Entanglement induced by the two-mode thermal noise

Abstract

The entanglement between two identical two-level atoms interacting with two mode thermal field through a nondegenerate two-photon process has been suggested. It has been shown that for some atomic initial state the entanglement induced by nondegenerate two-photon interaction is larger than that induced by one-photon and degenerate two-photon processes.PACS numbers: 42.50. Ct; The quantum entanglement plays a key role in quantum information and quantum computation [1]. Real quantum systems will inevitably be influenced by surrounding environments. Although the interaction between the environment and quantum systems can lead to decoherence, it can also induced entanglement. Recently, S.Bose et al. [2] have showed that entanglement can always arise in the interaction of an arbitrary large system in any mixed state with a single qubit in a pure state, and illustrated this using the Jaynes-Cummings interaction of a two-level atom in a pure state with a field in a thermal state at an arbitrary high temperature. M. Kim et al. [3] have investigated the entanglement of two identical two-level atoms with one-photon transition induced by a single-mode thermal field. L.Zhou et al [4] have considered the same problem for nonidentical atoms. The entanglement of two identical two-level atoms through nonlinear two-photon interaction with one-mode thermal field has been studied by L.Zhou et al. [5]. They have shown that atom-atom entanglement induced by nonlinear interaction is larger than that induced by linear interaction. It is of interest to investigate the entanglement between two identical atoms induced by thermal noise through other nonlinear processes. In this paper we dwell on two-photon nondegenerate interaction of two atoms with two mode of thermal field. The one-atom models with nondegenerate two-photon interaction in cavity have attracted much attention beginning with the paper of S.Gou [6]. We have obtained that for some atomic initial condition the entanglement induced by nondegenerate interaction may be larger than that induced by degenerate two-photon process.Let us consider the system of two identical two-level atoms with frequency of the atomic transition ω 0 interacting with two modes of quantum electromagnetic field with frequencies ω 1 and ω 2 through a nondegenerate two-photon process. For simplicity we ignore the Stark shift and assume the lossless cavity modes to be at two-photon resonance with the atomic transition, i.e. the condition ω 1 + ω 2 = ω 0 takes place. Then, the Hamiltonian of the considered system in interaction picture and RWA approximation can be written in the form:where a + j and a j are the creation and annihilation operators of photons of jth cavity mode (j = 1, 2), R + i and R − i are the raising and the lowering operators for the ith atom, g is the coupling constant between the atom and the cavity field.We denote by | + and | − the excited and ground states of a single two-level atom and by | n the Fock state of the electromagnetic field. The two-atom wave function can be expressed ...

Entanglement in Nondegenerate Two-Photon Tavis - Cummings Model

“…При этом авторы показали, что эффект мгно венной смерти перепутывания заметно ослабляется или полностью сводится на нет для определенных перепутанных беловских начальных состояний системы за счет включения диполь-дипольного взаимодействия. В нашей работе [3] найден точное 1 Работа выполнена в рамках Федеральной целевой программы "Научные и научно-педагогиче ские кадры инновационной России" на 2009-2013 годы по лоту "Проведение научных исследова ний коллективами научно-образовательных центров в области оптики, лазерной физики и лазер ных технологий", шифр "2010-1.1-122-084" (номер государственного контракта 14.740.11.0063).…”

Atom-atom entanglement in a not-resonant two-photon Tavis-Cummings model

“…Zhang [7] directly generalizes Kim's study to the case when the atoms are slightly detuned from the thermal field and showed that a slight detuning might cause high entanglement between the atoms. The entanglement between two two-level atoms through resonant nonlinear two-photon interaction with one-mode thermal field has been studied in [8][9][10][11][12][13]. It has been shown that entanglement induced by nonlinear interaction is larger than that induced by linear interaction.…”

Перепутывание Атомов, Индуцированное Двухмодовым Тепловым Шумом, При Наличии Диполь-Дипольного Взаимодействия И Атомной Когерентности

“…работе [2] было показано, что одномодовый тепловой шум может индуцировать атом-атомное перепутывание в системе двух двухуровневых атомов в идеальном резонаторе. Позднее аналогичное поведение было обнаружено и для атомов с многофотонными переходами [3,4]. При этом было показано, что при двухфотонном взаимодействии атомов с тепловым полем степень перепутывания атомных состояний может значительно превосходить соответствующую величину для однофотонного взаимодействия.…”