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arXiv:2307.01141 · Optics Express

Ultrafast electro-optic time-frequency fractional Fourier imaging at the single-photon level

Michał Lipka, Michal P. Parniak

Published Feb 20, 2024• 8 citations
arXivHTMLPDF

Abstract

The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g., the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical signal processing (e.g., time-correlated noise optimal filtering) to emerging quantum technologies (e.g., super-resolution TF sensing) which rely on or benefit from coherent low-noise TF operations. Here a versatile low-noise single-photon-compatible implementation of the FRT is presented. Optical TF FRT can be synthesized as a series of a spectral disperser, a time-lens, and another spectral disperser. Relying on the state-of-the-art electro-optic modulators (EOM) for the time-lens, our method avoids added noise inherent to the alternatives based on non-linear optical interactions (such as wave-mixing, cross-phase modulation, or parametric processes). Precise control of the EOM-driving radio-frequency signal enables fast all-electronic control of the FRT angle. In the experiment, we demonstrate FRT angles of up to 1.63 rad for pairs of coherent temporally separated 11.5 ps-wide pulses in the near-infrared (800 nm). We observe a good agreement between the simulated and measured output spectra in the bright-light and single-photon-level regimes, and for a range of pulse separations (20 ps to 26.7 ps). Furthermore, a tradeoff is established between the maximal FRT angle and optical bandwidth, with the current setup accommodating up to 248 GHz of bandwidth. With the ongoing progress in EOM on-chip integration, we envisage excellent scalability and vast applications in all-optical TF processing both in the classical and quantum regimes.

