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Journal of Optics B Quantum and Semiclassical Optics

Large Kerr nonlinearity with a single atom

S. Rebić, S. M. Tan, A. S. Parkins, Daniel F. Walls

Published Aug 1, 1999• 95 citations
Publisher

Abstract

We propose a scheme to generate a large Kerr nonlinearity based on electromagnetically induced transparency in a single atom placed in a high-finesse microcavity. We perform a thorough analysis of the system dynamics using a dressed states approach. This system is shown to create a photon blockade effect equivalent to that for an ideal Kerr nonlinearity as recently proposed by Imamoglu et al 1997 Phys. Rev. Lett. 79 1467.

DOI
10.1088/1464-4266/1/4/322

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We found the analytical expression for cross-Kerr nonlinear coefficient in a four-level Y-type atomic system. The analytical model is applied to 85Rb atoms and shown that under electromagnetically induced transparency, cross-Kerr nonlinear coefficient is enhanced by several orders of magnitude. At the same time, the amplitude and the sign of cross-Kerr nonlinear coefficient are controlled with respect to the intensity and the frequency of the coupling laser field. The analytical model can be useful to explain the experimental results and to study related effects in nonlinear optics. Full Text: PDF ReferencesC. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, P. Tombesi, "Polarization Qubit Phase Gate in Driven Atomic Media", Phys. Rev. Lett. 90, 197902 (2003). CrossRef C. Zhu, G. Huang, "Giant Kerr Nonlinearity, Controlled Entangled Photons and Polarization Phase Gates in Coupled Quantum-Well Structures", Opt. Express 19, 23364 (2011). CrossRef C. Hang, G. Huang, "Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet", Opt. Express 18(3), 2952 (2010). CrossRef M. Fleischhauer, I. Mamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media", Rev. Mod. Phys. 77, 633 (2005). CrossRef H. Schmidt, And A. Imamogdlu, "Giant Kerr nonlinearities obtained by electromagnetically induced transparency", Opt. Lett., 21(23), 1936 (1996). CrossRef H. Kang And Y. Zhu, Phys. "Observation of Large Kerr Nonlinearity at Low Light Intensities", Rev. Lett., 91, 093601 (2003). CrossRef J. Kou, R. G. Wan, Z. H. Kang, H. H. Wang, L. Jiang, X. J. Zhang, Y. Jiang, and J. Y. Gao, "EIT-assisted large cross-Kerr nonlinearity in a four-level inverted-Y atomic system", J. Opt. Soc. Am. B. 27(10), 2035 (2010). CrossRef X. Yang, S. Li, C. Zhang, and H. Wang, "Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system", J. Opt. Soc. Am. B. 26(7), 1423 (2009). CrossRef C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti and P. Tombesi, "Polarization Qubit Phase Gate in Driven Atomic Media", Phys. Rev. Lett. 90, 197902 (2003). CrossRef H. Sun, Y. Niu, S. Jin and S. Gong, "Phase control of cross-phase modulation with electromagnetically induced transparency", J. Phys. B: At. Mol. Opt. Phys. 40, 3037 (2007). CrossRef L.V. Doai, P.V. Trong, D.X. Khoa, and N.H. Bang, "Electromagnetically induced transparency in five-level cascade scheme of 85Rb atoms: An analytical approach", Optik, 125, 3666 (2014). CrossRef D. X. Khoa, P. V. Trong, L. V. Doai and N. H. Bang, "Electromagnetically induced transparency in a five-level cascade system under Doppler broadening: an analytical approach", Phys, Scr. 91, 035401 (2016). CrossRef D.X. Khoa, L.C. Trung, P.V. Thuan, L.V. Doai and N.H. Bang, "Measurement of dispersive profile of a multiwindow electromagnetically induced transparency spectrum in a Doppler-broadened atomic medium", J. Opt. Soc. Am. B 34 (6), 1255 (2017). CrossRef D. X. Khoa, L. V. Doai, D. H. Son, and N. H. Bang, "Enhancement of self-Kerr nonlinearity via electromagnetically induced transparency in a five-level cascade system: an analytical approach", J. Opt. Soc. Am. B., 31, 1330 (2014). CrossRef L.V. Doai, N.L.T. An, D.X. Khoa, V.N. Sau and N.H. Bang, "Manipulating giant cross-Kerr nonlinearity at multiple frequencies in an atomic gaseous medium", J. Opt. Soc. Am. B 36, 2856 (2019). CrossRef D. X. Khoa, L. V. Doai, L. N. M. Anh, L. C. Trung, P. V. Thuan, N. T. Dung, and N. H. Bang, "Optical bistability in a five-level cascade EIT medium: an analytical approach", J. Opt. Soc. Am. B, Vol. 33, 735 (2016). CrossRef N. T. Anh, L. V. Doai, and N. H. Bang, "Manipulating multi-frequency light in a five-level cascade-type atomic medium associated with giant self-Kerr nonlinearity", J. Opt. Soc. Am. B 35, 1233 (2018). CrossRef N. T. Anh, L. V. Doai, D. H. Son, and N. H. Bang, "Manipulating multi-frequency light in a five-level cascade EIT medium under Doppler broadening", Optik 171, 721 (2018). CrossRef D.A. Steck, Rb85 D Line Data: http://Steck.Us/Alkalidata/rubidium85numbers.pdf CrossRef

