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arXiv:0909.3203 · Physical Review Letters

Creation of Long-Term Coherent Optical Memory via Controlled Nonlinear Interactions in Bose-Einstein Condensates

Rui Zhang, Sean R. Garner, Lene Vestergaard Hau

Published Dec 4, 2009• 114 citations
arXivHTMLPDF

Abstract

A Bose-Einstein condensate confined in an optical dipole trap is used to generate long-term coherent memory for light, and storage times of more than 1 s are observed. Phase coherence of the condensate as well as controlled manipulations of elastic and inelastic atomic scattering processes are utilized to increase the storage fidelity by several orders of magnitude over previous schemes. The results have important applications for creation of long-distance quantum networks and for generation of entangled states of light and matter.

DOI
10.1103/physrevlett.103.233602

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A Bose-Einstein condensate confined in an optical dipole trap is used to generate long-term coherent memory for light, and storage times of more than 1 s are observed. Phase coherence of the condensate as well as controlled manipulations of elastic and inelastic atomic scattering processes are utilized to increase the storage fidelity by several orders of magnitude over previous schemes. The results have important applications for creation of long-distance quantum networks and for generation of entangled states of light and matter.
Our recent work has demonstrated the superradiant writing and reading of collective coherence in a Bose-Einstein condensate [Phys. Rev. Lett. 99, 220407 (2007)]. This time we report the drastic improvement of the storage time realized by loading the atoms into an optical dipole trap, wherein an unfavorable spin-dependent phase shift and spatial diffusion of atoms can be suppressed. The measured storage time was 0.57(2)ms0.57(2)\phantom{\rule{0.3em}{0ex}}\mathrm{ms}0.57(2)ms, which is limited by the temporal variation of atomic momentum due to harmonic oscillations in the trap.
We propose and analyze a scheme to generate squeezed light by storing a classical probe pulse in a Bose--Einstein condensate (BEC) and exploiting the nonlinear evolution caused by atom--atom collisions during the storage time. A ΛΛΛ-type optical memory interface maps a chosen temporal probe mode onto a single phase-matched collective spin wave; for a coherent input this prepares a tunable coherent spin state of a two-component BEC, with its initial spin orientation set by the stored mean excitation number and the phase relation between the probe and control fields. Collisional interactions during storage then implement one-axis-twisting dynamics and generate spin squeezing in the atomic ensemble. We account for realistic loss and finite memory and retrieval efficiencies, and model readout as a single-mode beam-splitter mapping that transfers the atomic quadrature squeezing onto a propagating optical mode. We identify optimal storage times and predict that, under realistic conditions, several dB of squeezing can be transferred to the retrieved light.
Recent experimental and theoretical progress in the studies of Bose-Einstein condensation (BEC) has precipitated an intense effort to understand and control interactions of nonlinear matter-waves. Key ingredients in manipulations of matter-waves in BECs are a) external localized impurities (generated by focused laser beams) and b) periodic potentials (generated by interference patterns from multiple laser beams illuminating the condensate). In this work we demonstrate the ability of time-dependent external optical potentials to drag, capture and pin a wide range of localized BEC states, such as dark and bright solitons. The stability and existence of pinned states is analyzed using perturbation techniques, which predict results that are well corroborated by direct numerical simulations. The control of these macroscopic quantum states has important applications in the realm of quantum storage and processing of information, with potential implications for the design of quantum computers.
Bose-Einstein condensates (BECs) have potential to be used in attractive applications. In particular, they have been thought to be suitable for being quantum optical dynamic memories to store coherent quantum optical information. In order to assess and enhance practical value of this proposal, we have performed various realistic examinations using detailed numerical and analytical methods. Firstly, propagation of short pulses of widths in microsecond to nanosecond range through the BEC has been considered. In this part, the influence of dispersion on the temporal characteristics and on the coherent optical information storage capacity is discussed. By modeling ultra-slow short pulses in the condensate under electromagnetically induced transparency (EIT) conditions, taking into account pulse broadening, we have determined optimum optical information