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Frontiers in Optics

Programmable unitary transformation of spectro-temporal modes

Valérian Thiel, Alex O. C. Davis, Peru d’Ornellas, Nicolas Treps, Brian J. Smith

Published Jan 1, 2017• 3 citations
Publisher

Abstract

We present realistic simulations of ultrafast temporal pulse shaping with a fiber-coupled electro-optical modulator and fiber Bragg grating. The scheme can be used to realize unitary transformations of pulse modes allowing, in principle, lossless manipulation of a multimode quantum state.
DOI
10.1364/fio.2017.jw4a.5

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Controlling the temporal mode shape of quantum light pulses has wide ranging application to quantum information science and technology. Techniques have been developed to control the bandwidth, allow shifting in the time and frequency domains, and perform mode-selective beam-splitter-like transformations. However, there is no present scheme to perform targeted multimode unitary transformations on temporal modes. Here we present a practical approach to realize general transformations for temporal modes. We show theoretically that any unitary transformation on temporal modes can be performed using a series of phase operations in the time and frequency domains. Numerical simulations show that several key transformations on temporal modes can be performed with greater than 95% fidelity using experimentally feasible specifications.
Programmable control of individual pulses in a high-repetition-rate (typically MHz) ultrafast pulse train is a long-standing goal for optical arbitrary waveform synthesis. Here, we report a programmable pulse-by-pulse shaper that enables deterministic spectral-temporal control of ultrafast pulses at a repetition rate of ∼\sim∼ 20~MHz. By synchronizing an FPGA-driven electro-optic modulation on the stretched waveform in a temporal 4fff shaping system, the regime writes pulse-index-dependent spectral phase profiles onto individual pulses. We demonstrate three levels of programmable ability: zero-order phase coding that maps pulse-by-pulse phase sequences into double-slit-like spectral-temporal interference; first-order phase programming that produces arbitrary temporal trajectories with deterministic delay; and fractional-order phase engineering that generates programmable temporal breathing. By launching the shaped pulse train into a nonlinear fiber stage, the programmed temporal breathing is converted into one spectral breathing. We further construct a phase-level-dependent regime map of nonlinear spectral breathing, revealing transitions from weak single-envelope breathing to multi-peak spectral splitting and strongly breathing merged-spectrum dynamics, in agreement with numerical simulations. This pulse-by-pulse spectral-temporal synthesis platform establishes pulse index as a programmable degree of freedom for ultrafast pulse shaping and provides a route toward real-time and pulse resolved optical arbitary waveform synthesis.
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.