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Versatile shaper-assisted discretization of energy-time entangled photons

Bänz Bessire, Christian Bernhard, Thomas Feurer, André Stefanov

Published Jan 1, 2014• 21 citations
Publisher

Abstract

We demonstrate the capability to discretize the frequency spectrum of broadband energy–time entangled photons by means of a spatial light modulator to encode qudits in various bases. Exemplarily, we implement three different discretization schemes, namely frequency bins, time bins and Schmidt modes. Entangled qudits up to dimension d = 4 are then revealed by two-photon interference experiments with visibilities violating a d-dimensional Bell inequality.

DOI
10.7892/boris.62373

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We demonstrate the capability to discretize the frequency spectrum of broadband energy–time entangled photons by means of a spatial light modulator to encode qudits in various bases. Exemplarily, we implement three different discretization schemes, namely frequency bins, time bins and Schmidt modes. Entangled qudits up to dimension d = 4 are then revealed by two-photon interference experiments with visibilities violating a d-dimensional Bell inequality.
Entanglement is a key feature of quantum mechanics and is best suited to study the peculiar nature of non-classical correlations. Higher dimensional entangled bipartite systems beyond qubits allow for new insights in generalized Bell inequalities and for enhanced bit rates within protocols for quantum key distribution. Entangled qutrits and ququarts in the time domain have been implemented interferometrically. This paper proposes and demonstrates the capability to encode qudits in the spectrum of energy-time entangled photons by means of spectral amplitude and phase modulation.
We experimentally study the violation of the CGLMP inequality for entangled 2-qubit and 2-qutrit states with different degrees of entanglement using numerically optimized measurement settings. The qudits are encoded and manipulated in the frequency spectrum of broadband energy-time entangled photons by taking into account a spatial light modulator (SLM). The latter allows to discretize the spectrum into bins. By controlling each frequency bin individually, the generation of maximally and non-maximally entangled qutrits is verified through quantum state tomography (QST).
Frequency modes of light are one of the most promising platforms that provide access to high-dimensional quantum states amongst different photonic degrees of freedom capable of high-dimensionality, enabling robust, error-tolerant, and scalable quantum optical information systems. We demonstrate engineering of precisely controlled two-photon high-dimensional states entangled in frequency through time-domain Fourier optical synthesis. We generate and convert a continuous broadband frequency-entangled state into a large range of discrete frequency bins suitable for ITU standards, with spacings ranging from 12.5 GHz to 750 GHz, and observe spectral anticorrelations over 38 frequency bins, including intra-bin pure states at a 100 GHz bin spacing. We characterize the full quantum state dimensionality via Schmidt decomposition and observe lower bounds on the frequency-binned Hilbert-space dimensionalities of at least 289, formed by two entangled qudits with dimension 17. Furthermore, we demonstrate quantum nonlocality via frequency correlations in a transmission experiment over a campus-scale two-node fiber network. This work represents a crucial step towards building a versatile and relatively simple way of generating precisely controlled high-dimensional spectral qudits, with the potential of harnessing in wavelength-multiplexed quantum networks, high-dimensional information processing, and communication of quantum states specifically, and fiber-optic quantum remote sensing.
Summary form only given. Entanglement is a fundamental resource for the quantum processing of information and to study the intrinsic nature of quantum correlations. Entangling higher dimensional bipartite systems (qudits) has been shown to give more insight on the nature of entanglement compared to the simplest entanglement system composed of two two level systems (two qubits) [1, 2]. For quantum key distribution, increasing the dimension of the alphabet by using qudits increases the effective bit rate of the protocol, still being secure [3]. Experimentally, higher dimensional entanglement in photonic systems have been demonstrated for various degrees of freedom of light, including time-bins [4,5], transverse momentum [6, 7] or orbital angular momentum modes [8].We demonstrate here a new way to encode qudits in the energy spectrum of the entangled photons by defining frequency bins within their spectra. Broadband entangled photons are generated by continuous wave spontaneous down-conversion and detected in coincidence by sum frequency generation. By means of experimental methods used for shaping fs-laser pulses, frequency bins can be addressed in the photons spectra. Furthermore, controlling each frequency component individually allows to manipulate and characterize the quantum states. The dimension of the generated states is in practice limited by the optical resolution of the setup only.
Entanglement and encoding in discrete frequency bins – essentially a quantum analogue of wavelength-division multiplexing – represents a relatively new degree of freedom for quantum information with photons. In this talk I discuss biphoton frequency combs, generated either by spontaneous four-wave mixing (SFWM) from on-chip microring resonators or by spectral filtering of spontaneous parametric down conversion (SPDC) in second order nonlinear crystals. Potential advantages include generation of high dimensional units of quantum information (qudits), which can carry multiple qubits per photon, robust transmission over fiber, frequency parallelism and routing, and compatibility with on-chip implementations, as well as hyperentanglement with other photonic degrees, e.g., time-frequency hyperentanglement. Since the initial experiments less than two years ago, frequency bin quantum photonics has been advancing rapidly [1-8]. In this talk I will discuss a method using pulse shapers and phase modulators in order to mix different frequencies and perform two photon interference experiments for characterization of the frequency-bin entanglement. Similar components (pulse shapers and phase modulators) may be used to manipulate the frequency-encoded quantum states; this will be described in another talk by our collaborators at Oak Ridge National Labs. I will also discuss the use of time bins and frequency bins as independent degrees of freedom in a quantum encoding fashion to realize what we believe to be the first deterministic two qudit gates. Finally, I comment briefly on potential applications and on prospects for realization of integrated frequency bin quantum photonics.