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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Conditionally prepared photon and quantum imaging

Alexander I. Lvovsky, Thomas Aichele

Published Oct 19, 2004• 4 citations
Publisher

Abstract

We discuss a classical model allowing one to visualize and characterize the optical mode of the single photon generated by means of a conditional measurement on a biphoton produced in parametric down-conversion. The model is based on Klyshko's advanced wave interpretation, but extends beyond it, providing a precise mathematical description of the advanced wave. The optical mode of the conditional photon is shown to be identical to the mode of the classical difference-frequency field generated due to nonlinear interaction of the partially coherent advanced wave with the pump pulse. With this "nonlinear advanced wave model" most coherence properties of the conditional photon become manifest, which permits one to intuitively understand many recent results, in particular, in quantum imaging.

DOI
10.1117/12.561885

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We discuss a classical model allowing one to visualize and characterize the optical mode of the single photon generated by means of a conditional measurement on a biphoton produced in parametric down-conversion. The model is based on Klyshko's advanced wave interpretation, but extends beyond it, providing a precise mathematical description of the advanced wave. The optical mode of the conditional photon is shown to be identical to the mode of the classical difference-frequency field generated due to nonlinear interaction of the partially coherent advanced wave with the pump pulse. With this "nonlinear advanced wave model" most coherence properties of the conditional photon become manifest, which permits one to intuitively understand many recent results, in particular, in quantum imaging.
The advanced-wave picture is ``... an intuitive treatment of two-photon correlation with the help of the concept of an effective field acting upon one of the two detectors and formed by parametric conversion of the advanced wave emitted by the second detector ...'' [A. V. Belinskii and D. N. Klyshko, Sov. Phys. JETP 78, 259 (1994)]. This quote from Belinskii and Klyshko nicely describes the concept of the advanced-wave picture: an intuitive tool for designing and predicting results from coincidence-based two-photon experiments. Up to now, the advanced-wave picture has been considered primarily for the case of an ideal plane-wave pump beam and only for design purposes. Here we study the advanced-wave picture for a structured pump beam and in the context of stimulated emission provoked by an auxiliary input laser beam. This suggests stimulated parametric down-conversion as a useful experimental tool for testing the experimental sets designed with the advanced-wave picture. We present experimental results demonstrating the strategy of designing the experiment with advanced-wave picture and testing with stimulated emission.
Photons are among the most important carriers of quantum information owing to their rich degrees of freedom (DoFs), including various spatiotemporal structures. The ability to characterize these DoFs, as well as the hidden correlations among them, directly determines whether they can be exploited for quantum tasks. While various methods have been developed for measuring the spatiotemporal structure of classical light fields, owing to the technical challenges posed by weak photon flux, there have so far been no reports of observing such structures in their quantum counterparts, except for a few studies limited to correlations within individual DoFs. Here, we propose and experimentally demonstrate a self-referenced, high-efficiency, and all-optical method, termed 3D imaging of photonic wave packets, for comprehensive characterization of the spatiotemporal structure of a quantum light field, i.e., the biphoton spatiotemporal wave packet. Benefiting from this developed method, we successfully observe the spatial-spatial, spectral-spectral, and spatiotemporal correlations of biphotons generated via spontaneous parametric down-conversion, revealing rich local and nonlocal spatiotemporal structure in quantum light fields. This method will further advance the understanding of the dynamics in nonlinear quantum optics and expand the potential of photons for applications in quantum communication and quantum computing.
A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.
This thesis presents a study of photon generation and conversion processes in nonlinear optics. Our results extend beyond the first order perturbative regime, in which only pairs of photons are generated in spontaneous parametric down-conversion or four wave mixing. They also allow us to identify the limiting factors for achieving unit efficiency frequency conversion, and to correctly account for the propagation of bright nonclassical photon states generated in the nonlinear material. This is done using the Magnus expansion, which allows us to incorporate corrections due to time-ordering effects in the time evolution of the state, while also respecting the quantum statistics associated with squeezed states (in photon generation) and single photons or coherent states (in photon conversion). We show more generally that this expansion should be the preferred strategy when dealing with any type of time-dependent Hamiltonian that is a quadratic form in the creation and annihilation operators of the fields involved. Using the Magnus expansion, simple figures of merit to estimate the relevance of these time-ordering corrections are obtained. These quantities depend on the group velocities of the modes involved in the nonlinear process and provide a very simple physical picture of the interactions between the photons at different times. These time-ordering effects are shown to be important only when the photons and pump beam overlap within the nonlinear material for a significant amount of time. We also discuss the possibility of preparing Fock states with many photons using parametric down-conversion sources and realistic photon-number-resolving detectors. After discussing photon generation processes, we study photon conversion processes in which a nonlinear material and a classical strong pump field are used modify the frequency of a second incoming low-intensity field. We show that time-ordering effects limit the efficiency of this conversion process, re-examine strategies to get around this problem, and show that it should be possible to have a clear observation of modified upconversion probabilities due to these effects, and thus have an experimental demonstration of time-ordering effects in nonlinear optics.
Parametric down-conversion is a widely used source of nonclassical light in quantum optics and photonic quantum technologies. While stimulated parametric down-conversion with strong classical seeds is well studied, the elementary physical mechanism of stimulation by individual photons has remained largely unexplored experimentally. Here, we study continuous-wave, low-gain down-conversion seeded by an ultra-weak coherent field with an average photon number well below one per coherence time. By measuring third-order temporal correlations, we access the regime in which the single-photon component of the seed can stimulate the emission of a photon pair, giving rise to a temporally correlated three-photon event. We observe a clear enhancement that cannot be explained by spontaneous processes or accidental coincidences alone, providing time-domain evidence of the fundamental stimulation mechanism at the single-photon level. Beyond its fundamental significance, these results suggest new ways to characterize seed–PDC mode overlap, phase matching, and weak nonlinear coupling in regimes where bright stimulated-emission measurements are not appropriate. Multimode and interferometric extensions could enable correlation-based imaging and phase-sensitive spectroscopy.
Quantum properties of parametric amplification and frequency conversion of an optical image in coupled parametric interactions are analyzed for the case of a remote object. The coupled-wave interaction consists of a traditional process of parametric amplification in the high-frequency pump field accompanied by the frequency mixing of generated and pump waves. The photon number density and signal-to-noise ratio at the interacting frequencies are studied in the image plane at the output of the nonlinear frequency converter in the fixed pump field approximation. The degree of entanglement of optical images at frequencies above and below the pump frequency is investigated.