Extending Phenomenological Crystal-Field Methods to C_{1} Point-Group Symmetry: Characterization of the Optically Excited Hyperfine Structure of

We show that crystal-field calculations for C_{1} point-group symmetry are possible, and that such calculations can be performed with sufficient accuracy to have substantial utility for rare-earth based quantum information applications. In particular, we perform crystal-field fitting for a C_{1}-symmetry site in ^{167}Er^{3+}:Y_{2}SiO_{5}. The calculation simultaneously includes site-selective spectroscopic data up to 20 000 cm^{-1}, rotational Zeeman data, and ground- and excited-state hyperfine structure determined from high-resolution Raman-heterodyne spectroscopy on the 1.5 µm telecom transition. We achieve an agreement of better than 50 MHz for assigned hyperfine transitions. The success of this analysis opens the possibility of systematically evaluating the coherence properties, as well as transition energies and intensities, of any rare-earth ion doped into Y_{2}SiO_{5}.

Precision measurement of electronic ion-ion interactions between neighboring Eu3+ optical centers.

We report measurements of discrete excitation-induced frequency shifts on the 7F0→5D0 transition of the Eu+ center in La:Lu:EuCl3·6D2O resulting from the optical excitation of neighboring Eu3+ ions. Shifts of up to 46.081±0.005 MHz were observed. The magnitude of the interaction between neighboring ions was found to be significantly larger than expected from the electric dipole-dipole mechanism often observed in rare earth systems. We show that a large network of interacting and individually addressable centers can be created by lightly doping crystals otherwise stoichiometric in the optically active rare earth ion, and that this network could be used to implement a quantum processor with more than ten qubits.

Multimodal properties and dynamics of gradient echo quantum memory.

We investigate the properties of a recently proposed gradient echo memory (GEM) scheme for information mapping between optical and atomic systems. We show that GEM can be described by the dynamic formation of polaritons in k space. This picture highlights the flexibility and robustness with regards to the external control of the storage process. Our results also show that, as GEM is a frequency-encoding memory, it can accurately preserve the shape of signals that have large time-bandwidth products, even at moderate optical depths. At higher optical depths, we show that GEM is a high fidelity multimode quantum memory.

Electro-optic quantum memory for light using two-level atoms.

We present a simple quantum memory scheme that allows for the storage of a light field in an ensemble of two-level atoms. The technique is analogous to the NMR gradient echo for which the imprinting and recalling of the input field are performed by controlling a linearly varying broadening. Our protocol is perfectly efficient in the limit of high optical depths and the output pulse is emitted in the forward direction. We provide a numerical analysis of the protocol together with an experiment performed in a solid state system. In close agreement with our model, the experiment shows a total efficiency of up to 15%, and a recall efficiency of 26%. We suggest simple realizable improvements for the experiment to surpass the no-cloning limit.

Quantum study of information delay in electromagnetically induced transparency.

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.

Photon echoes produced by switching electric fields.

We demonstrate photon echoes in Eu3+:Y2SiO5 by controlling the inhomogeneous broadening of the Eu3+ 7F0<-->5D0 optical transition. This transition has a linear Stark shift, and we induce inhomogeneous broadening by applying an external electric field gradient. After optical excitation, reversing the polarity of the field rephases the ensemble, resulting in a photon echo. This is the first demonstration of such a photon echo, and its application as a quantum memory is discussed.

Dynamic decoherence control of a solid-state nuclear-quadrupole qubit.

We report on the application of a dynamic decoherence control pulse sequence on a nuclear-quadrupole transition in Pr3+:Y(2)SiO(5). Process tomography is used to analyze the effect of the pulse sequence. The pulse sequence was found to increase the decoherence time of the transition to over 30 seconds. Although the decoherence time was significantly increased, the population terms were found to rapidly decay on the application of the pulse sequence. The increase of this decay rate is attributed to inhomogeneity in the ensemble. Methods to circumvent this limit are discussed.

Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid.

We report on the demonstration of light storage for times greater than a second in praseodymium doped Y2SiO5 using electromagnetically induced transparency. The long storage times were enabled by the long coherence times possible for the hyperfine transitions in this material. The use of a solid-state system also enabled operation with the probe and coupling beam counter-propagating, allowing easy separation of the two beams. The efficiency of the storage was low because of the low optical thickness of the sample; as is discussed, this deficiency should be easy to rectify.

Demonstration of conditional quantum phase shift between ions in a solid.

Because of their long coherence times, dopant ions have been considered promising candidates for scalable solid state quantum computing. Here we demonstrate a conditional phase shift between two qubits based on an optical transition of europium ions. The demonstration uses ensembles that have been selected from a randomly doped sample using spectral hole burning techniques. The electron dipole-dipole interaction between the ions that usually causes instantaneous spectral diffusion is used to generate the conditional phase shift.

Method of extending hyperfine coherence times in Pr3+:Y2SiO5.

In this Letter, we present a method for increasing the coherence time of praseodymium hyperfine ground state transitions in Pr(3+):Y(2)SiO5 by the application of a specific external magnetic field. The magnitude and angle of the external field is applied such that the Zeeman splitting of a hyperfine transition is at a critical point in three dimensions, making the first order Zeeman shift vanishingly small for the transition. This reduces the influence of the magnetic interactions between the praseodymium ions and the spins in the host lattice on the transition frequency. Using this method a phase memory time of 82 ms was observed, a value 2 orders of magnitude greater than previously reported. It is shown that the residual dephasing is amenable to quantum error correction.