We review the field of femtosecond pulse shaping, in which Fourier synthesis methods are used to generate nearly arbitrarily shaped ultrafast optical wave forms according to user specification. An emphasis is placed on programmable pulse shaping methods based on the use of spatial light modulators. After outlining the fundamental principles of pulse shaping, we then present a detailed discussion of pulse shaping using several different types of spatial light modulators. Finally, new research directions in pulse shaping, and applications of pulse shaping to optical communications, biomedical optical imaging, high power laser amplifiers, quantum control, and laser-electron beam interactions are reviewed.

Femtosecond pulse shaping using spatial light modulators

The distribution of quantum states over long distances is limited by photon loss. Straightforward amplification as in classical telecommunications is not an option in quantum communication because of the no-cloning theorem. This problem could be overcome by implementing quantum repeater protocols, which create long-distance entanglement from shorter-distance entanglement via entanglement swapping. Such protocols require the capacity to create entanglement in a heralded fashion, to store it in quantum memories, and to swap it. One attractive general strategy for realizing quantum repeaters is based on the use of atomic ensembles as quantum memories, in combination with linear optical techniques and photon counting to perform all required operations. Here the theoretical and experimental status quo of this very active field are reviewed. The potentials of different approaches are compared quantitatively, with a focus on the most immediate goal of outperforming the direct transmission of photons.

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Quantum repeaters based on atomic ensembles and linear optics

During the past decade the interaction of light with multiatom ensembles has attracted much attention as a basic building block for quantum information processing and quantum state engineering. The field started with the realization that optically thick free space ensembles can be efficiently interfaced with quantum optical fields. By now the atomic ensemble-light interfaces have become a powerful alternative to the cavity-enhanced interaction of light with single atoms. Various mechanisms used for the quantum interface are discussed, including quantum nondemolition or Faraday interaction, quantum measurement and feedback, Raman interaction, photon echo, and electromagnetically induced transparency. This review provides a common theoretical frame for these processes, describes basic experimental techniques and media used for quantum interfaces, and reviews several key experiments on quantum memory for light, quantum entanglement between atomic ensembles and light, and quantum teleportation with atomic ensembles. The two types of quantum measurements which are most important for the interface are discussed: homodyne detection and photon counting. This review concludes with an outlook on the future of atomic ensembles as an enabling technology in quantum information processing.

Quantum interface between light and atomic ensembles

The distribution of quantum states over long distances is limited by photon loss. Straightforward amplification as in classical telecommunications is not an option in quantum communication because of the no-cloning theorem. This problem could be overcome by implementing quantum repeater protocols, which create long-distance entanglement from shorter-distance entanglement via entanglement swapping. Such protocols require the capacity to create entanglement in a heralded fashion, to store it in quantum memories, and to swap it. One attractive general strategy for realizing quantum repeaters is based on the use of atomic ensembles as quantum memories, in combination with linear optical techniques and photon counting to perform all required operations. Here we review the theoretical and experimental status quo of this very active field. We compare the potential of different approaches quantitatively, with a focus on the most immediate goal of outperforming the direct transmission of photons.

Optical resonance and two-level atoms

Operation of a wideband, versatile optical spectrum analyzer for radio-frequency (RF) signals is demonstrated. The device is based on spectral hole burning (SHB). The demonstration features 2.3-GHz instantaneous bandwidth, 500-kHz resolution, and a 32-dB dynamic range. A true RF signal, transferred to the optical carrier with the help of a Mach-Zehnder modulator, is analyzed with optical carrier suppression and zooming capabilities. This is to the authors' knowledge the largest instantaneous bandwidth ever demonstrated for a SHB-based processor in rare-earth-doped crystals.

Wideband versatile radio-frequency spectrum analyzer

Spectral hole-burning (SHB) technology is considered for >10‐GHz instantaneous bandwidth signal-processing applications. In this context we report on what is believed to be the first demonstration of a SHB microwave spectrometer. A set of gratings engraved in a SHB crystal is used to filter one sideband of the optically carried microwave signal. The setup is confined to narrow-bandwidth operation, over a 35-MHz-wide interval. The first findings confirm the validity of the architecture in terms of spectral resolution, angular channel separation, and simultaneous detection of multiple spectral lines.

Demonstration of a radio-frequency spectrum analyzer based on spectral hole burning

Quantum information transfer from light to atom ensembles and vice versa has both basic and practical importance Among the relevant topics let us mention entanglement and decoherence of macroscopic systems, together with applications to quantum memory for long distance quantum cryptography Although the first experimental demonstrations have been performed in atomic vapors and clouds, rare earth ion doped crystals are also interesting media for such processes In this paper we address ${\mathrm{Tm}}^{3+}$ ions capability to behave as three-level $\ensuremath{\Lambda}$ systems, a key ingredient to convert optical excitation into a spontaneous-emission-free spin wave Indeed ${\mathrm{Tm}}^{3+}$ falls within reach of light sources that can be stabilized easily to the required degree In the absence of zero-field hyperfine structure we apply an external magnetic field to lift the nuclear spin degeneracy in ${\mathrm{Tm}}^{3+}:\mathrm{YAG}$ We experimentally determine the gyromagnetic tensor components with the help of spectral hole-burning techniques Then appropriate orientation of the applied field enables us to optimize the transition probability ratio along the two legs of the $\ensuremath{\Lambda}$ The resulting three-level $\ensuremath{\Lambda}$ system should suit quantum information processing requirements

https://hal.archives-ouvertes.fr/hal-00008646/document

Experimental tailoring of a three-level Λ system in Tm 3 + : YAG

We demonstrate the first 10-GHz instantaneous bandwidth radio-frequency spectrum analyzer based on spectral hole burning in Tm/sup 3+/:YAG. It exhibits 10 000 frequency channels and a resolution better than 1 MHz. Thanks to the fast and linear chirping capabilities of the laser used, it has a potential 100% probability of interception and a response time in the millisecond range. Its linear dynamic range of 16 dB is presently essentially limited by the modest amount of optical power available and can be further improved.

Ivan Lorgeré

Papers

Wideband versatile radio-frequency spectrum analyzer

Demonstration of a radio-frequency spectrum analyzer based on spectral hole burning

Experimental tailoring of a three-level Λ system in Tm 3 + : YAG

10-GHz bandwidth RF spectral analyzer with MHz resolution based on spectral hole burning in Tm/sup 3+/:YAG

Wideband radio frequency spectrum analyzer: improved design and experimental results