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The Role of Ultrafast Shaped Pulses in Classical and Quantum Optics

Ian A. Walmsley, Anderson, Matthew, Konrad Banaszek, Erdmann, Reinhardt, Alfred B. U’Ren

Published May 26, 2003• 0 citations
OpenAlex

Abstract

This report presents the results of studies of the generation and characterization of Electron Paramagnetic Resonance (EPR) and the entangled bi-photon state using optical parametric downconversion (PDC) with ultrashort-duration pump pulses. The authors have advanced a method of generating photon pairs that are highly entangled in their continuous space-time degree of freedom and have developed theoretical tools for quantifying the degree of entanglement for this and other continuum-variable systems. In addition, they have shown for the first time the violation of a Bell-type inequality for the EPR state generated in parametric downconversion. The studies also show, theoretically, that it is possible to design sources such that the photon entanglement causes complete nonlocal cancellation of dispersion of arbitrary order, and demonstrate the increase in visibility using properly mode-matched photons. In addition, the authors have analyzed the effects of nonmeasured degrees of freedom of photons generated by PDC on the basic elements of linear optical quantum logic gates, such as a prototypical Bell-state analyzer. The results have implications for novel methods of quantum communications using both entangled and unentangled modes and photons. A list of 13 related manuscripts is included.

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Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behaviour. To date, the theoretical models of filtered PDC, however, only account for filtering in the low gain regime, where only a few photon-pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and present a rigorous theoretical model for filtered type-II PDC. Our theoretical investigations reveal that filtering a multimode type-II PDC state, followed by a careful optimization of the measurement basis, effectively achieves a single-mode behaviour and further enables the generation of single-mode EPR-entanglement. Considering the ever increasing brightness of PDC sources our developed theoretical framework, enables the accurate description of filtered PDC in quantum optical experiments.

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Ultrafast quantum light pulses with durations of 1ps and below show great promise as information carriers in quantum communication and computation. In future they may also be used to probe physical processes at ultrashort timescales with a resolution beyond the limits of Heisenberg uncertainty. This thesis focuses on the creation and manipulation of quantum light pulses with second order nonlinear optical processes in optical waveguides. In chapter 1. Introduction, we lead the reader towards this work's topic by giving a brief qualitative overview over the EPR paradox, quantum entanglement, three-wave-mixing and quantum light pulses. Chapter 2. Basic concepts familiarizes the reader with the physical concepts and mathematical tools underlying this thesis. In chapter 3. Spectral engineering, we discuss the requirements to produce separable photon pair states with group velocity matching and examine several nonlinear materials widely used for optical waveguide inscription for their suitability to group velocity matching in the telecom wavelength regime. In chapter 4. A PP-KTP waveguide as parametric downconversion source, we give the basic spontaneous parametric downconversion source setup, as well as some initial measurements to characterize the single photon detectors, to demonstrate the production of correlated photons, and to determine the phasematching properties of the PP-KTP source. In the following chapter, 5. Fiber spectrometer, we present the single-photon fiber spectrometer. We discuss the experimental setup and calibration of the device, and measure the joint spectrum of photon pairs from our PP-KTP source. Finally, we investigate the behavior of a joint spectrum measurement of a high mean photon number source with binary detectors. In 6. Two-mode squeezed vacuum source, we characterize spectral correlations of an ultrafast SPDC source with the second order correlation function g². We present the g² measurement results and show that we can control the spectral correlations to produce a two-mode squeezed vacuum state of light. We then determine the mean photon number and gain of the source. 7. Quantum pulse gate: While the previous chapters focus on the creation and characterization of ultrafast quantum pulses of light, we now propose a way to manipulate the mode structure of a given quantum light state. We discuss the concept of an active optical filter sensitive to spectral/temporal pulse shape: The quantum pulse gate. In the final chapter 8. Conclusion and outlook, we recapitulate the main results of this thesis and provide a few pointers towards possibilities for future research building on it.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 7, 2009•0 citations

Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime

Andreas Christ, Benjamin Brecht, Wolfgang Mauerer +1 more

Frequency conversion (FC) and type-II parametric down-conversion (PDC) processes serve as basic building blocks for the implementation of quantum optical experiments: type-II PDC enables the efficient creation of quantum states such as photon-number states and Einstein–Podolsky–Rosen (EPR)-states. FC gives rise to technologies enabling efficient atom–photon coupling, ultrafast pulse gates and enhanced detection schemes. However, despite their widespread deployment, their theoretical treatment remains challenging. Especially the multi-photon components in the high-gain regime as well as the explicit time-dependence of the involved Hamiltonians hamper an efficient theoretical description of these nonlinear optical processes. In this paper, we investigate these effects and put forward two models that enable a full description of FC and type-II PDC in the high-gain regime. We present a rigorous numerical model relying on the solution of coupled integro-differential equations that covers the complete dynamics of the process. As an alternative, we develop a simplified model that, at the expense of neglecting time-ordering effects, enables an analytical solution. While the simplified model approximates the correct solution with high fidelity in a broad parameter range, sufficient for many experimental situations, such as FC with low efficiency, entangled photon-pair generation and the heralding of single photons from type-II PDC, our investigations reveal that the rigorous model predicts a decreased performance for FC processes in quantum pulse gate applications and an enhanced EPR-state generation rate during type-II PDC, when EPR squeezing values above 12 dB are considered.

