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arXiv:1102.2465 · Optics Express

Control of quantum transverse correlations on a four-photon system

Pierre-Louis de Assis, M. A. D. Carvalho, L. P. Berruezo, J. Ferraz, I. F. Santos, Fabio Sciarrino, Sebastião Pádua

Published Feb 11, 2011• 13 citations
arXivHTMLPDF

Abstract

Control of spatial quantum correlations in bi-photons is one of the fundamental principles of Quantum Imaging. Up to now, experiments have been restricted to controlling the state of a single bi-photon, by using linear optical elements. In this work we demonstrate experimental control of quantum correlations in a four-photon state comprised of two pairs of photons. Our scheme is based on a high-efficiency parametric downconversion source coupled to a double slit by a variable linear optical setup, in order to obtain spatially encoded qubits. Both entangled and separable pairs have been obtained, by altering experimental parameters. We show how the correlations influence both the interference and diffraction on the double slit.

DOI
10.1364/oe.19.003715

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Control of spatial quantum correlations in bi-photons is one of the fundamental principles of Quantum Imaging. Up to now, experiments have been restricted to controlling the state of a single bi-photon, by using linear optical elements. In this work we demonstrate experimental control of quantum correlations in a four-photon state comprised of two pairs of photons. Our scheme is based on a high-efficiency parametric downconversion source coupled to a double slit by a variable linear optical setup, in order to obtain spatially encoded qubits. Both entangled and separable pairs have been obtained, by altering experimental parameters. We show how the correlations influence both the interference and diffraction on the double slit.
We present an experimental study of the nonclassical correlations of a pair of spatial qubits formed by passing two down-converted photons through a pair of double slits. After confirming the entanglement generated in our setup by quantum tomography using separate measurements of the slit images and the interference patterns, we show that the complete Hilbert space of the spatial qubits can be accessed by measurements performed in a single plane between the image plane and the focal plane of a lens. Specifically, it is possible to obtain both the which-path and the interference information needed for quantum tomography in a single scan of the transversal distribution of photon coincidences. Since this method can easily be extended to multidimensional systems, it may be a valuable tool in the application of spatial qudits to quantum-information processes.
High-dimensional entanglement in the form of transverse spatial correlation between a pair of photons generated via spontaneous parametric downconversion is not only a valuable resource in many academic and real-life applications but also provides access to several intriguing quantum phenomena. One such non-intuitive phenomenon is phase entanglement, in which the biphoton state is correlated in the complex phase of its wavefunction. This state, which emerges during the propagation of the biphoton wavefunction, exhibits neither position nor momentum correlation, yet retains full entanglement. In this work, we experimentally explore this state in two distinct ways. The first is by tracking the vanishing spatial photon number correlation over propagation distances lying in [0,∞)\left[0,\infty\right)[0,∞), folded into a finite range using single-lens imaging. These observations show excellent agreement with our theoretical predictions based on the Double Gaussian (DG) approximation of the biphoton state. The second approach involves performing a two-photon interference experiment using a double slit and this state, which reveals the correlated phase front. We show, both theoretically and experimentally, that the observed two-photon interference structure is markedly different from that produced by position-correlated photons, as confirmed by computing the joint probability distribution of photons (JPD) and related metrics. Such interference using phase-entangled light has not been attempted before and opens avenues for advanced experiments and applications in the field of spatial entanglement.
This dissertation contains scientific research within the realm of quantum optics, which is a branch of physics. An experimental and theoretical study is made of two-photon interference phenomena in various optical systems. Spatially entangled photon pairs are produced via the nonlinear optical process of spontaneous parametric down-conversion. These entangled photons are then passed through different optical systems to study various aspects of two-photon interference. Firstly, an experimental analysis is made of the high-dimensional entanglement that is present in the orbital angular momentum of the photons. Secondly, we present a comprehensive description of two-photon quantum interference behind a double slit. We demonstrate how to control the quantum correlations and present the first observations of complete two-photon diffraction patterns behind a double slit. Finally, we present pioneering experiments on spatially entangled two-photon states that are scattered of random media. We have observed and theoretically analyzed the structure in the random two-photon interference patterns called two-photon speckle patterns. Spatial entanglement gives two-photon speckle a much richer structure than ordinary one-photon speckle. Our experiments also demonstrate a two-photon interference phenomenon that survives averaging over different realizations of disorder. The latter results are closely related to bosonic, fermionic, and anyonic particle exchange symmetries.
