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arXiv:1710.07159 · New Journal of Physics

Time reversal of arbitrary photonic temporal modes via nonlinear optical frequency conversion

Michael G Raymer, Dileep V Reddy, S. J. van Enk, Colin J McKinstrie

Published Apr 3, 2018• 6 citations
arXivHTMLPDF

Abstract

Single-photon wave packets can carry quantum information between nodes of a quantum network. An important general operation in photon-based quantum information systems is 'blind' reversal of a photon's temporal wave packet envelope, that is, the ability to reverse an envelope without knowing the temporal state of the photon. We present an all-optical means for doing so, using nonlinear-optical frequency conversion driven by a short pump pulse. The process used may be sum-frequency generation or four-wave Bragg scattering. This scheme allows for quantum operations such as a temporal-mode parity sorter. We also verify that the scheme works for arbitrary states (not only single-photon ones) of an unknown wave packet.

DOI
10.1088/1367-2630/aabb43

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Single-photon wave packets can carry quantum information between nodes of a quantum network. An important general operation in photon-based quantum information systems is 'blind' reversal of a photon's temporal wave packet envelope, that is, the ability to reverse an envelope without knowing the temporal state of the photon. We present an all-optical means for doing so, using nonlinear-optical frequency conversion driven by a short pump pulse. The process used may be sum-frequency generation or four-wave Bragg scattering. This scheme allows for quantum operations such as a temporal-mode parity sorter. We also verify that the scheme works for arbitrary states (not only single-photon ones) of an unknown wave packet.
The temporal shape of single photons provides a high-dimensional basis of temporal modes, and can therefore support quantum computing schemes that go beyond the qubit. However, the lack of linear optical components to act as quantum gates has made it challenging to efficiently address specific temporal-mode components from an arbitrary superposition. Recent progress towards realizing such a "quantum pulse gate," has been proposed using nonlinear optical signal processing to add coherently the effect of multiple stages of quantum frequency conversion. This scheme, called temporal-mode interferometry [D. V. Reddy, Phys. Rev. A 91, 012323 (2015)], has been shown in the case of three-wave mixing to promise near-unity mode-sorting efficiency. Here we demonstrate that it is also possible to achieve high mode-sorting efficiency using four-wave mixing, if one pump pulse is long and the other short - a configuration we call asymmetrically-pumped Bragg scattering.
In the last few decades, there has been much progress on low loss waveguides, very efficient photon-number detectors and nonlinear processes. Engineered sum-frequency conversion is now at a stage where it allows operation on arbitrary temporal broadband modes, thus making the spectral degree of freedom accessible for information coding. Hereby the information is often encoded into the temporal modes of a single photon. Here, we analyse the prospect of using multi-photon states or squeezed states in different temporal modes based on integrated optics devices. We describe an analogy between mode-selective sum-frequency conversion and a network of spatial beam splitters. Furthermore, we analyse the limits on the achievable squeezing in waveguides with current technology and the loss limits in the conversion process.This article is part of the themed issue 'Quantum technology for the 21st century'.
A slow-light scheme is proposed for simultaneous frequency conversion and spectral compression of a weak optical pulse, which may be in any quantum state including a single-photon state. Such a process plays crucial roles in schemes for constructing quantum networks. Assuming that appropriate slow-light waveguides can be fabricated, theoretical modeling shows that a 3-ps signal pulse can be converted by sum-frequency generation (SFG) into a pulse with duration in the ns regime with a corresponding spectral compression factor of the order of 1000 and a useful intrinsic efficiency up to 83%. With this design, deleterious spatial-temporal oscillations are suppressed because the continual delay of the SFG field suppresses back-conversion from SFG to the signal field. Independent of the input pulse shape (if it is short enough), the converted pulse will have a near-exponential rising shape, which is suitable for temporal-mode matching into an optical cavity.
All classical and quantum technologies that encode in and retrieve information from optical fields rely on the ability to selectively manipulate orthogonal field modes of light. Such manipulation can be achieved with high selectivity for polarization modes and transverse-spatial modes. For the time-frequency degree of freedom, this could efficiently be achieved for a limited choice of approximately orthogonal modes, i.e., nonoverlapping bins in time or frequency. We recently proposed a method that surmounts the selectivity barrier for sorting arbitrary orthogonal temporal modes [Opt. Lett. 39, 2924 (2014).] using cascaded interferometric quantum frequency conversion in nonlinear optical media. We call this method temporal-mode interferometry, as it has a close resemblance to the well-known separated-fields atomic interferometry method introduced by Ramsey. The method has important implications for quantum memories, quantum dense coding, quantum teleportation, and quantum key distribution. Here we explore the inner workings of the method in detail, and extend it to multiple stages with a concurrent asymptotic convergence of temporal-mode selectivity to unity. We also complete our analysis of pump-chirp compensation to counter pump-induced nonlinear phase modulation in four-wave mixing implementations.
Long-distance quantum communication relies on storing and retrieving photonic qubits in orthogonal field modes. The available degrees of freedom for photons are polarization, spatial-mode profile, and temporal/spectral profile. To date, methods exist for decomposing, manipulating, and analyzing photons into orthogonal polarization modes and spatial modes. Here we propose and theoretically verify the first highly efficient method to carry out analogous operations for temporally and spectrally overlapping, but field-orthogonal, temporal modes. The method relies on cascaded nonlinear-optical quantum frequency conversion.
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.