Photonics Letters of Poland•Sep 30, 2021•1 citation
We propose a scheme to generate a large Kerr nonlinearity based on electromagnetically induced transparency in a single atom placed in a high-finesse microcavity. We perform a thorough analysis of the system dynamics using a dressed states approach. This system is shown to create a photon blockade effect equivalent to that for an ideal Kerr nonlinearity as recently proposed by Imamoglu et al 1997 Phys. Rev. Lett. 79 1467.
This thesis investigates the properties of an atomic system exhibiting a giant Kerr nonlinearity. The atomic energy level scheme involves four energy levels. A three level A subsystem in the atom exhibits the effect of electromagnetically induced transparency (EIT), reducing the spontaneous emission noise. The fourth level leads to an ac-Stark shift of the ground state, which in turn leads to a giant, noiseless Kerr nonlinearity. Two different environments are explored. First, a system comprising of large number of atoms in an optical cavity is analysed. Detailed aspects of noise reduction in this system are investigated. In particular, strong squeezing in the quadrature in phase with the field driving the cavity mode is found, if the effective coupling of light to the atoms is strong. However, the linewidth of the predicted squeezing is found to be very narrow. This is attributed to a very steep linear susceptibility of the atomic medium. Since the widening of the squeezing window is possible only for weaker effective coupling, in turn reducing the squeezing level, a different environment is proposed. This involves a single four level atom, strongly coupled to the cavity mode. In such a strongly coupled system, the most appropriate approach is found to be that formulated in terms of polaritons – composite excitations of the 'atom-cavity molecule'. Adopting the polariton approach, nonclassical correlations in the field leaving the cavity are investigated. Strong photon antibunching is found and the effect of photon blockade predicted and described. The photon blockade effect can also be found in a system comprised of a two level atom coupled to the cavity mode, if the external driving is tuned to one of the vacuum Rabi resonances. A comparison between the two schemes is performed, and it is found that the four level scheme exhibits much better photon blockade. The reason for this is quantum interference between secondary transitions in the dressed states picture. Destructive interference cancels the transitions that would otherwise introduce a second photon into the system, hence producing a more robust photon blockade. All of these results are valid in the regime where external driving is weak. If the external driving strength is increased, the photon statistics (as measured by the zero-delay second order correlation function) changes from strong antibunching to strong bunching, over a relatively narrow range of driving strengths. The occurrence of this change can again be attributed to quantum interference. It is shown that the interference effect prevents the excitation of the composite system by a second photon, but not excitation by a two-photon transition (following the first excitation). Therefore, the third excitation manifold is excited, which then decays back to the first manifold in a two photon cascade. This two photon cascade is the source of correlated photon pairs causing an increase in the second order correlation function. The dynamics of forward scattering of light is presented, and nonclassical behaviour of the delay dependence of correlation function ('overshoots' and 'undershoots') is discussed. For the analytical treatment of this system, a method based on the polariton approach is devised, which includes the treatment of driving and damping. It is shown that this method is ideally suited to the analysis of strongly coupled systems, where only a few photons contribute to the dynamics.
