Temperature-dependent energy levels of electrons on liquid helium

Collin, Eddy; Bailey, Wm. F.; Fozooni, P.; Frayne, P.G.; Glasson, P.; Harrabi, K.; Lea, M. J.

doi:10.1103/physrevb.96.235427

Cited by 11 publications

(15 citation statements)

References 31 publications

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“…We find a good agreement with the experimental results on the spectra of inter-subband transitions [28] and the new results [29] that corroborate the theory. The theory also explains the long lifetime of the electron states, which are critical for a potential implementation of a quantum computer based on electrons on helium [30][31][32].…”

supporting

confidence: 80%

“…[29]. In the studied density range 0.67 × 10 7 − 2.4 × 10 7 cm −2 no dependence on the electron density was found, and the data for different densities are combined.…”

Section: (B)mentioning

confidence: 99%

“…(10) for ε (1) n . In order to compare the results with the experiment [28,29], we performed a detailed numerical study of the energies and the wave functions for the field E ⊥ = 106 V/cm used in the experiment. We calculated the energies E n as well as the matrix elements of the momentum p z (and of the electrostatic interaction, see below) for n ≤ 30 by numerically solving the Schrödinger equation (3).…”

Section: The Wkb Wave Functionsmentioning

confidence: 99%

“…It is calculated as a sum of the kinematic contribution (7) and the contribution from the electrostatic coupling given in SM, keeping only the Tdependent terms in the both expressions. To compare the theory with the experiment, the experimentally measured transition frequency [29] was extrapolated to T = 0 and the shift was counted off from the extrapolated value. The calculated T -dependent frequency shift is free from the ambiguity related to the form of the electron potential at the atomic distance from the helium surface.…”

Section: (B)mentioning

confidence: 99%

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Ripplonic Lamb Shift for Electrons on Liquid Helium

et al. 2017

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We study the shift of the energy levels of electrons on helium surface due to the coupling to the quantum field of surface vibrations. As in quantum electrodynamics, the coupling is known, and it is known to lead to an ultraviolet divergence of the level shifts. We show that there are diverging terms of different nature and use the Bethe-type approach to show that they cancel each other, to the leading-order. This resolves the long-standing theoretical controversy and explains the existing experiments. The results allow us to study the temperature dependence of the level shift. The predictions are in good agreement with the experimental data.Electrons above the surface of liquid helium were one of the first observed two-dimensional electron systems (2DESs) [1][2][3][4]. In this system the conceptual simplicity is combined with far from trivial behavior, which allows studying many-body effects in a well-characterized setting. The system displays the highest mobility known for 2DESs, exceeding 2 × 10 8 cm 2 /(V·s) [5] and can be exquisitely well controlled [6]. The electron-electron interaction is typically strong, so that the electrons can form a Wigner solid [7,8] or a strongly correlated liquid with unusual transport properties [9,10]. A number of new many-electron phenomena have been found recently [11][12][13][14][15].An advantageous feature of the system is the simple form of the confining potential. It is formed by the high Pauli barrier at the helium surface and the image potential. One then expects the electron energy spectrum to be well understood. Indeed, already the first experiment on transitions between the subbands of quantized motion normal to the surface showed a good, albeit imperfect agreement with the model [4]. Much work has been done on improving, sometimes empirically, the form of the confining potential, cf. [4,[16][17][18][19]. On the other hand, it has been known that the electrons are also coupled to a bosonic field, the capillary waves on the surface of helium (ripplons), and that this coupling affects the electron energy spectrum [20][21][22][23][24]. The importance of this effect was demonstrated in explaining the Wigner crystallization [8,25] and through cyclotron-resonance measurements [26].In terms of the coupling to a bosonic field, electrons on helium are a close condensed-matter analog of systems studied in quantum electrodynamics. The known form of the coupling [27] and the possibility to control it and to study the interplay of this coupling with the manyelectron effects make the system particularly attractive. In this context, a major problem is that the ripploninduced shift of the electron energy levels of motion normal to the surface contains diverging terms. They come from short-wavelength ripplons. The ultraviolet divergence is strong, as a high power of the wave number. Unless one deals with it carefully, the resulting level shifts become comparable to the electron binding energy for a short-wavelength cutoff approaching twice the interatomic distance. The problem bears ...

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supporting

confidence: 80%

“…[29]. In the studied density range 0.67 × 10 7 − 2.4 × 10 7 cm −2 no dependence on the electron density was found, and the data for different densities are combined.…”

Section: (B)mentioning

confidence: 99%

Section: The Wkb Wave Functionsmentioning

confidence: 99%

Section: (B)mentioning

confidence: 99%

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Ripplonic Lamb Shift for Electrons on Liquid Helium

et al. 2017

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“…More generally, the study of non equilibrium phenomena in electrons on helium is strongly connected with the prospect of using Rydberg states [32,33], created by the interaction of electrons with their image charge inside liquid helium, for quantum computing [34]. So the relaxation times for excited states and the absorption lineshapes have all been carefully investigated [35][36][37][38][39][40]. From this perspective the possibility of creating overheated electrons by excitation of cyclotron resonance that was reported in [41] is highly interesting since it challenges the view that energy relaxation rates are all relatively fast in the microsecond range [42] due to two riplon emission processes [43] which should prevent an overheating of the electrons.…”

mentioning

confidence: 99%

Can Warmer than Room Temperature Electrons Levitate Above a Liquid Helium Surface?

2019

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We address the problem of overheating of electrons trapped on the liquid helium surface by cyclotron resonance excitation. Previous experiments, suggest that electrons can be heated to temperatures up to 1000K more than three order of magnitude higher than the temperature of the helium bath in the sub-Kelvin range. In this work we attempt to discriminate between a redistribution of thermal origin and other out-of equilibrium mechanisms that would not require so high temperatures like resonant photo-galvanic effects, or negative mobilities. We argue that for a heating scenario the direction of the electron flow under cyclotron resonance can be controlled by the shape of the initial electron density profile, with a dependence that can be modeled accurately within the Poisson-Boltzmann theory framework. This provides an self consistency-check to probe if the redistribution is indeed consistent with a thermal origin. We find that while our experimental results are consistent with the Poisson-Boltzmann theoretical dependence but some deviations suggest that other physical mechanisms can also provide a measurable contribution. Analyzing our results with the heating model we find that the electron temperatures increases with electron density under the same microwave irradiation conditions. This unexpected density dependence calls for a microscopic treatment of the energy relaxation of overheated electrons. arXiv:1807.09501v1 [cond-mat.mes-hall]

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Anomalous temperature dependence of energy levels of electrons on helium

Nasyedkin

Watanabe

Kono

2023

Low Temperature Physics

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We report on magnetoconductivity measurements of electrons on helium exposed to resonant microwave irradiation within the temperature range associated with electron-ripplon scattering. Our findings reveal a non-monotonic temperature dependence of the intersubband frequency, with an abrupt decrease observed at temperatures below 0.3 K. We attribute this unexpected energy levels shift to the adsorption of 3He impurities near the liquid helium surface at low temperatures and such behavior is consistent with recent theoretical calculations of the surface electron energy spectra on 3He–4He mixtures.

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Temperature-dependent energy levels of electrons on liquid helium

Cited by 11 publications

References 31 publications

Ripplonic Lamb Shift for Electrons on Liquid Helium

Ripplonic Lamb Shift for Electrons on Liquid Helium

Can Warmer than Room Temperature Electrons Levitate Above a Liquid Helium Surface?

Anomalous temperature dependence of energy levels of electrons on helium

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