Time dependent quantum simulations of two-qubit gates based on donor states in silicon

Kerridge, Andrew; Savory, Seb J.; Harker, A. H.; Stoneham, A. M.

doi:10.1088/0953-8984/18/21/s04

Cited by 7 publications

(11 citation statements)

References 21 publications

(31 reference statements)

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“…construction and fidelity of two-qubit gates (e.g. such as the controlled-NOT) from this Hamiltonian Fowler et al, 2003;Hill andGoan, 2003, 2004;Kerridge et al, 2006;Tsai et al, 2009;Tsai and Goan, 2008). From a microscopic physics viewpoint, in general the exchange energy J is stronger than the dipole interaction for smaller separations, however it behaves as (Herring and Flicker, 1964)…”

Section: Two-donor Systems and Exchange Couplingmentioning

confidence: 99%

Silicon quantum electronics

et al. 2013

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This review describes recent groundbreaking results in Si, Si/SiGe and dopant-based quantum dots, and it highlights the remarkable advances in Si-based quantum physics that have occurred in the past few years. This progress has been possible thanks to materials development of Si quantum devices, and the physical understanding of quantum effects in silicon. Recent critical steps include the isolation of single electrons, the observation of spin blockade and single-shot read-out of individual electron spins in both dopants and gated quantum dots in Si. Each of these results has come with physics that was not anticipated from previous work in other material systems. These advances underline the significant progress towards the realization of spin quantum bits in a material with a long spin coherence time, crucial for quantum computation and spintronics.

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Section: Two-donor Systems and Exchange Couplingmentioning

confidence: 99%

Silicon quantum electronics

et al. 2013

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“…As with atoms in traps the ground states are tightly confined and well isolated from the environment, giving rise to extraordinarily sharp transitions (3)(4)(5) and very long spin coherence times (6,7), measured with magnetic resonance experiments. There are several proposals for quantum information processing based on the spin of silicon donors (8)(9)(10)(11)(12)(13) and such impurities can now be placed singly with atomic precision (14).…”

mentioning

confidence: 99%

Silicon as a model ion trap: Time domain measurements of donor Rydberg states

Vinh

Greenland

Litvinenko

et al. 2008

Proc. Natl. Acad. Sci. U.S.A.

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One of the great successes of quantum physics is the description of the long-lived Rydberg states of atoms and ions. The Bohr model is equally applicable to donor impurity atoms in semiconductor physics, where the conduction band corresponds to the vacuum, and the loosely bound electron orbiting a singly charged core has a hydrogen-like spectrum according to the usual Bohr-Sommerfeld formula, shifted to the far-infrared because of the small effective mass and high dielectric constant. Manipulation of Rydberg states in free atoms and ions by single and multiphoton processes has been tremendously productive since the development of pulsed visible laser spectroscopy. The analogous manipulations have not been conducted for donor impurities in silicon. Here, we use the FELIX pulsed free electron laser to perform time-domain measurements of the Rydberg state dynamics in phosphorus-and arsenicdoped silicon and we have obtained lifetimes consistent with frequency domain linewidths for isotopically purified silicon. This implies that the dominant decoherence mechanism for excited Rydberg states is lifetime broadening, just as for atoms in ion traps. The experiments are important because they represent a step toward coherent control and manipulation of atomic-like quantum levels in the most common semiconductor and complement magnetic resonance experiments in the literature, which show extraordinarily long spin lattice relaxation times-key to many well known schemes for quantum computing qubits-for the same impurities. Our results, taken together with the magnetic resonance data and progress in precise placement of single impurities, suggest that doped silicon, the basis for modern microelectronics, is also a model ion trap.coherence ͉ free electron laser ͉ quantum information ͉ picosecond population dynamics ͉ hydrogenic donor impurity H omogenous lifetime-broadened two-level atoms in ion traps (1) have become favorite objects of study for quantum optics with a view toward both fundamental physics and the eventual development of a quantum computer. Among the many schemes proposed (2), the states of ions in trap systems are attractive for the realization of quantum information ''qubits'' (quantum bits) because they are well isolated from the decohering effects of the environment and can be coherently controlled by lasers. The Bohr model is equally applicable to donor impurity atoms in semiconductor physics, where the conduction band corresponds to the vacuum, and the loosely bound electron orbiting a singly charged core has a hydrogen-like spectrum according to the usual Bohr-Sommerfeld formula, shifted to the far-infrared because of the small effective mass and high dielectric constant. As with atoms in traps the ground states are tightly confined and well isolated from the environment, giving rise to extraordinarily sharp transitions (3-5) and very long spin coherence times (6, 7), measured with magnetic resonance experiments. There are several proposals for quantum information processing based on the spin of silicon do...

