Quantum computing with naturally trapped sub-nanometre-spaced ions

The main aim of this work, was to lay the foundations for the experimental realisation of a quantum mechanical controlled NOT gate in rare-earth-metal-ion-doped crystals. Small amounts of rare-earth elements, added during the growth of some inorganic crystals, will become substituted into the crystal lattice as trivalent ions. The trivalent rare-earth-metal ions between cerium, with atomic number 58, and ytterbium, with atomic number 70, have a partly filled 4f shell, which does not extend spatially outside the full 5s and 5p shells. The 4f vacancies make electronic inner shell transitions possible between spectroscopic 4f terms. Some of these optical transitions have coherence times of the order of milliseconds, when the crystals are cooled down to ~ 4 K. There are several reasons for these extraordinary coherence times, which are approximately 8 orders of magnitude greater than those typical for electronic transitions in solids. The most important one is the cage-like shield which the outer 5s and 5p shells provide for the 4f electrons. Furthermore, since these ions are naturally trapped inside the crystal lattice there is no Doppler broadening of the line-width. The coherence properties of these optical transitions is one of the features that makes these materials attractive for use as a solid-state platform for quantum computing, using these ions as qubits. Another appealing characteristic is the fact that different ions have different optical resonance frequencies, which means that ions belonging to different qubits, which only have nm separation, can still be addressed separately by using different laser frequencies. Since the inter-ion spacing is so small, it is possible to make two ions interact strongly, although they are well shielded, through a permanent dipole-dipole interaction. This interaction can be turned on and off by switching between two different ways of encoding the qubit, a most useful feature. When the qubit is represented as a superposition between two ground state hyperfine levels, the interaction is turned off. The interaction is turned on selectively by transferring this superposition to the optical transition with a pi-pulse, for the specific ions that are to interact. This thesis describes how peaks of ions, absorbing on a single transition, residing in spectral pits with no other ions, have been isolated. It is shown how these ions can be coherently transferred between hyperfine levels via the optically excited state, how the interaction between such peaks of ions representing qubits can be turned on and off, and how subgroups of ions with strong interaction can be distilled out. All the work described here has been performed using the ensemble approach. The ensemble approach will, however, be difficult to scale up to large numbers of qubits. A method employing a single ion in each qubit, using a specialised ion for readout, has therefore also been proposed. The rare-earth-metal-ion-based quantum computing experiments require a laser with coherence properties which at least match those of the material. To this end a frequency stabilisation system was developed for a dye laser. This system uses a transient spectral hole in a rare-earth-metal-ion-doped crystal, of the same kind that is used in the experiments, as frequency reference, and is to the authors knowledge the first demonstration of locking a dye laser to a spectral hole. This system provides a line-width of 1 kHz on a 10 microseconds timescale and a frequency drift below 1 kHz/s

Efficient quantum memory using a weakly absorbing sample

A light-storage experiment with a total (storage and retrieval) efficiency $\eta=58 \pm 5$ is carried out by enclosing a sample, with a single pass absorption of 10%, in an impedance-matched cavity. The experiment is carried out using the Atomic Frequency Comb (AFC) technique in a praseodymium-doped crystal ($0.05$) and the cavity is created by reflection coating the crystal surfaces. The AFC technique has previously by far demonstrated the highest multi-mode capacity of all quantum memory concepts tested experimentally. We claim that the present work shows that it is realistic to create efficient, on-demand, long storage time AFC memories

Using electric fields for pulse compression and group velocity control

In this article, we experimentally demonstrate a new way of controlling the group velocity of an optical pulse by using a combination of spectral hole burning, slow light effect and linear Stark effect in a rare-earth-ion-doped crystal. The group velocity can be changed continuously by a factor of 20 without significant pulse distortion or absorption of the pulse energy. With a similar technique, an optical pulse can also be compressed in time. Theoretical simulations were developed to simulate the group velocity control and the pulse compression processes. The group velocity as well as the pulse reshaping are solely controlled by external voltages which makes it promising in quantum information and quantum communication processes. It is also proposed that the group velocity can be changed even more in an Er doped crystal while at the same time having a transmission band matching the telecommunication wavelength.Comment: 8 pages, 7 figure

Fast all-optical nuclear spin echo technique based on EIT

We demonstrate an all-optical Raman spin echo technique, using Electromagnetically Induced Transparency (EIT) to create the different pulses of the spin echo sequence: initialization, pi-rotation, and readout. The first pulse of the sequence induces coherence directly from a mixed state, and the technique is used to measure the nuclear spin coherence of an inhomogeneously broadened ensemble of rare-earth ions (Pr$^{3+}$). In contrast to previous experiments it does not require any preparatory hole burning pulse sequences, which greatly shortens the total duration of the sequence. The effect of the different pulses is characterized by quantum state tomography and is compared with simulations. We demonstrate two applications of the technique by using the spin echo sequence to accurately compensate a magnetic field across our sample, and to measure the coherence time at high temperatures up to 11 K, where standard preparation techniques are difficult to implement. We explore the potential of the technique and possible applications.Comment: 8 pages, 6 figure

