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Optics Express

Theoertical investigation of quantum waveform shaping for single photon emitters

Leno M. Pedrotti, Imad H. Agha

Published Jul 15, 2016• 3 citations
Publisher

Abstract

We investigate a new technique for quantum-compatible waveform shaping that extends the time lens method, and relies only on phase operations. Under realistic experimental conditions, we show that it is possible to both temporally compress and shape optical waveforms in the nanosecond to tens of picoseconds range, which is generally difficult to achieve using standard dispersive pulse-shaping techniques.

DOI
10.1364/oe.24.016687

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•Dec 1, 2016•0 citations
We investigate a new technique for quantum-compatible waveform shaping that extends the time lens method, and relies only on phase operations. Under realistic experimental conditions, we show that it is possible to both temporally compress and shape optical waveforms in the nanosecond to tens of picoseconds range, which is generally difficult to achieve using standard dispersive pulse-shaping techniques.
We experimentally demonstrate spectral broadening and shaping of exponentially-decaying nanosecond pulses via nonlinear mixing with a phase-modulated pump in a periodically poled lithium niobate (PPLN) waveguide. 1550 nm pump light is imprinted with a temporal phase and used to upconvert a weak 980 nm pulse to 600 nm while simultaneously broadening the spectrum to that of a Lorentzian pulse up to 10 times shorter. While the current experimental demonstration is for spectral shaping, we also provide a numerical study showing the feasibility of subsequent spectral phase correction to achieve temporal compression and reshaping of a 1 ns mono-exponentially decaying pulse to a 250 ps Lorentzian, which would constitute a complete spectrotemporal waveform shaping protocol. This method, which uses quantum frequency conversion in PPLN with >100:1 signal-to-noise ratio, is compatible with single photon states of light.
Control of the temporal waveform of photons produced during spontaneous emission from single quantum emitters provides a crucial tool in the establishment of hybrid quantum systems, optimization of quantum state transfer protocols and mitigation of effects due interferometric instability for network architectures based on flying qubits. We describe a method to generate photons of any temporal waveform from emitters of any excited state lifetime, limited only by the timing resolution of control hardware. We show how the temporal waveform of photons can be controlled by deterministically varying the population of an excited state which undergoes spontaneous emission. Our broadly applicable approach has only two requirements for a candidate quantum emitter: modulation of the (1) amplitude and (2) relative phase of a field coupling a ground state to the excited manifold. We detail how to identify optimal excitation pulses by employing variational algorithms to feed back on atomic populations. Additionally, we develop Quantum Monte Carlo based tools to determine photon-number statistics and establish techniques to identify optimal excitation strengths and post-selection thresholds for photon generation protocols. We situate our work in the context of other prior research on bespoke single photon sources and networking including post-emission pulse shaping, temporal gating and cavity-based methods. In comparison, our free-space process has greater flexibility in producing any waveform, requires less infrastructure, and can be readily applied across a wide range of quantum emitters. We discuss the applications and limits of this technique, including how increasing photon emission probabilities affects achievable temporal-mode overlap fidelities between emitted and target photon waveforms.
We experimentally demonstrate spectral broadening and shaping of exponentially-decaying nanosecond pulses via nonlinear mixing with a phase-modulated pump in a periodically-poled lithium niobate (PPLN) waveguide. A strong, 1550 nm pulse is imprinted with a temporal phase and used to upconvert a weak 980 nm pulse to 600 nm while simultaneously broadening the spectrum to that of a Lorentzian pulse up to 10 times shorter. While the current experimental demonstration is for spectral shaping, we also provide a numerical study showing the feasibility of subsequent spectral phase correction to achieve temporal compression and re-shaping of a 1 ns mono-exponentially decaying pulse to a 250 ps Lorentzian, which would constitute a complete spectro-temporal waveform shaping protocol. This method, which uses quantum frequency conversion in PPLN with> 100: 1 signal-to-noise ratio, is compatible with single photon states of light. 1.
The optimal properties for single photons may vary drastically between different quantum technologies. Along with central frequency conversion, control over photonic temporal waveforms will be paramount to the effective coupling of different quantum systems and efficient distribution of quantum information. Through the application of pulse shaping and the nonlinear optical process of sum-frequency generation, we examine a framework for manipulation of single-photon waveforms. We use a nonperturbative treatment to determine the parameter regime in which both high-efficiency and high-fidelity conversion may be achieved for Gaussian waveforms and study the effect such conversion techniques have on energy-time entanglement. Additionally, we prove that aberrations due to time ordering are negligible when the phase matching is nonrestrictive over the input bandwidths. Our calculations show that ideal quantum optical waveform conversion and quantum time lensing may be fully realized using these techniques.
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 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.