Si:P as a laboratory analogue for hydrogen on high magnetic field white dwarf stars

Abstract

Laboratory spectroscopy of atomic hydrogen in a magnetic flux density of 10 5 T (1 gigagauss), the maximum observed on high-field magnetic white dwarfs, is impossible because practically available fields are about a thousand times less. In this regime, the cyclotron and binding energies become equal. Here we demonstrate Lyman series spectra for phosphorus impurities in silicon up to the equivalent field, which is scaled to 32.8 T by the effective mass and dielectric constant. The spectra reproduce the high-field theory for free hydrogen, with quadratic Zeeman splitting and strong mixing of spherical harmonics. They show the way for experiments on He and H 2 analogues, and for investigation of He 2 , a bound molecule predicted under extreme field conditions.

High-field impurity magneto-optics of Si:Se

“…They are interesting for quantum information applications because they can be addressed with table-top lasers in the midinfrared. The advantages of silicon over other hosts are the same as those outlined in previous studies of Si:P [1]. The zero-field absorption spectrum is analogous to that of free helium atoms [9], and in this work we investigate experimentally the high-field spectrum of a range of excitedstate transitions in neutral selenium centers and compare them with the predictions for free helium, up to fields equivalent to 100,000 T. …”

“…This model successfully predicts the energy spectrum of the excited states of the shallow single donors, and their magnetic field dependence. The scaling means that experiments on Si:P at 30 T have been shown to correspond to hydrogen at 10 5 T, the highest field observed on a white dwarf [1,2]. This model also predicts the wave-function radii, for example, that of the 2p 0 state of Si:P is 5.4 nm.…”

“…The ground state of impurities in silicon and the field dependence is needed for certain quantum information schemes where electron and nuclear spins are used [4], and the excited states are also important for some gating control architectures [5]. In interpretation of the electric * Corresponding author: k.litvinenko@surrey.ac.uk dipole (Rydberg) spectrum, one usually treats the ground-state energy as a free parameter [1], and the calculated transitions are in excellent agreement with the theory.…”

“…If exchange and correlation internal to the Se were strong, the time evolution would be much more complex. The fact that the excited states are very closely hydrogenic also means that field tuning can be used to control the wave-function shape (and overlaps with neighbors) in the same way [1], with the additional benefit that midinfrared (rather than the far-infrared) lasers can be used for the optical excitation.…”

“…Helium at high field is of great interest for the study of magnetic white dwarfs [6] because it provides an independent control on the assignment of the field from hydrogen spectra, which are very complex [1]. Of course, there are no laboratory experiments up to fields of 1 atomic unit (a.u.…”