Abstract
A near-perfect storage time-extended photon echo-based quantum memory protocol has been analyzed by solving the Maxwell–Bloch equations for a backward scheme in a three-level system. The backward photon echo scheme is combined with a controlled coherence conversion process via controlled Rabi flopping to a third state, where the control Rabi flopping collectively shifts the phase of the ensemble coherence. The propagation direction of photon echoes is coherently determined by the phase-matching condition between the data (quantum) and the control (classical) pulses. Herein, we discuss the classical controllability of a quantum state for both phase and propagation direction by manipulating the control pulses in both single and double rephasing photon echo schemes of a three-level system. Compared with the well-understood uses of two-level photon echoes, the Maxwell–Bloch equations for a three-level system have a critical limitation regarding the phase change when interacting with an arbitrary control pulse area.
Highlights
We have introduced the controlled double rephasing (CDR) echo protocol [14] based on coherence conversion (CCC) [20]
We pointed out the absorptive echo problems in previously demonstrated single (AFC) and double rephasing photon echo schemes, where the mistake in the controlled atomic frequency comb (AFC) echoes arises from a wrong assumption applied to the Maxwell–Bloch approach for a three-level system
Maxwell–Bloch method never gives an exact solution to the phase change of the ensemble coherence in its interaction with an arbitrary optical pulse area, unless known a priori, as in the two-level system
Summary
Over the last decade, modified photon echo techniques have been intensively studied and applied to quantum memory applications to overcome the fundamental limitation of population inversion in conventional photon echoes, for which the population inversion excited by an optical π pulse results in quantum noises caused by spontaneous and/or stimulated emissions [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. The MB theory prevents us from obtaining exact answers to the phase change of the ensemble coherence, with respect to the pulse area of an interacting optical field This critical mistake means that the MB approach never reveals the induced π− phase shift [20] by the π−π control pulse sequence in a three-level system [8,9]. We comply with the MB equations, firstly to confirm the CDR echo protocol with previous results of CCC in references [17] and [20], secondly to analyze the critical mistakes in references [8,9,10,11,12,13], due to incorrect assumptions of π−π control pulse sequence [8,9] and the misunderstanding of the absorptive echo [10,11,12,13], and to discuss ensemble phase evolutions and their phase control in both single [8,9]. The present report of the near-perfect storage time-extended quantum memory protocol should shed light on future quantum information research using quantum memories
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