We analyse the possibilities for quantum state engineering offered by a model for Kerr-type nonlinearity enhanced by electromagnetically induced transparency (EIT), which was recently proposed by Petrosyan and Kurizki [2002, Phys. Rev. A, 65, 33833]. We go beyond the semiclassical treatment and derive a quantum version of the model with both a full Hamiltonian approach and an analysis in terms of dressed states. The preparation of an entangled coherent state via a cross-phase modulation effect is demonstrated. We briefly show that the violation of locality for such an entangled coherent state is robust against low detection efficiency. Finally, we investigate the possibility of a bi-chromatic photon blockade realized via the interaction of a low density beam of atoms with a bi-modal electromagnetic cavity which is externally driven. We show the effectiveness of the blockade effect even when more than a single atom is inside the cavity. The possibility to control two different cavity modes allows some insights into the generation of an entangled state of cavity modes.
Universal photon blockade in a two-mode Jaynes-Cummings model incorporating third-order Kerr nonlinearity is demonstrated with a single two-level atom coupled to a waveguide microcavity. Realization of this universal photon blockade is attributed to the cooperative effects of field-atom coupling and Kerr nonlinearity. More importantly, this antibunching is found to be robust against the atomic spontaneous emission, driving field strength, and defect-induced cavity mode coupling. The strong antibunching effect in this resonance-driven scheme is essentially different from those without Kerr nonlinearity. Moreover, this work expands the platform for achieving universal photon blockade and reveals the cooperative advantages of nonlinearities in enhancing the purity and brightness of single-photon sources, representing a novel strategy toward high-performance single-photon sources in integrated quantum optical devices.
Quantum limit of dissipation-free photon-photon interactions at the few photon level is studied in the context of giant Kerr nonlinearities in cavity electromagneti cally induced transparency (EIT). It is shown that photon-photon interaction is largest when the cavity contains a sing le atom. In contrast to conventional nonlinearities, increasing the number of atoms cannot in crease the interaction strength but will in general degrade the performance by enhancing di spersion. In the non-perturbative regime, the single-atom photon-photon interaction can be limited by lossy states excited from long-lived EIT states. Asymptotically, in the strong coupling limit, photon-photon interaction is determined by the single photon-atom coupling strength. Photon blockade occurs for single atoms but only partial blockade can occur for low dispersion and not at all in the high-dispersion limit of the multi-atom case.
We study the nonlinear effect in a three-level atomic system in Λ configuration. As two or more fields are confined within the common electromagnetically induced transparency (EIT) window, they directly disturb EIT dark state at the same time, which leads to the self- and cross-Kerr nonlinear interactions. Our scheme is different from the existed schemes based on three-level or multilevel systems only existing single type of nonlinear interactions. In the common EIT windows, the self- and cross-Kerr nonlinearities are established with suppressed linear absorption and our scheme can be generalized polychromatic Kerr nonlinearity. Because the atoms are almost trapped in the ground states and the atom population becomes unchanged, the scheme is robust to the atomic spontaneous emission. Our scheme is a promising avenue for preparation of squeezing and entanglement .
