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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Chronocyclic Wigner function of ultrafast time-frequency entangled parametric downconversion states

Benjamin Brecht, Christine Silberhorn

Published May 1, 2013• 0 citations
Publisher

Abstract

As of today, ultrafast waveguided parametric downconversion (PDC) sources are a well-established tool for the flexible generation of a large variety of quantum states. In the PDC process, the intrinsic broadband nature of the pump pulses gets translated into a rich spectral-temporal pulse-mode structure of the generated photon states [1]. This structure has already driven elaborate theoretical considerations, which aim for a complete understanding of the PDC process.

DOI
10.1109/cleoe-iqec.2013.6801659

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•May 26, 2003•0 citations
As of today, ultrafast waveguided parametric downconversion (PDC) sources are a well-established tool for the flexible generation of a large variety of quantum states. In the PDC process, the intrinsic broadband nature of the pump pulses gets translated into a rich spectral-temporal pulse-mode structure of the generated photon states [1]. This structure has already driven elaborate theoretical considerations, which aim for a complete understanding of the PDC process.
Pulsed parametric down-conversion (PDC) processes generate photon pairs with a rich spectral-temporal structure, which offer an attractive potential for quantum information and communication applications. We investigate the four-dimensional chronocyclic Wigner function ${W}_{\mathrm{PDC}}({\ensuremath{\omega}}_{\mathrm{s}},{\ensuremath{\omega}}_{\mathrm{i}},{\ensuremath{\tau}}_{\mathrm{s}},{\ensuremath{\tau}}_{\mathrm{i}})$ of the PDC state, which naturally lends itself to the pulsed characteristics of these states. From this function we derive the conditioned time-bandwidth product of one of the pair photons, a quantity which not only is a valid measure of entanglement between the PDC photons but also allows us to highlight a remarkable link between the discrete- and continuous-variable descriptions of PDC. We numerically analyze PDC processes with different conditions to demonstrate the versatility of our approach, which is applicable to a large number of current PDC sources.
Quantum information applications call for information encoding schemes which offer high bitrates and the possibility to encode many qubits onto one carrier. Ultrafast pulsed quantum states of light feature an inherent rich spectral and temporal broadband mode structure, which is uniquely defined by their generation process. In ultrafast parametric downconversion for instance, the pair photons are usually generated in superposition states of many orthogonal broadband modes. Thus, they carry the potential for high dimensional quantum information encoding and high bitrates. However, even though the pulsed mode structure of quantum light is well known (see e.g. [1]), feasible ways of exploiting this natural resource in practical systems have not yet been explored.
Parametric downconversion (PDC) in waveguides offers compact setups and high design flexibility in terms of the temporal-spectral properties of the generated photon pairs. It is thus a versatile source for a large number of quantum states with applications in quantum communication or quantum networks. One key element of those systems is the interference of quantum states from different, independent sources at e.g. beamsplitters with high visibility. Those sources should therefore not only meet demands of brightness and efficiency but also generate pure photons with identical properties, in particular in the frequency degree of freedom. In the context of PDC, such states are called decorrelated as there are no spatio-temporal correlations between signal and idler. They can be realized in bulk materials and waveguides by tailoring the pump and dispersion properties. The first source of this kind was demonstrated in bulk KDP at near-infrared wavelengths. For telecom wavelengths a bright, decorrelated source in a waveguide structure was realized in periodically poled KTP. However, in these sources the spectral properties of the signal and idler photons are still dissimilar.
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.
Parametric down-conversion (PDC) is the established standard for the practical generation of a multiplicity of quantum optical states. These include two-mode squeezed vacuum, heralded non-Gaussian states and entangled photon pairs. Detailed theoretical studies provide insight into the time-frequency (TF) structure of PDC, which are governed by the complex-valued joint spectral amplitude (JSA) function. However in experiments, the TF structure of PDC is mostly characterised by intensity measurementsthat forbid access to the important phase of the JSA. In this paper, we present an amplitude-sensitive quantum process tomography technique that combines methods from ultrafast optics and classical three-wave mixing. Our approach facilitates a direct and phase-sensitive time-frequency tomography of PDC with high spectral resolution and excellent signal-to-noise ratio. This is important for all quantum optical applications, which rely on engineered parametric processes and base on minute knowledge of the quantum wave-function for the generation of tailored photonic quantum states.
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.