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arXiv:1612.00115

Collective atom phase controls in photon echoes for quantum memory applications I: Population inversion removal

Byoung Seung HAM

Published Dec 1, 2016• 6 citations
arXivHTMLPDF

Abstract

Photon echo-based quantum memories demonstrated in rare-earth doped solids over the last decade have solved the major constraint of population inversion in conventional photon echoes by using collective atom phase controls. Both atomic frequency comb and gradient echoes have also made a breakthrough in higher echo efficiency, where conventional photon echo efficiency remains at a few per cent. Here we review, analyze, and discuss the collective atom phase control applied to conventional photon echoes for quantum memory applications to clarify fundamental physics of coherent transients in a three-level system specifically for optical-spin coherence conversion in a controlled double rephasing echoes. Some critical misunderstandings in various protocols are also analyzed, and corrected for near unity echo efficiency under no population inversion.

DOI
10.48550/arxiv.1612.00115

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Photon echo-based quantum memories demonstrated in rare-earth doped solids over the last decade have solved the major constraint of population inversion in conventional photon echoes by using collective atom phase controls. Both atomic frequency comb and gradient echoes have also made a breakthrough in higher echo efficiency, where conventional photon echo efficiency remains at a few per cent. Here we review, analyze, and discuss the collective atom phase control applied to conventional photon echoes for quantum memory applications to clarify fundamental physics of coherent transients in a three-level system specifically for optical-spin coherence conversion in a controlled double rephasing echoes. Some critical misunderstandings in various protocols are also analyzed, and corrected for near unity echo efficiency under no population inversion.
To overcome the fundamental limitations of the $\ensuremath{\pi}$ optical pulse-induced population inversion and optical decay-caused short storage time in conventional photon echoes, a coherent control of collective atoms is studied for inversion-free, optical decay-halted photon echoes, where the constraint of photon storage time is now replaced by a spin population decay process. Using phase-controlled double rephasing, an inversion-free photon echo scheme is obtained, where no spontaneous or stimulated emission-driven quantum noise exists. Thus, the present method can be applied for ultralong quantum memories in quantum repeaters for long-distance quantum communications.
Photon echo-based quantum memory protocols presented over the last decade are primarily to solve the population inversion constraint in conventional photon echoes. In addition to population inversion, other major constraints limiting quantum memory applications are the low retrieval efficiency and short storage time, in which the importance of these factors has recently increased because of the challenges of the entangled qubit scalability and quantum repeaters. Here, I present, analyze and discuss the solution model for a Controlled Double Rephasing (CDR) echo protocol to satisfy non-inversion, near-perfect retrieval efficiency, and ultra-long storage time. In the CDR echo, a coherent Rabi pulse pair plays a key role for controlling both the ensemble phase and echo propagation direction, where the followings are the major results. Firstly, a counter propagating control Rabi pulse-pair-induced backward echo is free from echo reabsorption, resulting in a near perfect retrieval efficiency. Secondly, the control Rabi pulse pair induces an optical-spin coherence conversion like in the ultraslow light-based photon storage, resulting in a storage time extension up to spin decay time. Finally, the control Rabi flopping to a third state induces a π phase shift to the ensemble coherence, resulting in an emissive echo in the double rephasing scheme, where the π phase shift is due to optical-spin coherence conversion process. Conclusion: This study reveals that the control Rabi flopping in a three-level system applied to conventional photon echoes for storage time extension induces a π phase shift to the coher ent ensemble.
Rephasing in photon echoes is a fundamental mechanism of retrieving optical information stored in a collective ensemble of atoms or ions. With an extremely weak quantum optical data, population inversion by the rephasing process is inevitable resulting in serious quantum noise. Here, an inversion-free rephasing method in photon echoes is presented by using deshelving-based atom phase control. The present method makes photon echoes directly applicable to quantum memories with benefits of extended photon storage time and nearly perfect retrieval efficiency. In this revised version only the rephasing pulse propagation direction is corrected to make a silent echo of E1 in Fig. 1.
Using on-demand coherence conversion via optical locking, a dynamic coherent control of the collective atom phase has been demonstrated for longer photon storage beyond the critical constraint of spin phase decay time, where the storage time can be extended up to hours in a rare-earth-doped solid. Coherent transient phenomena such as photon echoes have been investigated for frozen phase decay via coherent population transfer using a simple deshelving optical pulse pair. Unlike the rephasing halt applied to two-pulse photon echoes, where optical decoherence is accelerated by spin inhomogeneous broadening, a completely atom phase-locked coherence conversion has been observed in three-pulse photon echoes, resulting in spin dephasing-free coherence control. Here, the mechanism of the atom phase-locked coherence conversion via optical locking has been investigated in a solid medium whose optical transition is imperfect, where partial coherence is lost via optical depth-dependent imperfect population transfer. The relationship between coherence loss and optical depth is analyzed, where nearly perfect photon echo efficiency can be obtained for ultralong photon storage in an optically thick medium.
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 control 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 their well-understood use for two-level photon echoes, the Maxwell-Bloch equations to a three-level system have a critical limitation regarding the phase change when interacted with an arbitrary control pulse area.