Nanoscale Physics
Longitudinal quantum oscillations of surface electrons over helium film on a structured substrate for quantum computer 

V. A. Nikolaenko1,  A. G. Pashchenko2	 
1 B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Nauka Ave., Kharkiv, 61103, Ukraine
 2 Kharkiv National University of Radio Engineering and Electronics, 14 Nauka   Ave, Kharkiv, 61166, Ukraine 
E-mail: nikolaenko@ilt.kharkov.ua

Modeling the micro- nano-objects and the complex physical processes revolutionize quantum computer (QC). The quantum bit (QB) operates in superposition of two quantum states. The quantum entanglement of n bits for some time is essence of QC with 2n basis vector in opposite to classical logic with n2 basis. The quantum dots for QBs are preferred. The concept of Platzman and Dykman (Science., 284, p. 1967 (1999)) considers for QC a hydrogen-like levels of the surface electrons (SEs) on helium covered lattice of microelectrodes. Using both the Stark’s shift of Ridberg’s levels into resonance with mkm-radiation and the normal tunneling the SEs is the essence of QB tuning and reading the results.  Here proposed the use of the longitudinal spectrum of SEs over the lattice of governing microelectrodes coated with thin helium film on the dielectric plate. The longitudinal spectrum of electrons depending on the film thickness d is  ωd2 = e2 / [(1 + εs) m d3]  (here e and m are the charge and mass of electron correspondently and εs is the dielectric constant of plate). The energy of the inter-level transition vs d is shown in the figure (bottom curve is smooth He film and He film with dimple is upper curve). The size of localization of electron in potential well is L = (ħ / mωd)1/2. The Wigner crystallization (WC) temperature at the electron density ns is Tc <0.226 ns1/2. The quantum melting of WC and overlapping of the electron wave functions in periodic potential of a lattice takes place at energy of the electron ε > (π ns ħ2 / 2 m). Like theory is in work [1]. The smoothly of plate surface is additional need and this is achievable with modern nanotechnology. On estimates, at ns = 1014 – 1015 m-2 interval of Tc = (2.6 – 7.15) K and ε ~ (0.14 – 1.4) K; the value of L~10nm at d ~ 30nm. The QC can operate at super-low temperatures (~ 10 mK). 

1. Ginzburg Vl.L., Monarha Yu.P. Surface electrons in helium over macroscopic structures // Fiz. Nizk. Temp. – 1978. - 4, -P. 1236-1239.