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Multidimensional quantum optics of spin waves through ac-Stark modulation

Michal P. Parniak, Mateusz Mazelanik, Adam Leszczyński, Michał Lipka, Michał Dąbrowski, Wojciech Wasilewski

Published Apr 16, 2018• 2 citations

Abstract

Spatial structure of photons renders them extremely versatile carriers of quantum information, as it can be tailored with simple optical elements such as lenses, phase gratings or holograms. Substantial challenges emerge, however, when such spatially-structured photons carrying quantum information need to be stored in quantum memories or if advanced quantum information processing capability beyond linear optics is required. These quandaries are usually not shared by material systems, for which strong interaction can be engineered, leading to efforts in demonstrating quantum-interferometric properties of atoms, phonons or plasmons. Here we harness the full three-dimensional potential of material quasi-particles - collective atomic excitations known as spin waves. We demonstrate that the spatial structure of single spin waves can be manipulated via the off-resonant ac-Stark shift. Through spin-wave diffraction based beam-splitter transformation, we realize the Hanbury Brown-Twiss (HBT) type measurement at the spin-wave level, demonstrating nonclassical statistics of atomic excitations. Finally, we observe interference of two spin waves - an analogue of the Hong-Ou-Mandel (HOM) effect for photons. Thanks to the reversible photon-spin wave mapping via the Duan-Lukin-Cirac-Zoller (DLCZ) protocol, these techniques enable encoding states from a high-dimensional Hilbert space into the spatial structure of spin waves to facilitate not only new quantum communication schemes, but also high data rate classical telecommunication.

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We bring the set of linear quantum operations, important for many fundamental studies in photonic systems, to the material domain of collective excitations known as spin waves. Using the ac Stark effect we realize quantum operations on single excitations and demonstrate a spin-wave analog of the Hong-Ou-Mandel effect, realized via a beam splitter implemented in the spin-wave domain. Our scheme equips atomic-ensemble-based quantum repeaters with quantum information processing capability and can be readily brought to other physical systems, such as doped crystals or room-temperature atomic ensembles.

While several methods of information processing have been realized in quantum memories, thorough utilization of the spatial degree of freedom in highly-multimode memories demands a flexible method analogous to spatial light modulators (SLM) widely exploited in the broad field of optics to modulate the amplitude or phase of light. We want to present a spatial spin-wave modulator (SSM), allowing engineering of a spatial phase of spin-waves stored in a cold atomic memory. Using the SLM and polarizers we are able to shape a laser beam into an arbitrary shape. Such a prepared beam illuminates a cold rubidium cloud and due to ac-Stark effect the spatial phase of stored spin-waves is modified. The relative standard deviation of phase given by our SSM amounts to about 10%. We have also shown that losses scale quadratically with given phase. On one hand, that strongly limits the efficiency of SSM for strong phase modulation, but on the other hand enables efficient modulation in small range of several radians. During our research we have demonstrated a compensation of the quadratic phase introduced by a cylindrical lens placed in a readout path of our quantum memory. Moreover, introducing more complicated shapes of the ac-Stark beam, like saw or sine shape, we can shift and split spin-waves in Fourier domain [1]. Therefore we were able to interfere spin-waves stored in different spatial and temporal modes. This makes our SSM very robust tool which in conjugation with gradient echo memory can potentially allow to implement some new quantum protocols [2]. Finally, going to the single photon level we successfully observed a Hong-Ou-Mandel interference of two spin-waves stored in different spatial modes of our memory [3].

High performance quantum networks require extensive utilization of multiplexing techniques, relaying on photonic spatial and temporal structure. Multimode quantum memories for light, where photons are stored in the form of collective atomic excitations, may constitute building blocks of such networks; however, a requirement arises to implement complex linear operations on the stored excitations. In our photonic processor we experimentally demonstrate how the off-resonant ac-Stark shift (ACS) may be employed to manipulate the spatial and temporal structure of photons stored in a highly multimode quantum memory as the collective atomic excitations – spin waves.

Abstract A device being a pinnacle of development of an optical quantum memory should combine the capabilities of storage, inter-communication, and processing of stored information. In particular, the ability to capture a train of optical pulses, interfere them in an arbitrary way and finally, perform on-demand release could realize arbitrary optical computation. Here we demonstrate the operation of a coherent optical memory being able to store optical pulses in the form of collective spin-wave excitations in a two-dimensional wavevector space. During storage, we perform complex beamsplitter operations and demonstrate a variety of protocols implemented at the processing stage, including real-time controlled interference of a pair of spin-wave modes with 95% visibility. The highly multimode structure of the presented memory lends itself to enhancing classical optical telecommunication, as well as parallel processing of optical qubits at the single-photon level.