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arXiv:quant-ph/0402177 · Physical Review A

Non-Abelian geometric quantum memory with an atomic ensemble

Yahui Li, Peng Zhang, Paolo Zanardi A, C. P. Sun

Published Sep 29, 2004• 33 citations
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Abstract

We study a quantum information storage scheme based on an atomic ensemble with near (also exact) three-photon resonance electromagnetically induced transparency (EIT). Each 4-level-atom is coupled to two classical control fields and a quantum probe field. Quantum information is adiabatically stored in the associated dark polariton manifold. An intrinsic nontrivial topological structure is discovered in our quantum memory implemented through the symmetric collective atomic excitations with a hidden $\mathrm{SU}(3)$ dynamical symmetry. By adiabatically changing the Rabi frequencies of two classical control fields, the quantum state can be retrieved up to a non-Abelian holonomy and thus decoded from the final state in a purely geometric way.

DOI
10.1103/physreva.70.032330

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We study a quantum information storage scheme based on an atomic ensemble with near (also exact) three-photon resonance electromagnetically induced transparency (EIT). Each 4-level-atom is coupled to two classical control fields and a quantum probe field. Quantum information is adiabatically stored in the associated dark polariton manifold. An intrinsic nontrivial topological structure is discovered in our quantum memory implemented through the symmetric collective atomic excitations with a hidden SU(3)\mathrm{SU}(3)SU(3) dynamical symmetry. By adiabatically changing the Rabi frequencies of two classical control fields, the quantum state can be retrieved up to a non-Abelian holonomy and thus decoded from the final state in a purely geometric way.
Quantum information storage (QIS) is a physical process to write quantum states into a quantum memory (QM). We observe that in some general cases the quantum state can be retrieved up to a unitary transformation depicted by the non-Abelian Berry's geometric phase factor (holonomy). The QIS of photon with this geometric character can be implemented with the symmetric collective excitations of a ΛΛΛ-atom ensemble, which is adiabatically controlled by a classical light with a small detuning δδδ. The cyclic change of the controlled Rabi frequency Ω(t)Ω(t)Ω(t) with period T=2nπδT=\frac{2nπ}δT=δ2nπ​ accumulates additional geometric phases in different components of the final photon state. Then, in a purely geometric way the stored state can be decoded from the final state.
We study the influence of a lossless material medium on the coherent storage and quantum-state transfer of a quantized probe light in an ensemble of $\ensuremath{\Lambda}$-type atoms. The medium is modeled as uniformly distributed two-level atoms with the same energy level spacing, coupling to a probe light. This coupled system can be simplified to a collection of two-mode polaritons which couple to one transition of the $\ensuremath{\Lambda}$-type atoms. We show that, when the other transition of $\ensuremath{\Lambda}$-type atoms is controlled by a classical light, electromagnetically induced transparency can also occur for the polaritons. In this case the coherent storage and quantum transfer for photon states are achievable through novel dark states with respect to the polaritons. By calculating the corresponding dispersion relation, we find that the ensemble of three-level atoms with $\ensuremath{\Lambda}$-type transitions may serve as quantum memory for it slows or even stops light propagation through the mechanism of electromagnetically induced transparency.
We analyze electromagnetically induced transparency and light storage in an ensemble of atoms with multiple excited levels (multi-$\ensuremath{\Lambda}$ configuration) which are coupled to one of the ground states by quantized signal fields and to the other one via classical control fields. We present a basis transformation of atomic and optical states which reduces the analysis of the system to that of electromagnetically induced transparency in a regular three-level configuration. We demonstrate the existence of dark state polaritons and propose a protocol to transfer quantum information from one optical mode to another by an adiabatic control of the control fields.
We propose a quantum memory protocol based on dynamically changing the resonance frequency of an ensemble of two-level atoms. By sweeping the atomic frequency in an adiabatic fashion, photons are reversibly transferred into atomic coherences. We present a polaritonic description for this type of storage, which shares some similarities with electromagnetically induced transparency based quantum memories. On the other hand the proposed memory is also linked to the gradient echo memory due to the effective spatial gradient that pulses experience in the medium. We discuss a possible implementation of the protocol in hollow-core photonic crystal fibers.
We propose a quantum memory protocol based on dynamically changing the resonance frequency of an ensemble of two-level atoms. By sweeping the atomic frequency in an adiabatic fashion, photons are reversibly transferred into atomic coherences. We present a polaritonic description for this type of storage, which shares some similarities with electromagnetically induced transparency based quantum memories. On the other hand the proposed memory is also linked to the gradient echo memory due to the effective spatial gradient that pulses experience in the medium. We discuss a possible implementation of the protocol in hollow-core photonic crystal fibers.
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.