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arXiv:quant-ph/0507127 · Physical Review A

Control of decoherence in the generation of photon pairs from atomic ensembles

D. Felinto, C. W. Chou, Hugues de Riedmatten, Sergey Vladimirovich Polyakov, Harry J. Kimble

Published Nov 9, 2005• 92 citations
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Abstract

We report an investigation to establish the physical mechanisms responsible for decoherence in the generation of photon pairs from atomic ensembles, via the protocol of Duan et al. for long-distance quantum communication [Nature (London) 414, 413 (2001)] and present the experimental techniques necessary to properly control the process. We develop a theory to model in detail the decoherence process in experiments with magneto-optical traps. The inhomogeneous broadening of the ground state by the trap magnetic field is identified as the principal mechanism for decoherence. The theory includes the Zeeman structure of the atomic hyperfine levels used in the experiment, and the polarization of both excitation fields and detected photons. In conjunction with our theoretical analysis, we report a series of measurements to characterize and control the coherence time in our experimental setup. We use copropagating stimulated Raman spectroscopy to access directly the ground-state energy distribution of the ensemble. These spectroscopic measurements allow us to switch off the trap magnetic field in a controlled way, optimizing the repetition rate for single-photon measurements. With the magnetic field off, we then measure nonclassical correlations for pairs of photons generated by the ensemble as a function of the storage time of the single collective atomic excitation. We report coherence times longer than $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, corresponding to an increase of two orders of magnitude compared to previous results in cold ensembles. The coherence time is now two orders of magnitude longer than the duration of the excitation pulses. The comparison between these experimental results and the theory shows good agreement. Finally, we employ our theory to devise ways to improve the experiment by optical pumping to specific initial states.