We found the analytical expression for cross-Kerr nonlinear coefficient in a four-level Y-type atomic system. The analytical model is applied to 85Rb atoms and shown that under electromagnetically induced transparency, cross-Kerr nonlinear coefficient is enhanced by several orders of magnitude. At the same time, the amplitude and the sign of cross-Kerr nonlinear coefficient are controlled with respect to the intensity and the frequency of the coupling laser field. The analytical model can be useful to explain the experimental results and to study related effects in nonlinear optics. Full Text: PDF ReferencesC. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, P. Tombesi, "Polarization Qubit Phase Gate in Driven Atomic Media", Phys. Rev. Lett. 90, 197902 (2003). CrossRef C. Zhu, G. Huang, "Giant Kerr Nonlinearity, Controlled Entangled Photons and Polarization Phase Gates in Coupled Quantum-Well Structures", Opt. Express 19, 23364 (2011). CrossRef C. Hang, G. Huang, "Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet", Opt. Express 18(3), 2952 (2010). CrossRef M. Fleischhauer, I. Mamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media", Rev. Mod. Phys. 77, 633 (2005). CrossRef H. Schmidt, And A. Imamogdlu, "Giant Kerr nonlinearities obtained by electromagnetically induced transparency", Opt. Lett., 21(23), 1936 (1996). CrossRef H. Kang And Y. Zhu, Phys. "Observation of Large Kerr Nonlinearity at Low Light Intensities", Rev. Lett., 91, 093601 (2003). CrossRef J. Kou, R. G. Wan, Z. H. Kang, H. H. Wang, L. Jiang, X. J. Zhang, Y. Jiang, and J. Y. Gao, "EIT-assisted large cross-Kerr nonlinearity in a four-level inverted-Y atomic system", J. Opt. Soc. Am. B. 27(10), 2035 (2010). CrossRef X. Yang, S. Li, C. Zhang, and H. Wang, "Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system", J. Opt. Soc. Am. B. 26(7), 1423 (2009). CrossRef C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti and P. Tombesi, "Polarization Qubit Phase Gate in Driven Atomic Media", Phys. Rev. Lett. 90, 197902 (2003). CrossRef H. Sun, Y. Niu, S. Jin and S. Gong, "Phase control of cross-phase modulation with electromagnetically induced transparency", J. Phys. B: At. Mol. Opt. Phys. 40, 3037 (2007). CrossRef L.V. Doai, P.V. Trong, D.X. Khoa, and N.H. Bang, "Electromagnetically induced transparency in five-level cascade scheme of 85Rb atoms: An analytical approach", Optik, 125, 3666 (2014). CrossRef D. X. Khoa, P. V. Trong, L. V. Doai and N. H. Bang, "Electromagnetically induced transparency in a five-level cascade system under Doppler broadening: an analytical approach", Phys, Scr. 91, 035401 (2016). CrossRef D.X. Khoa, L.C. Trung, P.V. Thuan, L.V. Doai and N.H. Bang, "Measurement of dispersive profile of a multiwindow electromagnetically induced transparency spectrum in a Doppler-broadened atomic medium", J. Opt. Soc. Am. B 34 (6), 1255 (2017). CrossRef D. X. Khoa, L. V. Doai, D. H. Son, and N. H. Bang, "Enhancement of self-Kerr nonlinearity via electromagnetically induced transparency in a five-level cascade system: an analytical approach", J. Opt. Soc. Am. B., 31, 1330 (2014). CrossRef L.V. Doai, N.L.T. An, D.X. Khoa, V.N. Sau and N.H. Bang, "Manipulating giant cross-Kerr nonlinearity at multiple frequencies in an atomic gaseous medium", J. Opt. Soc. Am. B 36, 2856 (2019). CrossRef D. X. Khoa, L. V. Doai, L. N. M. Anh, L. C. Trung, P. V. Thuan, N. T. Dung, and N. H. Bang, "Optical bistability in a five-level cascade EIT medium: an analytical approach", J. Opt. Soc. Am. B, Vol. 33, 735 (2016). CrossRef N. T. Anh, L. V. Doai, and N. H. Bang, "Manipulating multi-frequency light in a five-level cascade-type atomic medium associated with giant self-Kerr nonlinearity", J. Opt. Soc. Am. B 35, 1233 (2018). CrossRef N. T. Anh, L. V. Doai, D. H. Son, and N. H. Bang, "Manipulating multi-frequency light in a five-level cascade EIT medium under Doppler broadening", Optik 171, 721 (2018). CrossRef D.A. Steck, Rb85 D Line Data: http://Steck.Us/Alkalidata/rubidium85numbers.pdf CrossRef