by coincidence measurements. Either a monochromator or etalon filters have been used to shape the idler photon while observing the conditioned signal autocorrelation with a Michelson interferometer. Alternatively, the unbalanced interferometer has been used to shape the signal photon while measuring the conditioned idler spectrum with the monochromator. The role of the pump spectrum has been investigated by shaping it with additional filters. A theoretical treatment has allowed us to completely describe all the observed features as a function of the different experimental parameters.
The spatial correlation between down-converted photons allows for non-local spatial filtering when two-photon coincidences are registered. This allows one to non-locally control the visibility of interference fringes, to observe ghost images and interference patterns, and to "retrieve" a coherent quantum image from an incoherent field distribution. We show theoretically that non-local spatial filtering can lead to counter-intuitive effects when the pump beam is no longer given by a Gaussian profile. Namely, increased non-local filtering can actually decrease the visibility of interference fringes, contrary to what has been observed so far. We explain this behavior through the transverse spatial parity entanglement of the down-converted photons.
We study the generation of single-photon pulses with the tailored temporal shape via nonlocal spectral filtering. A shaped photon is heralded from a time-energy entangled photon pair upon spectral filtering and time-resolved detection of its entangled counterpart. We show that the temporal shape of the heralded photon is defined by the time-inverted impulse response of the spectral filter and does not depend on the heralding instant. Thus one can avoid postselection of particular heralding instants and achieve a substantially higher heralding rate of shaped photons as compared to the generation of photons via nonlocal temporal modulation. Furthermore, the method can be used to generate shaped photons with a coherence time in the ns-$\ensuremath{\mu}\mathrm{s}$ range and is particularly suitable to produce photons with the exponentially rising temporal shape required for efficient interfacing to a single quantum emitter in free space.
Summary form only given. Pairs of entangled photons display a complex quantum state that cannot be represented through a product of single-particle states. The spontaneous parametric down-conversion (SPDC) process, that takes place when a laser pulse pumps a second-order nonlinear crystal has become recently a convenient source of such nonclassical states of light in quantum optics experiments. Nonstationary effects are mainly observed when the pump pulse temporal duration is significantly shorter than the characteristic interaction time in the nonlinear crystal. We introduce a nonstationary theory of SPDC to describe the results of fourth-order quantum-interference experiments when no spectral filtering is applied to the down-converted fields. Experiments involving nonlinear SPDC crystals with three different lengths were performed. The ultraviolet laser pulses were obtained from a Ti:sapphire femtosecond laser with a second-harmonic generator. These pulses were used to pump nonlinear crystals to initiate the process of nonstationary spdc and generate orthogonally-polarized photon pairs. These pairs then went into a polarization interferometer, and the coincidence counts of the detectors at the two output ports of the interferometer were recorded.
Fourth-order interference patterns of biphotons generated by type-I spontaneous parametric downconversion are examined for beams with partial angular and spectral entanglement, both for degenerate and nondegenerate constituent photons. Two-beam configurations using a single beam-splitter interferometer and a Mach-Zehnder interferometer are explicitly studied, as are four-beam configurations using pairs of beam splitters and Mach-Zehnder interferometers. The interference pattern generally comprises a number of harmonic functions of the path-length difference with frequencies and visibilities that usually depend on direction, and may have a finite or infinite duration (fourth-order coherence length). The relation between the visibility and the spectral indistinguishability of the two beams is established. Certain components of the interference pattern are independent of direction so that they are not washed out by the use of apertures of finite size.
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.