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Spontaneous Parametric Down-Conversion and Quantum Entanglement

Jesse Catalano

Published Jun 6, 2014• 1 citation
Publisher

Abstract

Quantum entanglement has been a topic of much research in modern physics, and an application in quantum computing is envisioned. This thesis address the use of polarization entangled photon pairs produced by spontaneous parametric down-conversion (SPDC) in entanglement transfer process and quantum computing. The simplicity of SPDC entanglement relative to other quantum phenomena is first emphasized by developing a complete classical theory of the photon-crystal interactions characteristic of SPDC. The methods of achieving polarization superposition via the Type-I and Type-II SPDC are described. A combination of superposition and polarization correlation between down-converted photons is shown to violate Bell’s inequality, thus revealing the entangled nature of the photon pairs. Finally, the possibility of controlling entangled photons through the manipulation of surface plasmons is highlighted as a way to transfer entanglement from photons to material particles.

DOI
10.15760/honors.474

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Quantum entanglement has been a topic of much research in modern physics, and an application in quantum computing is envisioned. This thesis address the use of polarization entangled photon pairs produced by spontaneous parametric down-conversion (SPDC) in entanglement transfer process and quantum computing. The simplicity of SPDC entanglement relative to other quantum phenomena is first emphasized by developing a complete classical theory of the photon-crystal interactions characteristic of SPDC. The methods of achieving polarization superposition via the Type-I and Type-II SPDC are described. A combination of superposition and polarization correlation between down-converted photons is shown to violate Bell’s inequality, thus revealing the entangled nature of the photon pairs. Finally, the possibility of controlling entangled photons through the manipulation of surface plasmons is highlighted as a way to transfer entanglement from photons to material particles.
This thesis deals with the production of entangled photons using spontaneous parametric down-conversion (SPDC). We start with a short overview of some important theoretical concepts. First we provide a brief reminder of the theory of entanglement. We then discuss how the state of quantum systems can be determined using quantum state tomography. We also explain SPDC, the physical process which we use to produce entangled photons. Finally, we give an overview of the methods which have been used to produce entangled photons in the past, both for two- and three-photon entanglement. \n \nThe first experiment is the design of an efficient source of entangled photon pairs based on a polarizing Sagnac interferometer configuration. With this configuration, we can use quasi-phasematched materials which allow for higher efficiencies than standard bulk nonlinear materials. The source is pumped by a low-power continuous-wave laser diode, and produces degenerate photon pairs at 809nm. It has a spectral brightness of 87,500 pairs/(s mW nm), and the fidelity of the produced quantum states with a Bell state is 98.9%. The source is used for experiments in quantum key distribution, cluster state quantum computing, remote state preparation, state discrimination, and entanglement-enhanced classical communication. \n \nThe second experiment discussed in this thesis is the generation of photon triplets using cascaded SPDC. In this experiment, a primary SPDC source is pumped with a low-power, continuous-wave laser diode, producing photon pairs. Single photons from these pairs serve as the pump for a second down-conversion, resulting in photon triplets. This is the first demonstration of the direct production of photon triplets, and the first observation of SPDC at the single photon level. This method could potentially be used to produce entangled photon triplets without post-selection, and as a source of triggered Bell pairs.
We present a theoretical and experimental study of preparing maximally entangled two-photon polarization states, or Bell states, using femtosecond-pulse-pumped spontaneous parametric down-conversion (SPDC). First, we show how the inherent distinguishability in femtosecond-pulse-pumped type-II SPDC can be removed by using an interferometric technique without spectral and amplitude postselection. We then analyze the recently introduced Bell-state preparation scheme using type-I SPDC. Theoretically, both methods offer the same results, however, type-I SPDC provides experimentally superior methods of preparing Bell states in femtosecond-pulse-pumped SPDC. Such a pulsed source of highly entangled photon pairs is useful in quantum communications, quantum cryptography, quantum teleportation, etc.
