Quantum Interferences in Cooperative Dicke Emission from Spatial Variation of the Laser Phase

Abstract

We report generation of a new quantum interference effect in spontaneous emission from a resonantly driven system of two identical two-level atoms due to the spatial variation of the laser phase at the positions of the atoms. This interference affects significantly the spectral features of the emitted radiation and the quantum entanglement in the system. The interference leads to dynamic coupling of the populations and coherences in a basis, determined by the laser phase and represents a kind of vacuum mediated super-exchange between the symmetric and antisymmetric states.PACS numbers: 42.50. Ct, 42.50.Nn, 03.67.Bg Spontaneous emission from cooperative systems has been extensively studied since the classic paper of Dicke [1,2,3]. The details of the emission depend on the interatomic distances and how the system is initially prepared. The emission can further be influenced if the system is continuously driven by a coherent field. The two atom problem has been especially attractive in this context as many features of cooperative emission can be analyzed in terms of this simple problem. There is renewed interest in these problems for quantum information sciences. Studies have shown that spontaneous emission from cooperative systems leads to quantum entanglement among atoms [3]. Further with the discovery of similarities between semiconductor quantum dots and two level atoms [4,5,6], we have a new class of systems where the cooperative effects can be studied in a regime which was difficult to achieve with atoms. In recent times such quantum dot systems are proving especially important in quantum information science [7,8].In this Letter we report a new quantum interference effect which arises from the spatial variation of the laser phase at the positions of the atoms. We show how this phase variation affects the spectral features of the emitted radiation as well as the quantum entanglement in the system. We further show how populations and coherences, in a basis determined by the laser phase, get coupled dynamically. We demonstrate a kind of superexchange between the symmetric and anti-symmetric states and show a strong connection to the well known vacuum induced coherence [9,10]. Further our results have implications for the decoherence of coupled qubits. The dynamical behavior of a system of atoms undergoing cooperative emission can be described by a master equation approach [2]. Let us specifically consider the system of two identical two-level atoms with transition frequency ω. Each atom is described by the spin half angular momentum algebra. The master equation for the dynamical behavior of this kind of a system in the Born, Markov and rotating wave approximation is then given } is the spontaneous decay rates for the cooperative system, 2γ = 2γ 11 = 2γ 22 = 4| d eg | 2 ω 3 /3 c 3 is the Einstein's A coefficient, k 0 = ω/c, d eg is the dipole moment and ρ is the density operator for the system. θ is the angle between the direction of the dipole moment and the line joining the jth and the kth atom, whose distan...

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