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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Large optical nonlinearities with few photons

Barry C. Sanders

Published Feb 10, 2011• 1 citation
Publisher

Abstract

Weak-light all-optical switches would enhance photonics capabilities and enable important optical quantum information processing tasks, but optical switching based on third-order optical nonlinearity is proving to be elusive and controversial. I discuss strategies to generate large cross-phase modulation by combining double electromagnetically induced transparency, competing atomic transitions, electron population engineering for pulse speed control, and using boundary conditions to confine the transverse field beyond the diffraction limit.

DOI
10.1117/12.873653

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Weak-light all-optical switches would enhance photonics capabilities and enable important optical quantum information processing tasks, but optical switching based on third-order optical nonlinearity is proving to be elusive and controversial. I discuss strategies to generate large cross-phase modulation by combining double electromagnetically induced transparency, competing atomic transitions, electron population engineering for pulse speed control, and using boundary conditions to confine the transverse field beyond the diffraction limit.
Strong optical cross-phase modulation (XPM) for weak fields is tremendously important for optical quantum information (QI) processing and for all-optical switches in classical communication. A sufficiently large XPM would allow the design of deterministic controlled quantum gates for photonic qubits and thus enable universal optical quantum computation. Recently, several proposals have been brought forward to create large XPM using double electromagnetically induced transparency (DEIT) in which two weak signal light pulses travel at equally slow group velocity, but creating DEIT still poses an experimental challenge. We give a brief overview about DEIT and discuss its applications and limitations. A scheme that combines the best features of previous proposals and optimizes the large XPM parameter for DEIT schemes is outlined. Finally we devise a scheme to perform universal quantum information processing, which respects the bound on the achievable nonlinearity and addresses the requirement of quantum error correction.
We experimentally demonstrate an all-optical switching (AOS) scheme based on double slow light (DSL) pulses, in which one pulse is switched by another due to the cross-Kerr nonlinearity. The interaction time is prolonged by optically dense atomic media and matched group velocities. The interaction strength is maintained at a high level by keeping both fields at their electromagnetically-induced-transparency resonances to minimize the linear loss. In the AOS without the DSL scheme, the group velocity mismatch sets an upper limit on the switching efficiency of two photons per atomic cross section as discussed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)]. Compared to that limit, we have obtained an enhanced switching efficiency by a factor of 3 with our DSL scheme. The nonlinear efficiency can be further improved by increasing the optical depth of the medium. Our work advances low-light-level nonlinear optics and provides essential ingredients for quantum many-body physics using strongly interacting photons.
In third order nonlinear mediums, the intensity of one optical field can modify the phase of another optical field. This is known as cross-phase modulation (XPM) and is important for Quantum Information Processing (QIP) as phase shifts of single-photons that exceed π rad can be used to implement two-qubit quantum logic gates. For a conventional XPM scheme, the Kerr nonlinearity responsible for XPM is too small for appreciable phase shifts to be achieved with low intensity optical fields. However, Electromagnetically Induced Transparency (EIT) can increase this nonlinearity by several orders of magnitude. This thesis discusses the experimental construction of a laser-atomic system capable of EIT modulated XPM. This includes construction of a rubidium magneto-optical trap (RbMOT), characterization of this RbMOT, demonstration of EIT in the RbMOT, and a system capable of detecting optical phase shifts produced by EIT. The talk will conclude with an outlook on further implementations to the experiment that will increase this nonlinearity such that phase shifts at the single-photon level are possible. | 76 pages
Electromagnetically induced transparency in an optically thick, cold medium creates a unique system where pulse-propagation velocities may be orders of magnitude less than c and optical nonlinearities become exceedingly large. As a result, nonlinear processes may be efficient at low-light levels. Using an atomic system with three, independent channels, we demonstrate a quantum interference switch where a laser pulse with an energy per area of $\ensuremath{\sim}23$ photons per ${\ensuremath{\lambda}}^{2}/(2\ensuremath{\pi})$ causes a 1/e1/e1/e absorption of a second pulse.
All-optical devices allow improvements in the speed of optical communication and computation systems by avoiding the conversion between the optical and electronic domains. The focus of this thesis is the experimental investigation of a new type of all-optical switch that is based on the control of optical patterns formed by nonlinear interactions between light and matter.\nThe all-optical switch consists of a pair of light beams that counterpropagate through warm rubidium vapor. These beams induce a nonlinear optical instability that gives rise to mirrorless parametric self-oscillation and generates light in the state of polarization that is orthogonal to that of the pump beams. In the far-field, the generated light forms patterns consisting of two or more spots. To characterize this instability, I observe experimentally the amount of generated power and the properties of the generated patterns as a function of pump beam intensity, frequency, and size. Near an atomic resonance, the instability has a very low threshold: with less than 1 mW of total pump power, >3 μW of power is generated.\nTo apply this system to all-optical switching, I observe that the orientation of the generated patterns can be controlled by introducing a symmetry-breaking perturbation to the system. A perturbation in the form of a weak switch beam injected into the nonlinear medium is suitable for controlling the orientation of the generated patterns. The device operates as a switch where each state of the pattern orientation corresponds to a state of the switch, and spatial filtering of the generated pattern defines the output ports of the device. Measurements of the switch response show that it can be actuated by as few as 600 ±40 photons. For a switch beam with 1/e field radius w0 = 185 ± 5μm, 600 ±40 photons correspond to an energy density of 5.4±0.7×10−4 photons/λ2/(2π) which is comparable to the best reported results from all-optical switches. The approach to all-optical switching I report here operates at very low light levels and exhibits cascadability and transistor-like response. Furthermore, the sensitivity is comparable to switches using cold-atom electromagnetically-induced transparency or cavity quantum-electrodynamics techniques, but is achieved with a simpler system, requiring only one optical frequency and occurring in warm atomic vapor.\nI develop a numerical model for the switch that exhibits patterns that rotate in the presence of a weak applied optical field. Results from this model, and from my experiment, show that the switch response time increases as the input power decreases. I propose that this increase is due to critical slowing down. Mapping the pattern orientation to a simple one-dimensional system shows that critical slowing down may account for the observed increase in response time at low input power. The ultimate performance of the device is likely limited by critical slowing down and I conclude that the minimum number of photons capable of actuating the switch is between 400 and 600 photons.\nMy approach to all-optical switching is simple, extremely sensitive and exhibits many of the properties necessary for use as an optical logic element. Additionally, this work has implications for a wide range of pattern forming systems, both in the field of optics and beyond, that may be applicable as novel devices for sensitive measurement and detection.