We demonstrate single-shot, high-resolution FWM time-lenses for measuring ultrafast quantum effects and present a concrete route to quantum time-lenses in which the lensing element is itself nonclassical. This architecture has no spatial equivalence, and it enables noise-engineered temporal magnification, below-shot-noise performance, and new tools for ultrafast quantum tomography and time-domain photonic processing.
We demonstrate single-shot, high-resolution FWM time-lenses for measuring ultrafast quantum effects and present a concrete route to quantum time-lenses in which the lensing element is itself nonclassical. This architecture has no spatial equivalence, and it enables noise-engineered temporal magnification, below-shot-noise performance, and new tools for ultrafast quantum tomography and time-domain photonic processing.
Temporal optics, and specifically time-lenses and time-stretch systems, revolutionized the field of ultrafast measurements. Over the last years, we utilized time-lenses to measure different quantum schemes and studied the temporal modes of correlated photons with high temporal resolution. We developed temporal schemes based on quantum light, for realizing quantum tomography in the time-domain. We developed low-resolution time-lenses for weak quantum measurements. Finally, we suggest how quantum time-lens can lead to optical deep learning systems. In the talk, I will give an overview of the different types of quantum temporal schemes, elaborate on the future challenges in the field, and discuss the prospects and future applications which may be possible.
A time-lens can image signals in time and map ultrafast signals from frequency to time. The concept of time-lens is based on the duality between the diffraction of light in space and the dispersion of pulses in time, which arises from the similarity between the equations describing these two phenomena. In this paper we explain how to use time-lenses in order to perform high-resolution temporal imaging on non-classical ultrafast signals. Such a scheme can be used e.g. for diagnosing quantum cryptography schemes on optical fiber networks or assessing the performance of photonic quantum computers and simulators.
Time-lenses can image ultrafast signals in time. Placing them in a 2-f configuration leads to Fourier transform of the input signal and ultrafast spectroscopy. We utilized two time-lenses in a 4-f configuration and formed an interferometer in the time domain. Our time lenses are based on four-wave mixing process, generating an idler beam which serves as the output. The output from the first time-lens is the input to the second time-lens. At the output of the second time-lens, we get an interference between the signal beams of both time-lenses and the idler beams of both time-lenses. This interference is sensitive to ultrafast phase shifts in time and can lead to interfere signals in different times. This interferometer is good for quantum imaging, and studying the temporal structure of entangled photons. In this talk we will demonstrate the interferometer, how we exploit time-lenses for interferometry, the application of the interferometer, and our experimental results.
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.
Single photons are a natural platform for quantum technologies as they support entanglement in many degrees of freedom and are inherently well protected from a detrimental type of noise called decoherence. In order to fully exploit photons for quantum technologies, it will be necessary to be able to shape, control, and measure their properties in all degrees of freedom: space, time, frequency, and polarization. \n \n The time-frequency degree of freedom of light is of particular interest for quantum information tasks as it supports various encodings, including frequency bins and time bins, and is intrinsically robust for propagation through long-distance fibre links. Applications which harness quantum correlations in this degree of freedom, referred to as energy-time entanglement, include dispersion cancellation and high-dimensional quantum key distribution. However, detection of this entanglement and observation of these effects requires time resolution beyond the capabilities of current photon detectors. Thus, for operations on ultrafast time scales, more powerful and complex methods are required. \n \n In this thesis, we use a nonlinear technique known as optical gating to surpass the limitations in current detectors and measure single photon pairs, improving the time resolution by two orders of magnitude. When a single photon enters a nonlinear medium at the same time as a strong laser pulse, it may upconvert to a higher energy photon. The strong laser pulse effectively acts as an ultrafast shutter or gate and this creates a high resolution snapshot of the photon in time. Optical gating in conjunction with single photon spectrometers then allow us to measure both the spectral and temporal features of photons on subpicosecond time scales. \n \n These high resolution measurements enable us to explore a host of quantum effects which remained previously inaccessible. First, we directly observe energy-time entanglement, analogous to Einstein-Rosen-Podolsky correlations but \\emph{in frequency and time}. Then, with full control over the dispersion of each photon, we observe nonlocal dispersion cancellation on femtosecond time scales. We also explore ultrafast interferometry in the quantum domain by temporally resolving two-photon interference from a Franson interferometer and observe a violation of the CHSH-Bell inequality. Finally, we show that, using these measurements, it is possible to reconstruct a two-photon energy-time entangled state. Such measurement capabilities will be essential to precisely control both the spectral and temporal shape of entangled photons and to develop new applications in quantum state engineering.
Temporal imaging is a technique enabling manipulation of temporal optical signals in a manner similar to manipulation of optical images in spatial domain. The quantum description of temporal imaging is relevant in the context of long range quantum communication. Indeed this technology relies on the efficiency of quantum repeaters for which the temporal mode matching between the quantum emitters, the communication network and the quantum memories is critical. In this work we address the problem of temporal imaging of a temporally broadband squeezed light generated by a traveling-wave optical parametric amplifier. We consider a single-lens temporal imaging system formed by two dispersive elements and a parametric temporal lens, based on a non- linear process such as sum-frequency generation or four-wave mixing. We derive a unitary transformation of the field operators performed by this kind of time lens and evaluate the squeezing spectrum at the output of the single-lens imaging system. When the efficiency factor of the temporal lens is smaller than unity, the vacuum fluctuations deteriorate squeezing at its output. For efficiency close to unity, when certain imaging conditions are satisfied, the squeezing spectrum at the output of the imaging system will be the same as that at the output of the OPA in terms of the scaled frequency ΩI = MΩ which corresponds to the scaled time tI = t/M . The magnification factor M gives the possibility of matching the coherence time of the broadband squeezed light to the response time of the photodetector.