arXiv:1210.8342•New Journal of Physics•May 24, 2013•151 citations
This report presents the results of studies of the generation and characterization of Electron Paramagnetic Resonance (EPR) and the entangled bi-photon state using optical parametric downconversion (PDC) with ultrashort-duration pump pulses. The authors have advanced a method of generating photon pairs that are highly entangled in their continuous space-time degree of freedom and have developed theoretical tools for quantifying the degree of entanglement for this and other continuum-variable systems. In addition, they have shown for the first time the violation of a Bell-type inequality for the EPR state generated in parametric downconversion. The studies also show, theoretically, that it is possible to design sources such that the photon entanglement causes complete nonlocal cancellation of dispersion of arbitrary order, and demonstrate the increase in visibility using properly mode-matched photons. In addition, the authors have analyzed the effects of nonmeasured degrees of freedom of photons generated by PDC on the basic elements of linear optical quantum logic gates, such as a prototypical Bell-state analyzer. The results have implications for novel methods of quantum communications using both entangled and unentangled modes and photons. A list of 13 related manuscripts is included.
Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behaviour. To date, the theoretical models of filtered PDC, however, only account for filtering in the low gain regime, where only a few photon-pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and present a rigorous theoretical model for filtered type-II PDC. Our theoretical investigations reveal that filtering a multimode type-II PDC state, followed by a careful optimization of the measurement basis, effectively achieves a single-mode behaviour and further enables the generation of single-mode EPR-entanglement. Considering the ever increasing brightness of PDC sources our developed theoretical framework, enables the accurate description of filtered PDC in quantum optical experiments.
Ultrafast quantum light pulses with durations of 1ps and below show great promise as information carriers in quantum communication and computation. In future they may also be used to probe physical processes at ultrashort timescales with a resolution beyond the limits of Heisenberg uncertainty. This thesis focuses on the creation and manipulation of quantum light pulses with second order nonlinear optical processes in optical waveguides. In chapter 1. Introduction, we lead the reader towards this work's topic by giving a brief qualitative overview over the EPR paradox, quantum entanglement, three-wave-mixing and quantum light pulses. Chapter 2. Basic concepts familiarizes the reader with the physical concepts and mathematical tools underlying this thesis. In chapter 3. Spectral engineering, we discuss the requirements to produce separable photon pair states with group velocity matching and examine several nonlinear materials widely used for optical waveguide inscription for their suitability to group velocity matching in the telecom wavelength regime. In chapter 4. A PP-KTP waveguide as parametric downconversion source, we give the basic spontaneous parametric downconversion source setup, as well as some initial measurements to characterize the single photon detectors, to demonstrate the production of correlated photons, and to determine the phasematching properties of the PP-KTP source. In the following chapter, 5. Fiber spectrometer, we present the single-photon fiber spectrometer. We discuss the experimental setup and calibration of the device, and measure the joint spectrum of photon pairs from our PP-KTP source. Finally, we investigate the behavior of a joint spectrum measurement of a high mean photon number source with binary detectors. In 6. Two-mode squeezed vacuum source, we characterize spectral correlations of an ultrafast SPDC source with the second order correlation function g². We present the g² measurement results and show that we can control the spectral correlations to produce a two-mode squeezed vacuum state of light. We then determine the mean photon number and gain of the source. 7. Quantum pulse gate: While the previous chapters focus on the creation and characterization of ultrafast quantum pulses of light, we now propose a way to manipulate the mode structure of a given quantum light state. We discuss the concept of an active optical filter sensitive to spectral/temporal pulse shape: The quantum pulse gate. In the final chapter 8. Conclusion and outlook, we recapitulate the main results of this thesis and provide a few pointers towards possibilities for future research building on it.
Frequency conversion (FC) and type-II parametric down-conversion (PDC) processes serve as basic building blocks for the implementation of quantum optical experiments: type-II PDC enables the efficient creation of quantum states such as photon-number states and Einstein-Podolsky-Rosen (EPR)-states. FC gives rise to technologies enabling efficient atom-photon coupling, ultrafast pulse gates and enhanced detection schemes. However, despite their widespread deployment, their theoretical treatment remains challenging. Especially the multi-photon components in the high-gain regime as well as the explicit time-dependence of the involved Hamiltonians hamper an efficient theoretical description of these nonlinear optical processes. In this paper, we investigate these effects and put forward two models that enable a full description of FC and type-II PDC in the high-gain regime. We present a rigorous numerical model relying on the solution of coupled integro-differential equations that covers the complete dynamics of the process. As an alternative, we develop a simplified model that, at the expense of neglecting time-ordering effects, enables an analytical solution. While the simplified model approximates the correct solution with high fidelity in a broad parameter range, sufficient for many experimental situations, such as FC with low efficiency, entangled photon-pair generation and the heralding of single photons from type-II PDC, our investigations reveal that the rigorous model predicts a decreased performance for FC processes in quantum pulse gate applications and an enhanced EPR-state generation rate during type-II PDC, when EPR squeezing values above 12 dB are considered.
We investigate the spatio-temporal structure of the biphoton entanglement in Parametric Down Conversion (PDC). In particular we study the biphoton amplitude at the output face of the nonlinear crystal (near-field) and we demonstrate its X-shaped geometry in the space-time dimensions, i.e. the non-factorability of the state with respect to spatial and temporal variables. Our analysis provides a precise and quantitative characterization of this structure in various regimes and types of phase matching of PDC. The key elements of novelty emerging from our analysis are the non-factorability of the state with respect to spatial and temporal variables, and the extreme relative localization of the entangled photons, both in space (few microns) and time (few femtoseconds). This extreme localization is connected to our ability to resolve the photon positions in the source near-field. The non factorability opens the possibility of tailoring the temporal entanglement by acting on the spatial degrees of freedom of twin photons.
Frequency conversion (FC) and type-II parametric down-conversion (PDC) processes serve as basic building blocks for the implementation of quantum optical experiments: type-II PDC enables the efficient creation of quantum states such as photon-number states and Einstein–Podolsky–Rosen (EPR)-states. FC gives rise to technologies enabling efficient atom–photon coupling, ultrafast pulse gates and enhanced detection schemes. However, despite their widespread deployment, their theoretical treatment remains challenging. Especially the multi-photon components in the high-gain regime as well as the explicit time-dependence of the involved Hamiltonians hamper an efficient theoretical description of these nonlinear optical processes. In this paper, we investigate these effects and put forward two models that enable a full description of FC and type-II PDC in the high-gain regime. We present a rigorous numerical model relying on the solution of coupled integro-differential equations that covers the complete dynamics of the process. As an alternative, we develop a simplified model that, at the expense of neglecting time-ordering effects, enables an analytical solution. While the simplified model approximates the correct solution with high fidelity in a broad parameter range, sufficient for many experimental situations, such as FC with low efficiency, entangled photon-pair generation and the heralding of single photons from type-II PDC, our investigations reveal that the rigorous model predicts a decreased performance for FC processes in quantum pulse gate applications and an enhanced EPR-state generation rate during type-II PDC, when EPR squeezing values above 12 dB are considered.