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arXiv:1108.1240

Quantum information transfer in degenerate Raman regime

Thiago Prudêncio

Published Aug 5, 2011• 0 citations
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Abstract

The interaction of a three level Rydberg atom of Lambda-type with a single mode optical field in far off-resonant and at large detuning regimes can be described by an effective degenerate Raman model, where the atomic state can be treated as a two-level system of degenerate states. By means of this approximation, we propose a quantum information transfer of an one-qubit state from a Rydberg atom of Lambda-type with degenerate levels to a single-mode field initially in a coherent state.

DOI
10.48550/arxiv.1108.1240

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The interaction of a three level Rydberg atom of Lambda-type with a single mode optical field in far off-resonant and at large detuning regimes can be described by an effective degenerate Raman model, where the atomic state can be treated as a two-level system of degenerate states. By means of this approximation, we propose a quantum information transfer of an one-qubit state from a Rydberg atom of Lambda-type with degenerate levels to a single-mode field initially in a coherent state.
We consider a single Rydberg atom having two degenerate levels interacting with the radiation field in a single-mode ideal cavity. The transition between the levels is carried out by a ΛΛΛ-type degenerate two-photon process via a third level far away from single-photon resonance. At the start of interaction, the atom is considered to be in a coherent superposition of its two levels and the field in a coherent state. We study the dynamics of the atomic as well as the field states. The squeezing in the quadratures of atomic states can reach up to 100%100\%100%. The cavity field evolves to a statistical mixture of two coherent fields with the phase difference between them decided by the interaction time. Analysis of entropies of the atom and the field shows that the two systems are dis-entangled periodically in certain cases.
I study the coherent interaction of a three-level atom in the lambda configuration with pump, Stoke, and anti-Stokes laser fields. The pump laser field drives transitions from the two non-degenerate lower levels to the excited state which is highly detuned for either transition. This excited state is also coupled to each of the lower states by Stokes or anti-Stokes transitions so that this system may represent a model of four-wave mixing. Assuming large detunings, the excited state is adiabatically eliminated from obtaining an effective two-level system with Raman coupling between the levels. Optical Bloch equations are obtained for this effective two-level system, and phenomenological damping terms are added for collisional dephasing of the Raman transitions. The equations are solved for the steady-state as well as by the method of adiabatic following. From these solutions we obtain the polarization.
Interaction of a V-type three-level atom with two mode fields is studied in detail. Under large-detuning condition, the ground state can be adiabatically eliminated, i.e., this model may be converted into a non-degenerate Raman coupled model which an effective two-level atom interacts with two mode cavity fields. We derive the modified effective Hamiltonian and their wave functions of both non-degenerate Raman coupled and a degenerate Raman coupled model respectively. Based on state-selective measurements on V-type three-level atoms crossing the cavity, We present a new scheme of generation of Schrdinger cat states which are made up of superposition of the coherent states with controllable weighting factors and phases, through Raman interaction of degenerate V-type three atoms with one cavity field.
A scheme is proposed to teleportation of an unknown multi-atom entangled state, considering the entangled states of two or more particles play an important role in both demonstrating quantum nonlocality and quantum information processing. The scheme is based on the degenerate Raman interaction of a Λ-type three-level atom with a single-mode field. First let n atoms cross a coherent cavity field in succession to prepare a quantum channel. Then the sender lets the other n atoms which carry the unknown state cross the cavity in succession and makes a joint measurement by detecting the cavity field and the atoms separately. When ｜α｜1, the cavity field can be detected with the measurement method of detecting orthogonal states. Finally the receiver reconstructs the initial state according to the outcome of the joint measurement transmitted through a classical channel. The advantage of the scheme is that it uses an entangled state of a coherent state with n atoms as a quantum channel, which makes the scheme simple and easy. The scheme is expected to be useful in demonstrating quantum nonlocality and information processing.
The Hamiltonian is derived for the interaction of a Λ-type three-level atom with a two-mode quantum cavity field from the general interaction Hamiltonian between a multi-level atom and a multi-mode radiation field, and it is reduced to an effective two-mode Raman-coupled model under a large detuning condition. We propose a modified effective Hamiltonian for the two-mode Raman-coupled model, find the time-dependent state vectors, and present the validity conditions for the involved interaction Hamiltonians. It is shown that in the study of the two-mode Raman-coupled model it is not enough to retain only the usually used effective Hamiltonian, one must also take into account the ac Stark shift of the atomic levels (at least one of the levels). Finally, we study the atomic dynamics in the interaction of a Λ-type three-level atom with a two-mode quantum cavity field and in the two-mode Raman-coupled model. We find that the number of collapse-revivals, the collapse time and the revival time show new characteristics.