Forbidden transitions often have moderate energy separations and long lifetimes. They can be induced in elements by external force including laser absorption, magnetic effect, crystal forces and collision with energetic particles. In this paper we discuss the prospects of quantum information processing involving forbidden transitions in the inner shell of Ytterbium. We derive the Schrodinger wave equation for the qubit states with the 3P and 1S as basis states. We also determine a coherent norm calculate the decoherence rate for trapped atoms.
Forbidden transitions often have moderate energy separations and long lifetimes. They can be induced in elements by external force including laser absorption, magnetic effect, crystal forces and collision with energetic particles. In this paper we discuss the prospects of quantum information processing involving forbidden transitions in the inner shell of Ytterbium. We derive the Schrodinger wave equation for the qubit states with the 3P and 1S as basis states. We also determine a coherent norm calculate the decoherence rate for trapped atoms.
In this paper we discuss the prospects of quantum information processing involving forbidden transitions in the inner shell of the rare-earth elements. We shall derive the selection rule for such transitions and investigate the prospects for rare-earth based quantum information procession that employ dipole-dipole forbidden transitions. The long decoherence time, degree of entanglement, lossless interconnectivity of these transitions will be model and their impact on quantum information processing will be examined.
Many approaches have been proposed towards the realization of practical quantum information processing. They include laser manipulation of the energy states in atomic or ion traps, nuclear magnetic resonance in molecules, quantum computation in optical lattices, and in Bose-Einstein condensates. For any of these system to be viable quantum computation, it should have stable and long-lived internal states. In addition it should be possible to quantum- mechanically entangle two or more qubits and the entangled states should be capable of non-local realism phenomena. The ground state and metastable states of low Z atoms especially the single and two-electron atoms and their ions are the most commonly used qubits for quantum information processing systems. Efforts to exhibit these phenomena in high Z elements has been much more challenging. In part because of the high energy needed to ionize the high Z elements into effective one- or two-electron system suitable for quantum information processing. Furthermore the energy difference between two stable states of the High Z elements that are possible qubits states turn to be very high. Preferably the energy difference of two qubits levels should be in the meV to a few tens of electron volts for practical realization of a quantum computing system. In general any two stable terms of an atomic or molecular system with low to moderate energy separation, that do not violate term rules for selection and symmetry, may be viable qubits states.
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.
The collision-induced absorption and emission coefficients for electric-dipole forbidden atomic transitions are calculated for weak radiation fields. The approximations used are valid for $\ensuremath{\hbar}\ensuremath{\omega}$ near $\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$, the atomic energy differences. The example case of $S\ensuremath{-}D$ transitions induced by a spherically symmetric perturber (e.g., a noble-gas atom) is treated in detail and compared to measurements. The case of "radiative collisions," in which both colliding atoms change their state, is included in the theory and is also compared to experiment.
A scalable multatom entangled system, capable of high-performance quantum computations, can be realized by resonant dipole-dipole interacting dopants in a solid state host. In one realization, the qubits are represented by ground and subradiant states of effective dimers formed by pairs of closely spaced two-level systems (TLS). Such qubits are highly robust against radiative decay. The two-qubit entanglement in this scheme relies on coherent excitation exchange between the dimers by external laser fields. This scheme is challenging because of the nanosize control and addressability it requires. Another realization involves dipole-dipole interacting TLS whose resonance frequency lies in a photonic band gap of a dielectric photonic crystal. A sequence of abrupt changes of the resonance frequency can produce controlled entanglement (logic gates) with improved protection from radiation decay and decoherence.
In this chapter a quantum mechanical treatment of atomic response to the fields of an electromagnetic wave is presented. Absorption and emission of energy by atoms involves transition between their quantized energy levels driven by an interaction Hamiltonian. Schrodinger equation is used to derive the equations of motion for the density matrix of the atom, which is better suited to include the effects of mechanisms other than the interaction Hamiltonian – collisions, level decays, level shifts, etc. that also affect the state of the atom. Using the density matrix equation of motion and focusing on two atomic levels, induced dipole moment for a single two-level atom and polarization and susceptibility for a collection of two-level atoms, including the effects of level decays, and collisions, are calculated. Equations of motion for level populations are also derived. These expressions naturally predict stimulated emission as well as absorption. Expressed in terms of spontaneous emission rate they confirm the validity of equations derived in Chapter 5 using the dipole oscillator model of atomic response. The limit in which quantum mechanical equations for atomic response reduce to the classical dipole oscillator equations is also discussed.