DOI
10.1103/physreva.72.053809

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We report an investigation to establish the physical mechanisms responsible for decoherence in the generation of photon pairs from atomic ensembles, via the protocol of Duan et al. for long-distance quantum communication [Nature (London) 414, 413 (2001)] and present the experimental techniques necessary to properly control the process. We develop a theory to model in detail the decoherence process in experiments with magneto-optical traps. The inhomogeneous broadening of the ground state by the trap magnetic field is identified as the principal mechanism for decoherence. The theory includes the Zeeman structure of the atomic hyperfine levels used in the experiment, and the polarization of both excitation fields and detected photons. In conjunction with our theoretical analysis, we report a series of measurements to characterize and control the coherence time in our experimental setup. We use copropagating stimulated Raman spectroscopy to access directly the ground-state energy distribution of the ensemble. These spectroscopic measurements allow us to switch off the trap magnetic field in a controlled way, optimizing the repetition rate for single-photon measurements. With the magnetic field off, we then measure nonclassical correlations for pairs of photons generated by the ensemble as a function of the storage time of the single collective atomic excitation. We report coherence times longer than 10\ensuremathμs10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}10\ensuremathμs, corresponding to an increase of two orders of magnitude compared to previous results in cold ensembles. The coherence time is now two orders of magnitude longer than the duration of the excitation pulses. The comparison between these experimental results and the theory shows good agreement. Finally, we employ our theory to devise ways to improve the experiment by optical pumping to specific initial states.
We present the quantum theory for creation of collective atomic memory and generation of nonclassically correlated photon pairs from an ensemble via the protocol of Duan et al. [Nature (London) 414, 413 (2001)]. The temporal evolution of photon numbers, photon statistics, and cross-correlation between the Stokes and anti-Stokes fields is found by solving the equation of motion for atomic spin-wave excitations. We consider a low-finesse cavity model with collectively enhanced signal-to-noise ratio, which remains still considerably large in the free-space limit. Our results describe analytically the dependence of quantum correlations on spin decoherence time and time delay between the write and read lasers and reproduce the observed data very well including the generated pulse shapes, strong violation of Cauchy-Schwarz inequality and conditional generation of anti-Stokes single-photon pulse. The approach we developed may be used also for quantum description of storage and retrieval of quantum information, especially when the statistical properties of nonclassical pulses are studied.
The limits of the well-established single-atom model for describing photon-pair generation via four-wave mixing in a diamond configuration in atomic ensembles are experimentally tested. Using a cold-atom source, biphotons are generated and detected through polarization analyzers that resolve the emitted light into horizontal and vertical components in the laboratory frame. The pump lasers driving the first and second excitation transitions are horizontally and vertically polarized, respectively. To predict single-photon counts and coincidence rates in all polarization channels, the first- and second-order correlation functions are calculated directly using a comprehensive model that accounts for all Zeeman sublevels of the relevant hyperfine states. Furthermore, the population dynamics with and without the re-pump laser of the magneto-optical trap are compared, revealing substantial differences in the populations of the Zeeman sublevels. This motivates the inclusion of two additional hyperfine levels and their corresponding Zeeman sublevels in the final model. The resulting density matrix is used to calculate expectation values of the far-field electric-field operators and compare them with experimental measurements over a range of pump-laser powers. Excellent agreement with the measured photon counts is obtained over most of this range. For the coincidence measurements, good agreement is found when the polarization of the photon generated by the first (second) decay is parallel to that of the first (second) pump beam. In contrast, the model consistently underestimates the experimental coincidence rates for the opposite polarization configuration. These findings indicate that effects beyond the internal level dynamics of individual atoms, most notably collective phenomena, are required to fully account for photon coincidences generated by four-wave mixing in atomic ensembles.
In this thesis, we explore the quantum dynamics of light interactions with optically thick collections of atoms. We provide a theoretical description of several recent experiments in which some key operations necessary for the implementation of quantum communication networks are demonstrated. Collective Raman scattering from an atomic ensemble is shown to produce probabilistic entanglement between the polarization of a scattered photon and an associated collective atomic excitation. The predicted correlations agree with experimental observations. We also propose a method to use cascade transitions to produce entanglement between a photon with a frequency in the telecom range (ideal for transmission over optical fibers) and a near infrared photon (ideal for storage in an atomic ensemble), and a description of the experimental demonstration is provided. We also propose and describe the implementation of a deterministic source of single photons.\n\nIn addition, we generalize the theory of dark-state polaritons in ensembles of three level Lambda atoms to account for the nuclear spin degeneracy of alkali atoms. This generalized theory provides a description of the first demonstration of single photon storage and retrieval from atomic ensembles. Additionally, in the presence of a uniform magnetic field, we predict the occurrence of collapses and revivals of the photon retrieval efficiency as a function of storage time within the ensemble. These predictions are in very good agreement with subsequent experimental observations. We also exploit the ability of photon storage to entangle remote atomic qubits.
