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European Quantum Electronics Conference (EQEC)

Stored light in linear and nonlinear dielectrics

R. Bullough, H. M. Gibbs, Andrei V. Rybin

Published Nov 15, 2004• 0 citations
Publisher

Abstract

Summary form only given. We compare old experimental and theoretical results for the storage and retrieval of quantum information in atomic dielectrics done on the /sup 23/Na D/sub 1/ lines and based on nonlinear degenerate self-induced transparency (SIT) with more recent experiments and theory based on linearised electromagnetically induced transparency (EIT) done on the /sup 87/Rb D/sub 1/ lines. Although the nonlinear SIT theory is very different from the recent linearised EIT theory there are remarkable conceptual similarities at the level of quantum expectation values between the two theories of quantum memory in their modes of storage and retrieval of quantum information. However it has been argued that the linearised theories have the merit of recording information on the atomic dielectric accurate to all (countable) orders of normally ordered correlation functions while this is not true for the nonlinear theories. By working from the closely related theoretical case of the quantum nonlinear dielectric formed from the condensed repulsive Bose gases we bring strong evidence to show that the quantum nonlinear SIT theories can in fact show similar levels of accuracy namely beyond expectation and to all (countable) orders of correlation functions. Up to neglect of incoherence effects the exact quantum theory of EIT is exactly solvable by methods such as the quantum inverse method or Bethe ansatz, and the 3-level /spl Lambda/ atom model of EIT induces dark quantum solitons. We explore the whole set of quantum dielectrics formed by the nonlinear and linearised EIT dielectrics interpreted as quantum memories. We explore how far it is possible in principle to store quantum information accurately for continuous wave optical inputs via a merely countable infinity of correlation functions. We hope to have evaluated quantum correlation functions of arbitrary countable order for the quantum nonlinear EIT system by exact quantum inverse methods and results for quantum memory purposes will be reported. We can already explore the complete Hilbert space for strictly (non-degenerate) resonant SIT at the level of the quantum sine-Gordon equation and quantised breathers here provide generalised qubits for quantum information purposes in which the number of breather states is in general greater than two and is bounded by an adjustable constant coupling in the nonlinearity.