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“…where the pair of donors are at R A = 0, R B = R and R >> a * 0 (effective Bohr radius). The second sum (in square brackets) in equation (26) refers to the reciprocallattice expansion of the periodic Bloch functions, u ν ( r) = K c ν K e i K· r , and k ν , k µ are band minima points. The full expression for J νµ is given in the Appendix of [15]; in the isotropic effective-mass approximation where the envelope functions F n ( r) are the same for each minimum, and assuming that rapidly oscillating terms in the integrals (proportional to e i( k (i) − k (j) )· r , where r is one of the integrated variables) are negligible, J µν can be replaced by the exchange J w computed using the radial functions derived from the Whittaker functions.…”

Section: Inter-valley Effectsmentioning

confidence: 99%

“…In order to find a solution to equation ( 5) that remains finite at the origin for a general given energy ǫ, we have to correct the potential at short distances. One way to do this is to look for corrections based on the local physics of the impurity (for example incorporating correctly the transition from a screened to an unscreened nuclear potential [24,25,26], or including self-consistently the scattering effects of the impurity by means of a pseudoptential based on the microscopic physics [27]); another way is to correct the potential at small r empirically solely in order to make the solution regular there at the experimentally observed energy eigenvalue. In this second case the potential will not correspond to the physics operating in the core region of the real defect, but it will produce the correct shift in binding energy.…”

Section: Model Central Cell Correctionsmentioning

confidence: 99%

Exchange between deep donors in semiconductors: A quantum defect approach

Fisher

2008

Phys. Rev. B

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Exchange interactions among defects in semiconductors are commonly treated within effectivemass theory using a scaled hydrogenic wave-function. However such a wave-function is only applicable to shallow impurities; here we present a simple but robust generalization to treat deep donors, in which we treat the long-range part of the wavefunction using the well established quantum defect theory, and include a model central-cell correction to fix the bound-state eigenvalue at the experimentally observed value. This allows us to compute the effect of binding energy on exchange interactions as a function of donor distance; this is a significant quantity given recent proposals to carry out quantum information processing using deep donors. As expected, exchange interactions are suppressed (or increased), compared to the hydrogenic case, by the greater localization (or delocalization) of the wavefunctions of deep donors (or 'super-shallow' donors with binding energy less then the hydrogenic value). The calculated results are compared with a simple scaling of the Heitler-London hydrogenic exchange; the scaled hydrogenic results give the correct order of magnitude but fail to reproduce quantitatively our calculations. We calculate the donor exchange in silicon including inter-valley interference terms for donor pairs along the {100} direction, and also show the influence of the donor type on the distribution of nearest-neighbour exchange constants at different concentrations. Our methods can be used to compute the exchange interactions between two donor electrons with arbitrary binding energy.

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Time dependent quantum simulations of two-qubit gates based on donor states in silicon

Cited by 7 publications

References 21 publications

Silicon quantum electronics

Silicon quantum electronics

Silicon as a model ion trap: Time domain measurements of donor Rydberg states

Exchange between deep donors in semiconductors: A quantum defect approach

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