storage capacity. Secondly, we have investigated conditions limiting the optimum number of optical modes that can be supported by an atomic BEC. In this part, in addition to EIT, a refractive index enhancement scheme was also considered, as it allows for accommodating many numbers of modes in the condensate. Furthermore, we have shown that multi-mode pulses, though less in number can also be realized at the cost of tolerable absorption in the case of EIT scheme. Secondly, we determine the number of optical modes supported by a wave guide in which refractive index enhancement is produced by an atomic BEC. Some analytical approximations have been made neglecting the spatial inhomogeneity. More accurate results have been obtained using a numerical model where the spatial inhomogeneity is taken into account. In the refractive index enhancement model, the predictions of (WKB) theory have been compared with those of fully numerical simulations. In this study, we investigate potential of atomic Bose-Einstein condensates as dynamic memory devices for coherent optical information processing. Specifically, the number of ultra-slow pulses that can be simultaneously present within the storage time in the condensate has been analyzed. By modeling short pulse propagation through the condensate, taking into account high-order dispersive properties, constraints on the information storage capacity has been discussed. The roles of temperature, spatial inhomogeneity, the interatomic interactions and the coupling laser on the pulse shape have been pointed out. For a restricted set of parameters, it has been found that coherent optical information storage capacity would be optimized. Coherent optical information storage capacity of an atomic Bose-Einstein condensate is examined. Theory of slow light propagation in atomic clouds is generalized to short pulse regime by taking into account group velocity dispersion. It is shown that the number of stored pulses in the condensate can be optimized for a particular coupling laser power, temperature and interatomic interaction strength. Analytical results are derived for semi-ideal model of the condensate using effective uniform density zone approximation. Detailed numerical simulations are also performed. It is found that axial density profile of the condensate protects the pulse against the group velocity dispersion. We examine the conditions determining the number of optical modes that can be supported by an atomic Bose-Einstein condensate. We show that under the conditions of refractive index enhancement via quantum coherence, it is possible to control the number of modes by means of experimentally accessible parameters including trap size, temperature, condensate number density and scattering lengths. Analytical results for the single and two-mode conditions are found. In order to slow down the group velocity we use electromagnetically induced transparency and find detuning parameter corresponding to number of modes. Results of numerical simulations are compared with analytical calculations of the propagation constants for a parabolic-refractive index profile. Furthermore, taking into account finite radial size of the condensate, multi-mode light propagation in atomic Bose-Einstein condensate is investigated. The number of modes that can be supported by a condensate is found. Single mode condition is determined as a function of experimentally accessible parameters including trap size, temperature, condensate number density and scattering length. Quantum coherent atom-light interaction schemes are proposed for enhancing multi-mode light propagation effects. Keywords: Optical memories, Coherent optical effects, Pulse shaping, and Bose-Einstein condensate.
We report the experimental demonstration of quantum memory for collective atomic states in a far-detuned optical dipole trap. Generation of the collective atomic state is heralded by the detection of a Raman scattered photon and accompanied by storage in the ensemble of atoms. The optical dipole trap provides confinement for the atoms during the quantum storage while retaining the atomic coherence. We probe the quantum storage by cross correlation of the photon pair arising from the Raman scattering and the retrieval of the atomic state stored in the memory. Nonclassical correlations are observed for storage times up to 60 mus.
A scheme based on electromagnetically induced transparency is used to store light in a Bose-Einstein condensate. In this process, a photonic polarization qubit is stored in atomic Zeeman states. The performance of the storage process is characterized and optimized. The average process fidelity is $1.000\ifmmode\pm\else\textpm\fi{}0.004$. For long storage times, temporal fluctuations of the magnetic field reduce this value, yielding a lifetime of the fidelity of $(1.1\ifmmode\pm\else\textpm\fi{}0.2)$ ms. The write-read efficiency of the pulse energy can reach $0.53\ifmmode\pm\else\textpm\fi{}0.05$.