Radii of Rydberg states of isolated silicon donors

Li, Juerong; Le, Nguyen H.; Litvinenko, K. L.; Clowes, S. K.; Engelkamp, Hans; Pavlov, S. G.; Hübers, Heinz‐Wilhelm; Shuman, V. B.; Portsel, L. М.; Lodygin, А. N.; Astrov, Yu. A.; Abrosimov, Nikolai V.; Pidgeon, C. R.; Fisher, A. J.; Zeng, Zaiping; Niquet, Yann-Michel; Murdin, B. N.

doi:10.1103/physrevb.98.085423

Cited by 13 publications

(17 citation statements)

References 46 publications

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“…For silicon and germanium donors, the factors inside the bracket are renormalized, and of particular importance here I a is ten orders of magnitude smaller for silicon than it is for hydrogen. This is apparent from the formulae of the Hartree energy and Bohr radius for donors in these materials: , and , where m t is the transverse effective mass and the dielectric constant 12 . Both germanium and silicon have a s m all m t and large , raising the Bohr radius and lowering the binding energy.…”

Section: Resultsmentioning

confidence: 99%

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Giant non-linear susceptibility of hydrogenic donors in silicon and germanium

Ланский

Aeppli

et al. 2019

Light Sci Appl

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Implicit summation is a technique for the conversion of sums over intermediate states in multiphoton absorption and the high-order susceptibility in hydrogen into simple integrals. Here, we derive the equivalent technique for hydrogenic impurities in multi-valley semiconductors. While the absorption has useful applications, it is primarily a loss process; conversely, the non-linear susceptibility is a crucial parameter for active photonic devices. For Si:P, we predict the hyperpolarizability ranges from χ(3)/n3D = 2.9 to 580 × 10−38 m5/V2 depending on the frequency, even while avoiding resonance. Using samples of a reasonable density, n3D, and thickness, L, to produce third-harmonic generation at 9 THz, a frequency that is difficult to produce with existing solid-state sources, we predict that χ(3) should exceed that of bulk InSb and χ(3)L should exceed that of graphene and resonantly enhanced quantum wells.

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Section: Resultsmentioning

confidence: 99%

“…3. We took the parameters for silicon obtained from spectroscopic 17 and magneto-optical measurements 12,18 , which are γ ≈ 0.208, a B ≈ 3.17 nm and E H ≈ 39.9 meV. The parameters for germanium are γ ≈ 0.0513, a B ≈ 9.97 nm and E H ≈ 9.40 meV 19 .…”

Section: Discussionmentioning

confidence: 99%

Giant non-linear susceptibility of hydrogenic donors in silicon and germanium

Ланский

Aeppli

et al. 2019

Light Sci Appl

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“…The other envelope functions are obtained by using F µ = F −µ and cyclic permutations of x, y, z. The excited state energies and wavefunctions of Si:P are identical to those of Si:As [74,75], and is dependent on the polarization of the light field [76]. For polarization with the unit vector = [ x , y , z ] the excited states are also given by Eq.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Optically controlled entangling gates in randomly doped silicon

Crane

Schuckert

et al. 2019

Phys. Rev. B

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Randomly-doped silicon has many competitive advantages for quantum computation; not only is it fast to fabricate but it could naturally contain high numbers of qubits and logic gates as a function of doping densities. We determine the densities of entangling gates in randomly doped silicon comprising two different dopant species. First, we define conditions and plot maps of the relative locations of the dopants necessary for them to form exchange interaction mediated entangling gates. Second, using nearest neighbour Poisson point process theory, we calculate the doping densities necessary for maximal densities of single and dual-species gates. We find agreement of our results with a Monte Carlo simulation, for which we present the algorithms, which handles multiple donor structures and scales optimally with the number of dopants and use it to extract donor structures not captured by our Poisson point process theory. Third, using the moving average cluster expansion technique, we make predictions for a proof of principle experiment demonstrating the control of one species by the orbital excitation of another. These combined approaches to density optimization in random distributions may be useful for other condensed matter systems as well as applications outside physics.

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“…|r is 2p0 polarised along {0,0,1} with 235ps experimental lifetime for P and 1ns lifetime for Se+. White: excluded area to avoid the molecular limit [26]. Fidelity calculated within a Lindblad Master equation simulating the full pulse sequence, taking into account spontaneous decay and dephasing from |r (Tab.…”

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confidence: 99%

Rydberg Entangling Gates in Silicon

Crane,

Schuckert,

et al. 2020

Preprint

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Spin qubits of donors in silicon show some of the longest coherence times recorded and hold the promise of scalability with seamless integration of quantum computing into semiconductor fabrication. However, current entangling gate implementations rely on highly challenging precision donor placement and substantial gate tuning, rendering scaling challenging. In this work, we show how to implement placement-insensitive ultrafast entangling gates in deep and shallow donors in silicon by relying on the Rydberg blockade induced by strong interactions between low lying orbital excited states. We calculate multivalley interactions for several donor species using the Finite Element Method, and show that Van der Waals interactions between donors, calculated here for the first time, are important even for low-lying excited states. We show that blockade entangling gate operation is possible within the short lifetime of donor excited states with over 99% fidelity for the creation of a Bell state in the presence of decoherence. This gate substantially relaxes the requirements on single donor placement while allowing for billions of entangling gate operations within the single-qubit lifetime, thus paving the way for large scale quantum computation in silicon.

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Radii of Rydberg states of isolated silicon donors

Cited by 13 publications

References 46 publications

Giant non-linear susceptibility of hydrogenic donors in silicon and germanium

Giant non-linear susceptibility of hydrogenic donors in silicon and germanium

Optically controlled entangling gates in randomly doped silicon

Rydberg Entangling Gates in Silicon

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