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arXiv:1604.03588 · Physical Review Letters

Spectrally Engineering Photonic Entanglement with a Time Lens

John M. Donohue, Morgan Mastrovich, Kevin J. Resch

Published Dec 6, 2016• 38 citations
arXivHTMLPDF

Abstract

A time lens, which can be used to reshape the spectral and temporal properties of light, requires the ultrafast manipulation of optical signals and presents a significant challenge for single-photon application. In this work, we construct a time lens based on dispersion and sum-frequency generation to spectrally engineer single photons from an entangled pair. The strong frequency anticorrelations between photons produced from spontaneous parametric down-conversion are converted to positive correlations after the time lens, consistent with a negative-magnification system. The temporal imaging of single photons enables new techniques for time-frequency quantum state engineering.

DOI
10.1103/physrevlett.117.243602

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A time lens, which can be used to reshape the spectral and temporal properties of light, requires the ultrafast manipulation of optical signals and presents a significant challenge for single-photon application. In this work, we construct a time lens based on dispersion and sum-frequency generation to spectrally engineer single photons from an entangled pair. The strong frequency anticorrelations between photons produced from spontaneous parametric down-conversion are converted to positive correlations after the time lens, consistent with a negative-magnification system. The temporal imaging of single photons enables new techniques for time-frequency quantum state engineering.
Single photons provide a natural platform for quantum communication and quantum networking, as they can be entangled in many degrees of freedom and maintain coherence over long-distance links. However, while their minimal interactions with the environment isolate them from detrimental noise, it can make them difficult to measure and manipulate. In particular, manipulation on the ultrafast timescale is necessary to fully exploit the energy-time (or spectral) photonic degree of freedom. Full control over the spectral properties of single photons is key to many quantum technologies and opens the door to natural high-dimensional quantum encodings. \n \nIn this thesis, we theoretically and experimentally examine the use of nonlinear optical processes mediated by strong laser pulses as a method to control the spectral properties of ultrafast single photons. By mixing single-photon pulses with strong escort pulses that have been shaped through dispersion in a nonlinear crystal, the shape of the escort is imprinted on the photon, resulting in a custom-tailored upconverted pulse. We theoretically examine this process for quadratic spectral phases and show that it has the potential to be simultaneously effective and efficient for the customization of single-photon spectral waveforms, and can be performed in an entanglement-conserving manner. \n \nWe then experimentally demonstrate the range of this technique through three applications. First, we show that sum-frequency generation with shaped pulses can be used to coherently measure time-bin encoded photons with bin separations on the order of picoseconds, well below the timing resolution of our detectors. Secondly, we show that this technique can be adapted to convert a train of pulses to a frequency comb, which can be read out in a straightforward manner using diffraction-based spectrometry. We also show here that this process can be performed in a polarization-maintaining fashion, and demonstrate that entanglement with a partner photon is conserved with high fidelity. Finally, we show that this process can be viewed as a time lens, which modulates a temporal waveform in an analogous fashion to a lens focusing a beam of light. We apply the time lens to a photon from an energy-time entangled pair, and show negative magnification of the joint spectrum through a reversal of the spectral correlations. Such processes could find application in quantum state engineering and high-speed single-photon measurement.
A common challenge in quantum information processing with photons is the limited ability to manipulate and measure correlated states. An example is the inability to measure picosecond-scale temporal correlations of a multiphoton state, given state-of-the-art detectors have a temporal resolution of about 100 ps. Here, we demonstrate temporal magnification of time-bin-entangled two-photon states using a time lens and measure their temporal correlation function, which is otherwise not accessible because of the limited temporal resolution of single-photon detectors. Furthermore, we show that the time lens maps temporal correlations of photons to frequency correlations and could be used to manipulate frequency-bin-entangled photons. This demonstration opens a new avenue to manipulate and analyze spectral and temporal wave functions of many-photon states.
We propose an application of quantum temporal imaging to restoring the indistinguishability of the signal and the idler photons produced in type-II spontaneous parametric down-conversion with a pulsed broadband pump. It is known that in this case, the signal and the idler photons have different spectral and temporal properties. This effect deteriorates their indistinguishability and the visibility of the Hong-Ou-Mandel interference, respectively. We demonstrate that inserting a time lens in one arm of the interferometer and choosing properly its magnification factor restores perfect indistinguishability of the signal and the idler photons and provides 100% visibility of the Hong-Ou-Mandel interference in the limit of high focal group delay dispersion of the time lens.
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.
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.
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.