Cavity enhanced storage - preparing for high efficiency quantum memories

Cavity assisted quantum memory storage has been proposed [PRA 82, 022310 (2010), PRA 82, 022311 (2010)] for creating efficient (close to unity) quantum memories using weakly absorbing materials. Using this approach we experimentally demonstrate a significant (about 20-fold) enhancement in quantum memory efficiency compared to the no cavity case. A strong dispersion originating from absorption engineering inside the cavity was observed, which directly affect the cavity line-width. A more than 3 orders of magnitude reduction of cavity mode spacing and cavity line-width from GHz to MHz was observed. We are not aware of any previous observation of several orders of magnitudes cavity mode spacing and cavity line-width reduction due to slow light effects.Comment: 13 pages, 5 figure

Spectral Engineering of Slow Light, Cavity Line Narrowing, and Pulse Compression

More than 4 orders of magnitude of cavity-linewidth narrowing in a rare-earth-ion-doped crystal cavity, emanating from strong intracavity dispersion caused by off-resonant interaction with dopant ions, is demonstrated. The dispersion profiles are engineered using optical pumping techniques creating significant semipermanent but reprogrammable changes of the rare-earth absorption profiles. Several cavity modes are shown within the spectral transmission window. Several possible applications of this phenomenon are discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1304.445

Scalable designs for quantum computing with rare-earth-ion-doped crystals

Due to inhomogeneous broadening, the absorption lines of rare-earth-ion dopands in crystals are many order of magnitudes wider than the homogeneous linewidths. Several ways have been proposed to use ions with different inhomogeneous shifts as qubit registers, and to perform gate operations between such registers by means of the static dipole coupling between the ions. In this paper we show that in order to implement high-fidelity quantum gate operations by means of the static dipole interaction, we require the participating ions to be strongly coupled, and that the density of such strongly coupled registers in general scales poorly with register size. Although this is critical to previous proposals which rely on a high density of functional registers, we describe architectures and preparation strategies that will allow scalable quantum computers based on rare-earth-ion doped crystals.Comment: Submitted to Phys. Rev.

Hyperfine characterization and coherence lifetime extension in Pr3+:La2(WO4)3

Rare-earth ions in dielectric crystals are interesting candidates for storing quantum states of photons. A limiting factor on the optical density and thus the conversion efficiency is the distortion introduced in the crystal by doping elements of one type into a crystal matrix of another type. Here, we investigate the system Pr3+:La2(WO4)3, where the similarity of the ionic radii of Pr and La minimizes distortions due to doping. We characterize the praseodymium hyperfine interaction of the ground state (3H4) and one excited state (1D2) and determine the spin Hamiltonian parameters by numerical analysis of Raman-heterodyne spectra, which were collected for a range of static external magnetic field strengths and orientations. On the basis of a crystal field analysis, we discuss the physical origin of the experimentally determined quadrupole and Zeeman tensor characteristics. We show the potential for quantum memory applications by measuring the spin coherence lifetime in a magnetic field that is chosen such that additional magnetic fields do not shift the transition frequency in first order. Experimental results demonstrate a spin coherence lifetime of 158 ms - almost three orders of magnitude longer than in zero field.Comment: 14 pages, 6 figure

Deep tissue imaging with acousto-optical tomography and spectral hole burning with slow light effect: a theoretical study

Biological tissue is a highly scattering medium that prevents deep imaging of light. For medical applications, optical imaging offers a molecular sensitivity that would be beneficial for diagnosing and monitoring of diseases. Acousto-optical tomography has the molecular sensitivity of optical imaging with the resolution of ultrasound and has the potential for deep tissue imaging. Here, we present a theoretical study of a system that combines acousto-optical tomography and slow light spectral filters created using spectral hole burning methods. Using Monte Carlo simulations, a model to obtain the contrast-to-noise ratio (CNR) deep in biological tissue was developed. The simulations show a CNR  >  1 for imaging depths of ∼5  cm in a reflection mode setup, as well as, imaging through ∼12 cm in transmission mode setups. These results are promising and form the basis for future experimental studies

Measurement of line widths and permanent electric dipole moment change of the Ce 4f-5d transition in Y_2SiO_5 for a qubit readout scheme in rare-earth ion based quantum computing

In this work the inhomogeneous (zero-phonon line) and homogeneous line widths, and one projection of the permanent electric dipole moment change for the Ce 4f-5d transition in Y_2SiO_5 were measured in order to investigate the possibility for using Ce as a sensor to detect the hyperfine state of a spatially close-lying Pr or Eu ion. The experiments were carried out on Ce doped or Ce-Pr co-doped single Y_2SiO_5 crystals. The homogeneous line width was measured to be about 3 MHz, which is essentially limited by the excited state lifetime. Based on the line width measurements, the oscillator strength, absorption cross section and saturation intensity were calculated to be about 9*10^-7, 5*10^-19 m^2 and 1*10^7 W/m^2, respectively. One projection of the difference in permanent dipole moment, Delt_miu_Ce, between the ground and excited states of the Ce ion was measured as 6.3 * 10^-30 C*m, which is about 26 times as large as that of Pr ions. The measurements done on Ce ions indicate that the Ce ion is a promising candidate to be used as a probe to read out a single qubit ion state for the quantum computing using rare-earth ions.Comment: 9 figures, 8 page