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, and frequency parallelism and routing. Since the initial experiments 2-3 years ago, frequency bin quantum photonics has been advancing rapidly [1, 2]. In this talk I will give special attention to high dimensional entanglement. One of the interesting possibilities is to perform mixing of multiple frequency bins in a single operation, going well beyond nearest neighbor “interactions.” In this vein I will comment on two recent experiments in our lab, each involving more than a dozen frequency bins. One experiment focuses on quantum walks of frequency entangled photon pairs, in which the input state can be coherently steered toward either correlated or anticorrelated quantum walk behavior [3]. In the second case, we show that high-dimensional frequency bin entanglement enables measurement of signal-idler delay at the few picosecond level, ~30× faster than the single photon detectors employed [4].
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, and frequency parallelism and routing. Since the initial experiments 2-3 years ago, frequency bin quantum photonics has been advancing rapidly [1, 2]. In this talk I will give special attention to high dimensional entanglement. One of the interesting possibilities is to perform mixing of multiple frequency bins in a single operation, going well beyond nearest neighbor “interactions.” In this vein I will comment on two recent experiments in our lab, each involving more than a dozen frequency bins. One experiment focuses on quantum walks of frequency entangled photon pairs, in which the input state can be coherently steered toward either correlated or anticorrelated quantum walk behavior [3]. In the second case, we show that high-dimensional frequency bin entanglement enables measurement of signal-idler delay at the few picosecond level, ~30× faster than the single photon detectors employed [4].
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.
Quantum networking holds tremendous promise in transforming computation and communication. Entangled-photon sources are critical for quantum repeaters and networking, while photonic integrated circuits are vital for miniaturization and scalability. In this talk, we focus on generating and manipulating frequency-bin entangled states within integrated platforms. We encode quantum information as a coherent superposition of multiple optical frequencies; this approach is favorable due to its amenability to high-dimensional entanglement and compatibility with fiber transmission. We successfully generate and measure the density matrix of biphoton frequency combs from integrated silicon nitride microrings, fully reconstructing the state in an 8 × 8 two-qudit Hilbert space, the highest so far for frequency bins. Moreover, we employ Vernier electro-optic phase modulation methods to perform time-resolved measurements of biphoton correlation functions. Currently, we are exploring bidirectional pumping of microrings to generate indistinguishable entangled pairs in both directions, aiming to demonstrate key networking operations such as entanglement swapping and Greenberger–Horne–Zeilinger state generation in the frequency domain.
The on-chip generation of optical quantum states will enable accessible advances for quantum technologies. We demonstrate that integrated quantum frequency combs (based on high-Q microring resonators made from a CMOS-compatible, high refractive-index doped-glass platform) can enable the generation of pure heralded single photons, cross-polarized photon pairs, as well as bi- and multi-photon entangled qubit states over a broad frequency comb covering the S, C, L telecommunications band, with photon frequencies corresponding to standard telecommunication channels spaced by 200 GHz. Exploiting a self-locked, intra-cavity excitation configuration, a highly-stable source of multiplexed heralded single photons is demonstrated, operating continuously for several weeks with less than 5% fluctuations. The photon bandwidth of 110 MHz is compatible with quantum memories, and high photon purity was confirmed through single-photon auto-correlation measurements. In turn, by simultaneously exciting two orthogonal polarization mode resonances, we demonstrate the first realization of type-II spontaneous FWM (in analogy to type-II spontaneous parametric down-conversion), allowing the direct generation of orthogonally-polarized photon pairs on a chip. By using a double-pulse excitation, we demonstrate the generation of time-bin entangled photon pairs. We measure qubit entanglement with visibilities above 90%, enabling the implementation of quantum information processing protocols. Finally, the excitation field and the generated photons are intrinsically bandwidth-matched due to the resonant characteristics of the ring cavity, enabling the multiplication of Bell states and the generation of a four-photon time-bin entangled state. We confirm the generation of this four-photon entangled state through four-photon quantum interference.
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.
Abstract Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with an S-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (Eof) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).
Abstract High-dimensional quantum entanglement is a cornerstone for advanced technology enabling large-scale noise-tolerant quantum systems, fault-tolerant quantum computing, and distributed quantum networks. The recently developed biphoton frequency comb (BFC) provides a powerful platform for high-dimensional quantum information processing in its spectral and temporal quantum modes. Here we propose and generate a singly-filtered high-dimensional BFC via spontaneous parametric down-conversion by spectrally shaping only the signal photons with a Fabry-Pérot cavity. High-dimensional energy-time entanglement is verified through Franson-interference recurrences and temporal correlation with low-jitter detectors. Frequency- and temporal- entanglement of our singly-filtered BFC is then quantified by Schmidt mode decomposition. Subsequently, we distribute the high-dimensional singly-filtered BFC state over a 10 km fiber link with a post-distribution time-bin dimension lower bounded to be at least 168. Our demonstrations of high-dimensional entanglement and entanglement distribution show the singly-filtered quantum frequency comb’s capability for high-efficiency quantum information processing and high-capacity quantum networks.