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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Photon echo quantum memory and state transformation

Ahdiyeh Delfan Abazari, Cecilia La Mela, Wolfgang Tittel

Published Jan 8, 2008• 2 citations
Publisher

Abstract

A recently proposed, photon echo related approach to quantum state storage in atomic ensembles employs controlled reversible inhomogeneous broadening (CRIB). Beyond storage, a modified version of CRIB promises controlled quantum state manipulations. As the implementation of CRIB is currently still challenging, we investigate state transformation based on stimulated photon echoes. Specifically, we show how to translate an all optical, beamsplitter based setup into a photon echo based setup, and we simulate a photon echo based POVM (positive operator valued measure) measurement using Maxwell-Bloch equations.

DOI
10.1117/12.772309

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A recently proposed, photon echo related approach to quantum state storage in atomic ensembles employs controlled reversible inhomogeneous broadening (CRIB). Beyond storage, a modified version of CRIB promises controlled quantum state manipulations. As the implementation of CRIB is currently still challenging, we investigate state transformation based on stimulated photon echoes. Specifically, we show how to translate an all optical, beamsplitter based setup into a photon echo based setup, and we simulate a photon echo based POVM (positive operator valued measure) measurement using Maxwell-Bloch equations.
We develop the theory of an optical quantum memory protocol based on the three pulse photon echo (PE) in an optically dense medium with controlled reversible inhomogeneous broadening (CRIB). The wave-function of the retrieved photon echo field is derived explicitly as a function of an arbitrary input Data light field. The storage and retrieval of time-bin qubit states based on the described quantum memory is discussed, and it is shown that the memory allows to measure the path length difference in an imbalanced interferometer using short light pulses.
We propose a method to implement a quantum memory for light based on ensembles of two-level atoms. Our protocol is based on controlled reversible inhomogeneous broadening (CRIB), where an external field first dephases the atomic polarization and thereby stores an incoming light pulse into collective states of the atomic ensemble, and later a reversal of the applied field leads to a rephasing of the atomic polarization and a reemission of the light. As opposed to previous proposals for CRIB-based quantum memories, we propose only applying the broadening for a short period after most of the pulse has already been absorbed by the ensemble. We show that with this procedure there exist certain modes of the incoming light field that can be stored with an efficiency approaching 100% in the limit of high optical depth and long coherence time of the atoms. These results demonstrate that it is possible to operate an efficient quantum memory without any optical control fields.
We report experimental storage and retrieval of weak coherent states of light at telecommunication wavelengths using erbium ions doped into a solid. We use two photon-echo-based quantum storage protocols. The first one is based on controlled reversible inhomogeneous broadening (CRIB). It allows the retrieval of the light on demand by controlling the collective atomic coherence with an external electric field, via the linear Stark effect. We study how atoms in the excited state affect the signal-to-noise ratio of the CRIB memory. Additionally we show how CRIB can be used to modify the temporal width of the retrieved light pulse. The second protocol is based on atomic frequency combs. Using this protocol we verify that the reversible mapping is phase preserving by performing an interference experiment with a local oscillator. These measurements are enabling steps toward solid-state quantum memories at telecommunication wavelengths. We also give an outlook on possible improvements.
Quantum memory is a key element for quantum repeaters and linear optical quantum computers. In addition to memory, repeaters and computers also require manipulating quantum states by means of unitary transformations, which is generally accomplished using interferometric optical setups. We experimentally investigate photon-echo type atom-light interaction for the possibility to combine storage with controlled transformation of quantum states. As an example, we demonstrate unambiguous state discrimination of qubits and qutrits in an Ti:Er:LiNbO3_33​ waveguide cooled to 3K using states encoded into large ensembles of identically prepared photons in superposition of different temporal modes. The high robustness and flexibility of our approach makes it promising for quantum communication and computation as well as precision measurements.
We have analyzed an efficient integration of the multi-qubit echo quantum memory into the quantum computer scheme on the atomic resonant ensembles in quantum electrodynamics cavity. Here, one atomic ensemble with controllable inhomogeneous broadening is used for the quantum memory node and other atomic ensembles characterized by the homogeneous broadening of the resonant line are used as processing nodes. We have found optimal conditions for efficient integration of multi-qubit quantum memory modified for this analyzed physical scheme and we have determined a specified shape of the self temporal modes providing a perfect reversible transfer of the photon qubits between the quantum memory node and arbitrary processing nodes. The obtained results open the way for realization of full-scale solid state quantum computing based on using the efficient multi-qubit quantum memory.
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.