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arXiv:1009.2996 · Journal of Physics B Atomic Molecular and Optical Physics

Zitterbewegung of optical pulses in nonlinear frequency conversion

Stefano Longhi

Published Oct 5, 2010• 10 citations
arXivHTMLPDF

Abstract

Pulse walk-off in the process of sum frequency generation in a nonlinear χ (2) crystal is shown to be responsible for pulse jittering which is reminiscent to the Zitterbewegung (trembling motion) of a relativistic freely moving Dirac particle. An analytical expression for the pulse centre of mass trajectory is derived in the no-pump-depletion limit, and the numerical examples of Zitterbewegung are presented for sum frequency generation in periodically poled lithium niobate. The proposed quantum-optical analogy indicates that frequency conversion in nonlinear optics could provide an experimentally accessible simulator of the Dirac equation.

DOI
10.1088/0953-4075/43/20/205402

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Pulse walk-off in the process of sum frequency generation in a nonlinear χ (2) crystal is shown to be responsible for pulse jittering which is reminiscent to the Zitterbewegung (trembling motion) of a relativistic freely moving Dirac particle. An analytical expression for the pulse centre of mass trajectory is derived in the no-pump-depletion limit, and the numerical examples of Zitterbewegung are presented for sum frequency generation in periodically poled lithium niobate. The proposed quantum-optical analogy indicates that frequency conversion in nonlinear optics could provide an experimentally accessible simulator of the Dirac equation.
Ultracold atoms which are subject to ultra-relativistic dynamics are investigated. By using optically induced gauge potentials we show that the dynamics of the atoms is governed by a Dirac-type equation. To illustrate this we study the trembling motion of the centre of mass for an effective two-level system, historically called Zitterbewegung. Its origin is described in detail, where in particular the role of the finite width of the atomic wave packets is seen to induce a damping of both the centre of mass dynamics and the dynamics of the populations of the two levels.
We present a geometrical representation of the process of sum frequency generation in the undepleted pump approximation, in analogy with the known optical Bloch equations. We use this analogy to propose a technique for achieving both high efficiency and large bandwidth in sum frequency conversion using the adiabatic inversion scheme. The process is analogous with rapid adiabatic passage in NMR, and adiabatic constraints are derived in this context. This adiabatic frequency conversion scheme is realized experimentally using an aperiodically poled potassium titanyl phosphate (KTP) device, where we achieved high efficiency signal-to-idler conversion over a bandwidth of 140nm140\phantom{\rule{0.3em}{0ex}}\mathrm{nm}140nm.
We develop the theory of frequency up-conversion of an arbitrary spatially-broadband quantum state (quantum image), deriving the analytical solutions for the cases of plane-wave pump and short crystal with arbitrary pump. By using an example of the quantum image imposed by the orbital angular momentum of the pump beam in spontaneous parametric down-conversion, we show that 99%-fidelity up-conversion of quantum images from an infrared wavelength to the visible wavelength can be obtained in periodically-poled lithium-niobate crystals at reasonable pump intensities well below the crystal damage threshold.
We demonstrate the coherent frequency conversion of structured light, optical beams in which the phase varies in each point of the transverse plane, from the near infrared (803nm) to the visible (527nm). The frequency conversion process makes use of sum-frequency generation in a periodically poled lithium niobate (ppLN) crystal with the help of a 1540-nm Gaussian pump beam. We perform far-field intensity measurements of the frequency-converted field, and verify the sought-after transformation of the characteristic intensity and phase profiles for various input modes. The coherence of the frequency-conversion process is confirmed using a mode-projection technique with a phase mask and a single-mode fiber. The presented results could be of great relevance to novel applications in high-resolution microscopy and quantum information processing.
Efficient nonlinear optical frequency conversion is proposed and theoretically demonstrated by use of stopped short light pulses in a doubly resonant Bragg reflector. The pump pulse is shown to decelerate and stop in the reflector, and the stopped pump field reinforces the interaction with stimulated Raman scattering. The temporal walk-off between the pump pulse and the generated Raman pulse can be substantially reduced with the doubly resonant Bragg structure. Numerical simulations show that the conversion from the picosecond pump pulse to Stokes wave can reach 85%.
Frequency conversion of single photons is an important technology for quantum interface and quantum communication networks. Here, single-photon frequency conversion in the telecommunication band is experimentally demonstrated via cascaded quadratic nonlinear processes. Using cascaded quasi-phase-matched sum and difference frequency generation in a periodically poled lithium niobate waveguide, the signal photon of a photon pair from spontaneous down-conversion is precisely shifted to identically match its counterpart, i.e., the idler photon, in frequency to manifest a clear nonclassical dip in the Hong-Ou-Mandel interference. Moreover, quantum entanglement between the photon pair is maintained after the frequency conversion, as is proved in time-energy entanglement measurement. The scheme is used to switch single photons between dense wavelength-division multiplexing channels, which holds great promise in applications in realistic quantum networks.