This paper demonstrates the engineering of spatially entangled two-photon states behind a double slit by tailoring the incident pure two-photon state. We experimentally characterize many different two-photon states by measuring their complete two-photon interference patterns in the far field of the double slit. Spatial entanglement right behind the double slit can reside in either the modulus or the phase of the two-photon field. The balance between these two types of entanglement is fully controlled by experimentally utilizing the phase-front curvatures of the pump beam and the phase-matching profile. We project either a far-field image or a magnified near-field image of the two-photon source onto the double slit. Our theoretical analysis shows how the two-photon interference pattern behind the double slit effectively acts as a phase-sensitive probe of the incident two-photon field profile. We thus present phase-sensitive measurements of the generated two-photon field profile probed in an image plane of the two-photon source.
Multi-particle entangled states are becoming more and more interesting for different applications in quantum information, such as quantum multi-particle teleportation, entangled based cryptography and quantum communication schemes based on multi-particle states, but also for fundamental reasons such as testing local realism by means of the Greenberger-Horne-Zeilinger states (GHZ) arguments . The advantage of multiparticle entanglement versus the most common two particle one lies in the fact that the greater the number of particles involved in the entangled state, the more clearly the quantum effects are exhibited. Our final goal is to exploit the multi-photon entangled states for quantum metrology. By the interaction of those states with nanostructures (mostly nanoholes, but in a future also nanospheres), we expect to reach sub-wavelength sensitivity phase measurements beating the Standard Quantum Limit as well as to detect plasmonic effects. In this thesis we present our work consisting on designing and building an experimental setup for the generation of states of 4-photon entangled in the transverse linear momentum. In the first part we explain some basics in the form of a technical introduction. We then adapt a general theoretical model to our particular case, explaining the physics of the process of generation of entangled states of photons. We proceed explaining the details of our setup, as well as the procedure of measurement. We then present the results of our tests in a "standard" 2-photon regime to show the correct functioning of the setup itself. Some more sophisticated measurements using structured light in the form of a first-order Hermite-Gaussian mode has been performed to generate entanglement in higher spatial modes are also presented. We conclude with theoretical and experimental details regarding the 4-photon experiments feasible with our setup. Our source is based on Spontaneous Parametric Down-Conversion (SPDC). In the last two decades it has been extensively studied for the generation of two-photon entangled states, since Kwiat et al. published in 1995 the new scheme based on polarization entangled photons. Most of the studies regarding entangled states involving more than two photons are indeed based on quantum correlations in the polarization or in the path of the down converted beams. The great advantage of entangling a spatial degree of freedom (as we do) is related to the dimensionality of the Hilbert space in which the state is defined. In the particular case of linear momentum, which is a continuous variable, we are dealing with infinite dimensions. Since in each dimension of the state one quanta of information can be encoded, the advantage of having multidimension entanglement for the field of quantum communication and computing is clear. The specs of our setup include a periodically-poled KTP crystals offering high conversion efficiency and cut for type-0 SPDC. The photons generated are well known to be inherently entangled in different degrees of freedom such as polarization, energy-time, linear momentum, and orbital angular momentum. Since each single SPDC event generates one photon pair, in order to reach four photon we entangle two consecutive SPDC events per each state. Furthermore, it is possible to manipulate (to enhance) the dimensionality of the entanglement by properly tailoring the pump spatial profile. The key point for the generation of four-photon entangled states is that, under some conditions, two consecutive pairs generated via SPDC cannot be described as two independent pairs but necessarily as a four-photon state showing genuine entanglement. This can happen when using a pulsed laser to generate the entangled photons; in particular, in the regime in which the coherence time of the down-converted photons τc is (much) longer than the temporal length of the pumping pulse Δt. In this condition the emission of a second pair is stimulated by the presence of the first one. That effect can be ultimately seen as a constructive multi-particle interference effect, the deep origin of which has to be sought in the boson statistic of photons.
Two-photon states generated through degenerate spontaneous parametric downconversion (SPDC) can exhibit sharp correlations in the transverse spatial coordinates. This property leads to unique free-space propagation features. Here, we show that a phase object placed in the image plane of the source affects the free space propagation of the SPDC in a way that is mathematically analogous to the Fresnel diffraction of a first-order coherent source. This effect can be observed via the extraction of correlation images. We demonstrate this prediction with an experiment where the diffraction of correlated bi-photons is detected using an event-based camera. The results allow us to reconstruct the phase structure of the sample via non-interferometric phase retrieval methods. We verify that the retrieved phase patterns exhibit a factor of two contrast enhancement due to the probe’s two-photon nature. Our findings offer a proof of principle application for quantitative phase imaging, particularly in regimes where low light conditions are required to prevent photo-damage and, at the same time, is desirable to preserve high resolution, contrast, and low noise.