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arXiv:1401.6700 · Optics Letters

Efficient sorting of quantum-optical wave packets by temporal-mode interferometry

Dileep V. Reddy, M. G. Raymer, Colin J. McKinstrie

Published May 8, 2014• 53 citations
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Abstract

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.

DOI
10.1364/ol.39.002924

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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.
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.
Quantum frequency conversion (QFC) of photonic signals preserves quantum information while simultaneously changing the signal wavelength. A common application of QFC is to translate the wavelength of a signal compatible with the current fiber-optic infrastructure to a shorter wavelength more compatible with high quality single-photon detectors and optical memories. Recent work has investigated the use of QFC to manipulate and measure specific temporal modes (TMs) through tailoring of the pump pulses. Such a scheme holds promise for multidimensional quantum state manipulation that is both low loss and re-programmable on a fast time scale. We demonstrate the first QFC temporal mode sorting system in a four-dimensional Hilbert space, achieving a conversion efficiency and mode separability as high as 92% and 0.84, respectively. A 20-GHz pulse train is projected onto 6 different TMs, including superposition states, and mode separability with weak coherent signals is verified via photon counting. Such ultrafast high-dimensional photonic signals could enable long-distance quantum communication with high rates.
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.
A new, and thus far only, method to overcome a selectivity barrier in parametrically pumped quantum pulse gates is proposed and experimentally demonstrated for the first time, using frequency conversion of optical temporal modes in second-order nonlinear waveguides. Temporal modes and quantum pulse gates are defined and their utilities are explored. Pulsed operation of three-field and four-field, parametric, optical processes are modeled and numerically investigated. A maximum limit to achievable selectivity for quantum pulse gating in uniform media is discovered and theoretically explained. An interferometric means of overcoming said limit and asymptotically approaching unit selectivity is proposed. The principle is experimentally verified by double-passing specifically shaped optical pulses derived from an ultrafast Ti:sapphire laser through a periodically-poled lithium niobate waveguide phasematched for sum-frequency generation. Further improvements and future implications for quantum technologies are discussed.
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.