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Journal of the Optical Society of America B

Fifth-order nonlinearity and 3-qubit phase gate in a five-level tripod atomic system

Fuli Li, Ying Gu, Lijun Wang, Qihuang Gong

Published Mar 20, 2008• 8 citations
Publisher

Abstract

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.

DOI
10.1364/josab.25.000504

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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.
It is known that photons are the ideal carriers of quantum information and ensemble of atoms can be acted as the long lived storage and processing units. In the coherently prepared atomic ensemble with the light resonantly interacting with the atoms, various schemes have been proposed to implement quantum state transfer and storage, quantum phase gate, generation of entangled photons, and the long-distance quantum communication [1]. We first proposed the dark-state polaritons in a five-level M-type atomic ensemble in the electro magnetically induced transparency (EIT) [2], Under conditions of the low excitation limit and adiabatic following, the quantum field can be mapped onto the atomic polarization states, forming the shape preserving quantum states of polaritons. Two channels for robust quantum memory are provided. Then, we investigated the nonlinear optical response of a five-level tripod atomic system in the EIT, and proposed a three-qubit phase gate protocol based on the fifth-order nonlinearity [3]. The cross phase modulation among three weak fields induced by the fifth-order nonlinearity in EIT can produce the phase shift of order n, which can be used to realize the three-qubit polarization phase gate. Finally, we proposed a cavity-QED scheme that can effectively generate EPR polarization-entangled photon pairs [4], A four-level tripod atom successively couples to two high-Q optical cavities possessing polarization degeneracy, assisted by a classical π-polarized pump field. The stimulated Raman adiabatic passage process in the atom-cavity system is used to produce the polarization-entangled photon pairs. The proposal is particularly robust against atomic spontaneous decay. The above protocols should have potential applications in quantum information processing.
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.
We investigate, both theoretically and experimentally, the cross-Kerr nonlinearity generated in a four-level tripod system in the 87Rb D1 line. The system exhibits simultaneous electromagnetically induced transparency (EIT) windows for two weak (probe and trigger) fields and the enhanced cross-Kerr nonlinearity by EIT. The cross-Kerr nonlinear phase shifts for probe (trigger) field are measured at several different intensities of trigger (probe) field. The results show that large cross-phase modulation (XPM) coefficients can be achieved at low light intensities.
We present a full quantum treatment of a five-level atomic system coupled to two quantum and two classical light fields. The two quantum fields undergo a cross-phase-modulation induced by electromagnetically induced transparency. The performance of this configuration as a two-qubit quantum phase gate for traveling single photons is examined. A trade-off between the size of the conditional phase shift and the fidelity of the gate is found. Nonetheless, a satisfactory gate performance is still found to be possible in the transient regime, corresponding to a fast gate operation.
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