Spontaneous parametric down-conversion (SPDC) is a reliable platform for entanglement generation. Routinely, a coherent laser beam is an essential prerequisite for pumping the nonlinear crystal. Here we break this barrier to generate polarization entangled photon pairs by using a commercial light-emitting diode (LED) source to serve as the pump beam. This effect is counterintuitive, as the LED source is of extremely low spatial coherence, which is transferred during the down-conversion process to the biphoton wavefunction. However, the type-II phase-matching condition naturally filters the specific frequency and wavelength of LED light exclusively to participate in SPDC such that localized polarization Bell states can be generated, regardless of the global incoherence over the full transverse plane. In our experiment, we characterize the degree of LED light-induced polarization entanglement in the standard framework of the violation of Bell inequality. We have achieved the Bell value S=2.33±0.097S=2.33\pm 0.097S=2.33±0.097, obviously surpassing the classical bound S=2S=2S=2 and thus witnessing the quantum entanglement. Our work can be extended to prepare polarization entanglement by using other natural light sources, such as sunlight and bio-light, which holds promise for electricity-free quantum communications in outer space.
Quantum states of photons such as entangled and single photons are indispensable components for applications in optical quantum information processing. Being able to generate and manipulate quantum states of photons on a chip is a crucial step towards realizing real-world quantum information processing systems such as an optical quantum computer. In this thesis, theoretical and experimental research was carried out for on-chip generation of quantum states of photons via the nonlinear process of spontaneous parametric down-conversion (SPDC), including polarization entangled photons, hyperentangled photons and heralded pure single photons. A majority of the study was based on III-V semiconductor AlGaAs, which could lead to monolithic integration of pump lasers and enable electrically pump sources operating at room temperature. The generation of cross-polarized entangled photons via a type-II SPDC in an AlGaAs Bragg reflection waveguide (BRW) was first investigated. The lack of material birefringence enables the direct generation of wavelength-multiplexed polarization entangled photons with a concurrence of at least 0.77 in a bandwidth of 95 nm. Second, a technique using concurrent type-0 and type-I processes on an AlGaAs chip to generate polarization entangled photon was developed. This technique allows the generation of both co-polarized and cross-polarized entangled photons on the same chip without the need of off-chip compensation, interferometer and bandpass filter. Third, a technique of generating hyperentangled photons on an AlGaAs chip was developed by utilizing spatial modes of different guiding mechanisms. High quality entanglement could be achieved with bandpass filtering of a few nanometers without off-chip phase compensation. Four, a generic technique using nonlinear photonic nanowires to engineer two-photon quantum states was proposed. Via dispersion engineering which controls the group velocity of each mode, maximally entangled polarization entangled photons and pure heralded single photons can be generated on-chip. Design examples were applied to III-V semiconductor and ferroelectric materials. Last, a strategy to enhance the bandwidths of wavelength conversion and SPDC spectrum was developed by tapering the waveguides. Combined with further integration of pump lasers, photonic circuits and detectors, the techniques developed in this thesis provides a viable route to achieve fully integrated generation and manipulations of photonic quantum qubits.
Spontaneous parametric down-conversion (SPDC) is a reliable platform for entanglement generation. Routinely, a coherent laser beam is an essential prerequisite for pumping the nonlinear crystal. Here we break this barrier to generate polarization-entangled photon pairs by using a commercial light-emitting diode (LED) source to serve as the pump beam. This effect is counterintuitive, as the LED source is of extremely low spatial coherence, which is transferred during the down-conversion process to the biphoton wave function. However, the type-II phase matching condition naturally filters the specific frequency and wavelength of LED light exclusively to participate in SPDC such that localized polarization Bell states can be generated, regardless of the global incoherence over the full transverse plane. In our experiment, we characterize the degree of LED light-induced polarization entanglement in the standard framework of the violation of Bell's inequality. We achieve the Bell value $S=2.33\ifmmode\pm\else\textpm\fi{}0.097$, obviously surpassing the classical bound S=2S=2S=2 and thus witnessing the quantum entanglement. Our work can be extended to prepare polarization entanglement by using other natural light sources, such as sunlight and biolight, which holds promise for electricity-free quantum communications in outer space.