The light wave propagating in a dispersive medium can be formularized as electromagnetic (EM) fields or quantized as a pair of Hermitian operators. The fascinating optical phenomena display classical and nonclassical properties, depending on whether they can be described by the classical EM field theory. A cold atomic ensemble with neligible inhomogenous Doppler broadening is ideal to explore the interaction between light and matter. A typical problem in classical pulse propagation is optical transients, which induced by rapid response of dispersive medium to the sudden change of the driving radiation fields. With cold atoms confined in the two-dimensional magneto-optical trap, whose optical depth is controllable in our system, optical precursor and free-induction decay both classified as optical transients are observed in a single experiment with different conditions. Moreover, the information velocity limit is verified in superluminal medium, with the observation and analysis of precursors. Characterized with narrow linewidth and long coherence time, paired photons generated from cold atomic ensemble in four-wave mixing process possess irreplaceable advantage in quantum optics area. Temporal modulation of narrow-band paired photons can be achieved by directly modulating the generated photons or by modulating the classical control fields. After successfully reshaping the temporal waveform of the paired photons, heralded single photon source is well prepared for studying the propagation of nonclassical single photon in dispersive medium. The speed limit imposed by Einstein Causality principle is firstly experimentally verified on single photon level.
The experiments discussed in this thesis investigate the application of atomic ensembles in building a quantum network. Specifically, the atomic ensembles refer to cesium atoms in magneto-optical traps. Chapter 1 gives an introduction to quantum networks, along with the difficulty in extending the range due to the optical loss of communication channels. Chapter 2 describes the protocol proposed by Duan, Lukin, Cirac, and Zoller (DLCZ) for overcoming the limit of channel loss on scaling up a quantum network, exploiting relatively simple setups with atomic ensembles. The protocol introduces many capabilities and simplifies many tasks in quantum information processing with atoms and light. Chapter 3 summarizes the first step in our lab toward realizing the DLCZ protocol. In particular, we observed nonclassical correlation between two optical fields generated from one atomic ensemble. Chapter 4 is a sidetrack apart from the DLCZ protocol. We demonstrated that the atomic ensemble can be used as a conditional source of single photons. In addition to a description of the experiment, details of the simple model we used to fit the data are also included. Chapter 5 augments chapter 4 in that the temporal behavior of the nonclassical correlation is investigated. We found that the correlation decayed rapidly, which is a major obstacle for further implementation of the DLCZ protocol. Chapter 6 describes our effort to fight the fast decay of correlation observed in the experiment. A theoretical model is used to better understand the source of decoherence. Chapter 7 is the follow-up in the direction of implementing the DLCZ protocol. Two atomic ensembles located in vacuum chambers on two optical tables are entangled in a heralded fashion. The details on controlling the phases of the interferometers and data processing are elaborated. Chapter 8 is a practical proposal on how to proceed further toward realization of the DLCZ protocol. Four atomic ensembles are involved in the proposed setup, which merely requires relative phase stability. Chapter 9 concludes the thesis and provides several possible directions toward building a large-scale quantum network through the DLCZ protocol.
Single photons are the best carriers of quantum information for long-distance transmission. Nevertheless, maximal achievable distance is limited by the exponential decay of photons as a function of link length. The protocol of quantum repeater provides a promising solution by replacing direction transmission with segmented entanglement distribution and entanglement connection via swapping. The quantum repeater necessitates a key element of quantum memory for making efficient interconnections. An atomic ensemble is very suitable for this purpose due to the collective enhanced interaction. Single photons are stored as collective excitations in an atomic ensemble. Thus a comprehensive study of the physics relating to collective excitations is crucially important for improving the quantum memory performance and its reachable applications in quantum repeater and quantum network. In this article, we review our experimental work on cold atomic ensembles in recent years, focusing on the coherent manipulation of collective excitations. We first briefly introduce the general concept of collective excitations and the preparation process through spontaneous Raman scattering, and we review our experimental work on extending the coherence time, such as suppressing motional dephasing by increasing the spin-wave wavelength, by confining atoms with a three-dimensional optical lattice. Afterwards, we discuss about the retrieval process of collective excitations and review our experiments on using a ring-cavity enhanced setup to improve the retrieval efficiency. The coherent qubit operation in a quantum memory is very useful for enabling new functionalities for a quantum network, in a subsequent section, we thus review our work on developing Raman-based coherent operations for single excitations. Afterwards, we mention our experiments on creating a pair of atom-photon entanglement by interfering two modes of a collective excitation. Improving the entanglement preparation efficiency is crucially important, and Rydberg-based interaction provides a promising solution. Our experimental work in this direction is also reviewed. Additionally, as an application in coherent manipulation with collective excitations, we show several experiments on using excitations in remote atomic memories and demonstrating basic functionality of quantum repeater and quantum network. In short, significant progress has been made in the coherent manipulation of single collective excitations in cold atomic ensembles, and further improvement will be accelerated by the Rydberg-enabled interactions; practical applications in quantum repeater and quantum network is foreseeable in the near future.