Electrons above a helium surface and the one-dimensional Rydberg atom

Nieto, Michael Martin

doi:10.1103/physreva.61.034901

Cited by 44 publications

(30 citation statements)

References 32 publications

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“…In this erratum we want to set the argument straight. We work in units such that = e = m = 1.As we proved in our paper, the normalized z-space eigenfunctions of the 1D Coulomb problem are [1,2] …”

mentioning

confidence: 73%

Erratum: Quantum solution for the one-dimensional Coulomb problem [Phys. Rev. A83, 064101 (2011)]

Núñez‐Yépez¹,

Salas‐Brito²,

Solis³

2014

Phys. Rev. A

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In our paper a superselection rule (SSR) was derived as part of a detailed analysis of the one-dimensional (1D) Coulomb problem. Here we set straight some inaccuracies in our arguments that could give rise to objections over the existence of such SSR. We emphasize that the lack of recognition of such SSR lies at the root of the many erroneous claims made about the system. Our paper is devoted to the discussion of the properties of the 1D Coulomb problem. We exhibit that the peculiar properties of its quantum solutions can be traced back to the complete independence between the right and the left sides of the singularity at z = 0 in the 1D Coulomb potential V (z) = −k/|z|, k > 0. We argued that such feature is related to a SSR effectively separating the left states ψ − n (z), which vanish for z > 0, from the right states ψ + n (z), which vanish for z < 0. However, though the SSR exists and the separation operates, the proof given in our paper is flawed. In this erratum we want to set the argument straight. We work in units such that = e = m = 1.As we proved in our paper, the normalized z-space eigenfunctions of the 1D Coulomb problem are [1,2]

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mentioning

confidence: 73%

Erratum: Quantum solution for the one-dimensional Coulomb problem [Phys. Rev. A83, 064101 (2011)]

Núñez‐Yépez¹,

Salas‐Brito²,

Solis³

2014

Phys. Rev. A

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“…This makes it possible to calculate the sum over ν, m ν in Eq. (27) for v qq ′ j . The calculation is simplified in the case k B T ≫ ω r where q ≫ 1/a and q · q ′ ≈ qq ′ ≫ a −2 .…”

Section: Dephasing Due To Ripplon Scatteringmentioning

confidence: 99%

“…It goes up to ∼ 1.5 × 10 4 s −1 for E ⊥ = 300 V/cm and ω /2π = 20.6 GHz (in this case ν c = 12). The values of ω were adjusted here to meet the condition δE = E 2 −E 1 −ν ch ω ≈hω for the energy spectrum calculated for a sharp helium boundary; the real level spacing is a few percent smaller [24,26,27], leading to a slightly smaller Γ (s;k) ph for ω /2π ∼ 20 GHz. We expect a more significant change (reduction) of Γ …”

Section: Decay Due To Phonon-induced Surface Displacementmentioning

confidence: 99%

Qubits with electrons on liquid helium

Platzman²,

2003

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We study dissipation effects for electrons on the surface of liquid helium, which may serve as qubits of a quantum computer. Each electron is localized in a 3D potential well formed by the image potential in helium and the potential from a submicron electrode submerged into helium. We estimate parameters of the confining potential and characterize the electron energy spectrum. Decay of the excited electron state is due to two-ripplon scattering and to scattering by phonons in helium. We identify mechanisms of coupling to phonons and estimate contributions from different scattering mechanisms. Even in the absence of a magnetic field we expect the decay rate to be < ∼ 10 4 s −1 . We also calculate the dephasing rate, which is due primarily to ripplon scattering off an electron. This rate is < ∼ 10 2 s −1 for typical operation temperatures.

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“…Very recently additional analytic properties of these "quantum shapelets" have been expounded [10]. The one-dimensional Coulomb problem has recently reappeared as a model in quantum computing with electrons on liquid helium films [26,25]. In addition, given the self-reciprocal Fourier transform property of Hermite polynomials, there are several applications in Fourier optics [8,16].…”

Section: Introductionmentioning

confidence: 99%

Theta and Riemann xi function representations from harmonic oscillator eigensolutions

Coffey

2007

Physics Letters A

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Electrons above a helium surface and the one-dimensional Rydberg atom

Abstract: Isolated electrons resting above a helium surface are predicted to have a bound spectrum corresponding to a one-dimensional hydrogen atom. But in fact, the observed spectrum is closer to that of a quantum-defect atom. Such a model is discussed and solved in analytic closed form.

Cited by 44 publications

References 32 publications

Erratum: Quantum solution for the one-dimensional Coulomb problem [Phys. Rev. A83, 064101 (2011)]

Erratum: Quantum solution for the one-dimensional Coulomb problem [Phys. Rev. A83, 064101 (2011)]

Qubits with electrons on liquid helium

Theta and Riemann xi function representations from harmonic oscillator eigensolutions

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