Jianming Wen

The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics

The Talbot effect, also referred to as self-imaging or lensless imaging, is of the phenomena manifested by a periodic repetition of planar field distributions in certain types of wave fields. This phenomenon is finding applications not only in optics, but also in a variety of research fields, such as acoustics, electron microscopy, plasmonics, x ray, and Bose–Einstein condensates. In optics, self-imaging is being explored particularly in image processing, in the production of spatial-frequency filters, and in optical metrology. In this article, we give an overview of recent advances on the effect from classical optics to nonlinear optics and quantum optics. Throughout this review article there is an effort to clearly present the physical aspects of the self-imaging phenomenon. Mathematical formulations are reduced to the indispensable ones. Readers who prefer strict mathematical treatments should resort to the extensive list of references. Despite the rapid progress on the subject, new ideas and applications of Talbot self-imaging are still expected in the future.

Narrowband biphoton generation near atomic resonance

Generating nonclassical light offers a benchmark tool for fundamental research and potential applications in quantum optics. Conventionally, it has become a standard technique to produce nonclassical light through the nonlinear optical processes occurring in nonlinear crystals. We describe this process using cold atomic-gas media to generate such nonclassical light, especially focusing on narrowband biphoton generation. Compared with the standard procedure the new biphoton source has such properties as long coherence time, long coherence length, high spectral brightness, and high conversion efficiency. Although there exist two methodologies describing the physical process, we concentrate on the theoretical aspect of the entangled two-photon state produced from the four-wave mixing in a multilevel atomic ensemble using perturbation theory. We show that both linear and nonlinear optical responses to the generated fields play an important role in determining the biphoton waveform and, consequently, on the two-photon temporal correlation. There are two characteristic regimes determined by whether the linear or nonlinear coherence time is dominant. In addition, our model provides a clear physical picture that brings insight into understanding biphoton optics with this new source. We apply our model to recent work on generating narrowband (and even subnatural linewidth) paired photons using the technique of electromagnetically induced transparency and slow-light effect in cold atoms and find good agreement with experimental results.

Optimal storage and retrieval of single-photon waveforms

We report an experimental demonstration of optimal storage and retrieval of heralded single-photon wave packets using electromagnetically induced transparency (EIT) in cold atoms at a high optical depth. We obtain an optimal storage efficiency of (49 ± 3)% for single-photon waveforms with a temporal likeness of 96%. Our result brings the EIT quantum light-matter interface closer to practical quantum information applications.

Fractional second-harmonic Talbot effect

We report the fractional second-harmonic Talbot effect associating with the χ⁽²⁾ in periodically-poled LiTaO₃ (PPLT) crystals. Our results show that the images are sensitive to the duty circle and the background of the array.

Theory of nonlinear Talbot effect

The nonlinear Talbot effect, in which self-images are formed by generated parametric light from the nonlinear optical process, is presented in this paper. The comparison is made between the conventional Talbot effect and the newly observed nonlinear case. The essence of such nonlinear self-images is provided and future work on this effect is also discussed. The conceptional extension achieved here not only opens a door for broader scopes of applications in imaging techniques but also offers a way for other research fields such as visualizing various ferric domains and subwavelength lithography.

Overcoming erasure errors with multilevel systems

We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum polynomial codes to encode quantum information and generalizes teleportation based error correction for multilevel systems to correct photon losses and operation errors in a fault-tolerant manner. We discuss the application of quantum polynomial codes to one-way quantum repeaters. For various types of operation errors, we identify different parameter regions where quantum polynomial codes can achieve a superior performance compared to qubit based quantum parity codes.

Acousto-optic tunable second-harmonic Talbot effect based on periodically poled LiNbO 3 crystals

Based on nonlinear Talbot effect, we propose an acousto-optic tunable second-harmonic (SH) array in a one-dimensional periodically poled LiNbO3 (PPLN) crystal. The SH array is the self-imaging of χ(2) in the PPLN crystal. By applying an acoustic wave, we can tune the period, the distribution, and even the dimension of the array. Such a phenomenon has potential applications in tunable high-resolution Talbot illuminators, beam shapers, and image processing.

Coherence-Assisted Resonance with Sub-Transit-Limited Linewidth

We demonstrate a novel approach to obtain a resonance linewidth below the transit limit. The cross correlation between the induced intensity modulation of two lasers coupling the target resonance exhibits a narrow spectrum. 1/30 of the transit-limited width is achieved in a proof-of-principle experiment where two ground states are the target resonance levels. Attainable linewidth is only limited by laser shot noise in principle. The experimental results qualitatively agree with an intuitive analytical model and numerical calculations. This technique can be easily implemented and should be applicable to many atomic, molecular, and solid state spin systems for spectroscopy, metrology, and resonance-based sensing and imaging.