DOI
10.1364/oe.507911

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The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g., the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical signal processing (e.g., time-correlated noise optimal filtering) to emerging quantum technologies (e.g., super-resolution TF sensing) which rely on or benefit from coherent low-noise TF operations. Here a versatile low-noise single-photon-compatible implementation of the FRT is presented. Optical TF FRT can be synthesized as a series of a spectral disperser, a time-lens, and another spectral disperser. Relying on the state-of-the-art electro-optic modulators (EOM) for the time-lens, our method avoids added noise inherent to the alternatives based on non-linear optical interactions (such as wave-mixing, cross-phase modulation, or parametric processes). Precise control of the EOM-driving radio-frequency signal enables fast all-electronic control of the FRT angle. In the experiment, we demonstrate FRT angles of up to 1.63 rad for pairs of coherent temporally separated 11.5 ps-wide pulses in the near-infrared (800 nm). We observe a good agreement between the simulated and measured output spectra in the bright-light and single-photon-level regimes, and for a range of pulse separations (20 ps to 26.7 ps). Furthermore, a tradeoff is established between the maximal FRT angle and optical bandwidth, with the current setup accommodating up to 248 GHz of bandwidth. With the ongoing progress in EOM on-chip integration, we envisage excellent scalability and vast applications in all-optical TF processing both in the classical and quantum regimes.
Techniques to control the spectro-temporal properties of quantum states of light at ultrafast time scales are crucial for numerous applications in quantum information science. In this work, we report an all-optical time lens for quantum signals based on Bragg-scattering four-wave mixing with picosecond resolution. Our system achieves a temporal magnification factor of 158 with single-photon level inputs, which is sufficient to overcome the intrinsic timing jitter of superconducting nanowire single-photon detectors. We demonstrate discrimination of two terahertz-bandwidth, single-photon-level pulses with 2.1 ps resolution (electronic jitter corrected resolution of 1.25 ps). We draw on elegant tools from Fourier optics to further show that the time-lens framework can be extended to perform complex unitary spectro-temporal transformations by imparting optimized temporal and spectral phase profiles to the input waveforms. Using numerical optimization techniques, we show that a four-stage transformation can realize an efficient temporal mode sorter that demultiplexes 10 Hermite–Gaussian (HG) modes. Our time-lens-based framework represents a new toolkit for arbitrary spectro-temporal processing of single photons, with applications in temporal mode quantum processing, high-dimensional quantum key distribution, temporal mode matching for quantum networks, and quantum-enhanced sensing with time-frequency entangled states.
Quantum physics holds promise to revolutionise a number of technologies by enabling performance beyond what is feasible with classical resources, such as secure communications, precision measurement and high-speed simulation and computation. To realise this, quantum information must be encoded into one of the physical degrees of freedom of light. The time-frequency (TF) domain provides a infinite-dimensional space which is naturally compatible with integrated optical platforms. Additionally, future quantum networks will require coherent coupling of quantum systems that do not necessarily exhibit TF mode overlap. The ability to generate, coherently control and measure a variety of TF states of quantum light is therefore a necessary step towards implementing optical quantum technologies. Developing the building blocks for future optical quantum applications calls for an assortment of methods for measuring the properties of TF states of quantum light. Whilst much progress has been made towards this goal recently, deficiencies with existing methods remain. Efficient spectrally-resolved detection away from the telecoms wavelength range and a robust approach to single-photon state characterisation that is sensitive to the spectral phase have so far proven challenging. Additionally, accessing quantum advantages requires measurements that are sensitive to the nonclassical correlations that can exist between separate subsystems. However, until now a flexible approach to determining the full quantum state of systems of multiple time/frequency entangled photons has been lacking. Here we develop a toolbox of techniques for the measurement of TF quantum states of light for few-photon systems, and apply these to the task of precision measurement. Firstly, we propose, construct and demonstrate efficient single-photon spectrometers based on dispersive time-to-frequency mapping, using chirped fibre Bragg gratings to apply the necessary group delay dispersion. We use two such devices operating in coincidence to realise a full phase-sensitive reconstruction of the TF state of a single photon, by spectrally resolving the output of a nonclassical interference process with an external reference. We also demonstrate a complementary, optical reference-free method. This characterisation tool, an implementation of electro-optic spectral shearing interferometry with coincident spectrally-resolved single-photon detection, melds techniques from ultrafast metrology and quantum optics. We proceed to demonstrate the flexibility of this device by reconstructing a wide range of test pulses generated with a pulse shaper. By implementing this technique in conjunction with spectrally-resolved detection of a second photon, we realise complete characterisation of the TF wave function of a spectrally-entangled broadband photon pair. This method is robust to a wide range of inputs and is generalisable to spectrally mixed states and across a wide range of wavelengths, including to spectrally non-degenerate photon pairs. To demonstrate, we generate an entangled photon pair with controllable TF entanglement and perform a full reconstruction. Lastly, we present a new technique for using TF entangled photon pairs to realise quantum-enhanced measurement of a time delay in a quantum channel in the presence of environmental noise. This scheme is based on entanglement-enhanced rejection of background light. A simple experiment demonstrating the feasibility of such a measurement is presented.
Spectral-temporal manipulation of optical pulses has enabled numerous developments within a broad range of research topics, ranging from fundamental science to practical applications. Within quantum optics spectral-temporal degree of freedom of light offers a promising platform for integrated photonic quantum information processing. An important challenge in experimentally realizing spectral-temporal manipulation of quantum states of light is the need for highly efficient manipulation tools. In this context the intrinsically deterministic electro-optic methods show great promise for quantum applications. We experimentally demonstrate application of electro-optic platform for spectral-temporal manipulation of ultrashort pulsed quantum light. Using techniques analogous to serrodyne frequency shifting we show active spectral translation of few-picosecond single photon pulses by up to 0.5 THz. By employing an approach based on an electro-optic time lens we demonstrate up to 6-fold spectral compression of heralded single photon pulses with efficiency that enables us to significantly increase single photon flux through a narrow bandpass filter. We realize the required temporal phase manipulation by driving a lithium niobate waveguided electrooptic modulator with 33 dBm sinusoidal RF field at the frequency of either 10 GHz or 40 GHz. We use a phase lock loop to temporally lock the RF field to the 80 MHz repetition rate of approximately 1 ps long optical pulses. Heralded single photon wavepackets are generated by means of spontaneous parametric down-conversion in potassium dihydrogen phosphate (KDP) crystal, which enables preparation of spectrally pure single photon wavepackets without the need for spectral filtering. Spectral shifting is achieved by locking single-photon pulses to the linear slope of sinusoidal 40 GHz RF phase modulation. We verify the spectral shift by performing spectrally resolved heralded single photon counting, using frequency-to-time conversion by means of a highly dispersive chirped fiber Bragg grating. We verify the non-classicality of spectrally shifted single photons by measuring high-visibility Hong-Ou-Mandel interference using a reference single photon pulse. Spectral compression is based on the time lens principle, which requires locking optical pulses to approximately quadratic region of sinusoidal phase modulation. We utilize both 10 GHz and 40 GHz RF driving frequencies. Bandwidth compression is achieved by chirping the single photon pulse using an appropriate length of single-mode fibre and subsequently subjecting it to the action of the time lens. We verify spectral compression directly using the aforementioned spectrally-resolved heralded single photon counting method. We achieve 3-fold spectral compression of 2 nm bandwidth single photon pulses using 40 GHZ modulation frequency, and 6-fold spectral compression of 0.9 nm bandwidth single photon pulses using 10 GHz modulation frequency. Overall transmission of our set-up exceeding 30% enables practical usability of our spectral compression method which we demonstrate experimentally by showing an increased photon flux through a narrowband filter. Our results present an important contribution towards implementing quantum information processing in the spectral-temporal degree of freedom of a photon. In the context of quantum networks they present an enabling tool towards efficient photonic interfacing of different quantum information processing platforms.
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Despite the multitude of available methods, the characterization of ultrafast pulses remains a challenging endeavor, especially at the single-photon level. We introduce a pulse characterization scheme that maps the magnitude of its short-time Fourier transform. Contrary to many well-known solutions it does not require nonlinear effects and is therefore suitable for single-photon-level measurements. Our method is based on introducing a series of controlled time and frequency shifts, where the latter is performed via an electro-optic modulator allowing a fully-electronic experimental control. We characterized the full spectral and temporal width of a classical and single-photon-level pulse and successfully tested the applicability of the reconstruction algorithm of the spectral phase and amplitude. The method can be extended by implementing a phase-sensitive measurement and is naturally well-suited to partially-incoherent light.
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