DOI
10.1109/eqec.2003.1314271

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Summary form only given. We compare old experimental and theoretical results for the storage and retrieval of quantum information in atomic dielectrics done on the /sup 23/Na D/sub 1/ lines and based on nonlinear degenerate self-induced transparency (SIT) with more recent experiments and theory based on linearised electromagnetically induced transparency (EIT) done on the /sup 87/Rb D/sub 1/ lines. Although the nonlinear SIT theory is very different from the recent linearised EIT theory there are remarkable conceptual similarities at the level of quantum expectation values between the two theories of quantum memory in their modes of storage and retrieval of quantum information. However it has been argued that the linearised theories have the merit of recording information on the atomic dielectric accurate to all (countable) orders of normally ordered correlation functions while this is not true for the nonlinear theories. By working from the closely related theoretical case of the quantum nonlinear dielectric formed from the condensed repulsive Bose gases we bring strong evidence to show that the quantum nonlinear SIT theories can in fact show similar levels of accuracy namely beyond expectation and to all (countable) orders of correlation functions. Up to neglect of incoherence effects the exact quantum theory of EIT is exactly solvable by methods such as the quantum inverse method or Bethe ansatz, and the 3-level /spl Lambda/ atom model of EIT induces dark quantum solitons. We explore the whole set of quantum dielectrics formed by the nonlinear and linearised EIT dielectrics interpreted as quantum memories. We explore how far it is possible in principle to store quantum information accurately for continuous wave optical inputs via a merely countable infinity of correlation functions. We hope to have evaluated quantum correlation functions of arbitrary countable order for the quantum nonlinear EIT system by exact quantum inverse methods and results for quantum memory purposes will be reported. We can already explore the complete Hilbert space for strictly (non-degenerate) resonant SIT at the level of the quantum sine-Gordon equation and quantised breathers here provide generalised qubits for quantum information purposes in which the number of breather states is in general greater than two and is bounded by an adjustable constant coupling in the nonlinearity.
Despite the importance of quantum interference and coherent population trapping to the theory of electromagnetically induced transparency (EIT), it is shown that the recent experiments which slow down and even stop a light pulse in a dielectric really rely on a linear, refractive index type theory. From this point of view and in considerable contrast, the experiment on degenerate self-induced transparency (SIT) done 27 years ago which slowed down an optical pulse (in principle to zero velocity) was based on an intrinsically nonlinear (soliton type) theory. In quantum mechanical terms both theories are developed at the level of expectation values only and at this level the two different theories come together in terms of the storage and retrieval of information. In the Appendix we analyse the nature of this information in terms of the quantum equations governing linear EIT and nonlinear SIT.
We return to the notion of optical solitons as these were first introduced—namely as exact soliton and multi-soliton solutions of the semi-classical self-induced transparency (SIT) equations. The SIT equations, even in their most general inhomogeneously broadened forms, are infinite dimensional, completely integrable Hamiltonian systems, and thus display much mathematical structure, yet their exact soliton solutions display well the nonlinear (self-induced) transparency features of the physical phenomenon. The mathematical feature of complete integrability is handed down from the SIT equations to the nonlinear Schrödinger equations and from this point of view the nonlinear Schrödinger (NLS) equations equations are studied first of all at classical level and then at quantum level. The ‘quantum soliton’ of the quantum attractive NLS model is defined and its properties investigated in detail, particularly in a comparison with the particular properties ascribed to the ‘quantum soliton’ as described in a recently published article (Abraham 1999 Phys. World (February) 21) with this title; as suggested in that article, the quantum NLS soliton is seen as a qubit for quantum information purposes. The covariant form of the quantum attractive NLS model is the quantum sine-Gordon model and this is briefly studied in the context of quantum information also; new results for large area Josephson junctions are reported in this context. The quantum soliton of the one dimensional attractive NLS model has apparently been observed in 2002 in a Bose condensed metal vapour ( 7 Li, (Khaykovich et al 2002 Science 296 1290)) and a detailed calculation suggests that the condensate undergoes a ‘collapse’ from three to one space dimensions thus forming an exact soliton solution of the one dimensional quantum attractive NLS model.
This thesis set out to investigate light storage based on dynamic electromagnetically induced transparency (EIT) in a room-temperature atomic ensemble of rubidium as a means to provide a quantum memory for single-photons created by a single rubidium atom coupled to a high-finesse optical resonator. Setting up the light storage medium presented a new addition to the research group's portfolio of experimental techniques and led to investigations of EIT, slow light and stored light in warm rubidium-87 vapour. Lambda level schemes connecting Zeeman or hyperfine substates on the D1 and D2 lines were addressed in rubidium vapour cells containing different buffer gases and different isotopic fractions of rubidium-87 and rubidium-85. Single beam spectroscopy with a weak probe was used to characterise the vapour cells. A numerical method to fit the D line spectrum to a theoretical model to include isotopic fractions and collisional broadening of a buffer gas has been implemented. Temperature and isotopic fractions could be reliably extracted from the fit parameters. For an offset-stabilisation of two lasers to address a lambda level scheme connecting the two different hyperfine groundstates in rubidium a phase locked loop including a frequency divider has been designed and implemented. Light storage and retrieval has been demonstrated using a Zeeman scheme on the D1 line. Two microsecond long classical light pulses containing one million photons on average were stored and retrieved with an efficiency of 15% after a delay of one microsecond. Several methods of attenuating the strong co-propagating control laser beam to allow for lowering the signal pulse intensity in future experiments are discussed.
We investigate the storage and retrieval of electromagnetic waves using a nonlinear metamaterial, analogous to the electromagnetically induced transparency (EIT) observed in atomic systems. We experimentally demonstrate the storage of the electromagnetic wave by reducing an auxiliary “control” wave; the stored wave is then released by recovering the control wave. We also confirm that the metamaterial can store and reproduce the phase distribution of the original input wave. These effects confirm a remarkable analogy between the metamaterial and an atomic EIT medium.
This thesis presents theoretical models and results of numerical simulations describing the propagation of optical pulses through dense, thermal atomic vapours. In particular we investigate the nonlinear effects of optical solitons due to self-induced transparency (SIT) in two-level systems, optical simultons in V-type three-level systems and electromagnetically induced transparency (EIT) in Λ-type systems, including the storage and retrieval of dark-state polaritons. An investigation is made into two-photon excitation of the 5D states of rubidium in a high-intensity beam including the hyperfine structure of the relevant atomic levels. Decay from these states to the 6P manifolds is ruled out as a cause of experimentally observed fluorescence due to the amount of power broadening associated with intensities necessary to provide any significant level of population in these highly excited states. We combine the nonlinear effects of optical solitons and EIT to explain experimentally observed steepened pulses in a V-type system in a micron-length cell. We explain the behaviour as the early formation of a simulton pulse drawn from a CW probe field by a strong coupling pulse, due to coherent population trapping. We predict that in a longer cell it may be possible to facilitate propagation of matched pulses, even when the transitions in the system have different propagation coefficients, as long as decoherence from collision broadening can be controlled. The fact that weak pulses can propagate with this scheme suggests an approach to achieving transparent propagation of single or few photon pulses distinct from, but related to, both SIT and EIT.
Using electromagnetically induced transparency (EIT), it is possible to delay and store light in atomic ensembles. Theoretical modeling and recent experiments have suggested that the EIT storage mechanism can be used as a memory for quantum information. We present experiments that quantify the noise performance of an EIT system for conjugate amplitude and phase quadratures. It is shown that our EIT system adds excess noise to the delayed light that has not hitherto been predicted by published theoretical modeling. In analogy with other continuous-variable quantum information systems, the performance of our EIT system is characterized in terms of conditional variance and signal transfer.