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Physical Review A

Phase gate with a four-level inverted-Y system

Amitabh Joshi, Min Xiao

Published Dec 14, 2005• 99 citations
Publisher

Abstract

The four-level atomic system in an inverted-Y configuration is investigated for large Kerr nonlinearities. The cross-Kerr nonlinearity generated in such a system can produce a phase shift of order $\ensuremath{\pi}$ and can be used for realizing polarization quantum phase gates.

DOI
10.1103/physreva.72.062319

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The four-level atomic system in an inverted-Y configuration is investigated for large Kerr nonlinearities. The cross-Kerr nonlinearity generated in such a system can produce a phase shift of order \ensuremathπ\ensuremath{\pi}\ensuremathπ and can be used for realizing polarization quantum phase gates.
We analyze the nonlinear optical response of a four-level atomic system driven into a tripod configuration. The large cross-Kerr nonlinearities that occur in such a system are shown to produce nonlinear phase shifts of order $\ensuremath{\pi}$. Such a substantial shift may be observed in a cold atomic gas in a magneto-optical trap where it could be feasibly exploited towards the realization of a polarization quantum phase gate. The experimental feasibility of such a gate is here examined in detail.
A four-level inverted-Y scheme with an electromagnetically induced transparency (EIT) core is investigated for the enhancement of cross-Kerr effect in rubidium atoms. When detunings of the coupling and control fields are appropriately set, an enhanced EIT window is observed, and the induced phase shift of the probe field due to cross-phase modulation (XPM) is obtained by measuring the dispersive property of the probe transition. The maximal XPM phase shift is about 12° under the current experimental conditions. The experimental measurements agree well with the theoretical calculations. The enhanced XPM phase shift in such an atomic system has applications in quantum nonlinear optics and quantum information science.
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
We first investigate the nonlinear optical response of a five-level tripod atomic system in electromagnetically induced transparency and then propose a 3-qubit phase gate protocol based on the fifth-order nonlinearity. The cross-phase modulation among the three weak fields induced by the fifth-order nonlinearity in electromagnetically induced transparency can produce the phase shift of order π, which can be used to realize the 3-qubit polarization phase gate. This protocol should have potential applications in quantum information processing.
Large optical nonlinearities occurring in a coherently prepared atomic system are shown to produce phase shifts of order πππ. Such an effect may be observed in ultracold rubidium atoms where it could be feasibly exploited toward the realization of a polarization phase gate.