The New Concept of Nano-Device Spectroscopy Based on Rabi–Bloch Oscillations for THz-Frequency Range

2017 Applied Sciences  
We considered one-dimensional quantum chains of two-level Fermi particles coupled via the tunneling driven both by ac and dc fields in the regimes of strong and ultrastrong coupling. The frequency of ac field is matched with the frequency of the quantum transition. Based on the fundamental principles of electrodynamics and quantum theory, we developed a general model of quantum dynamics for such interactions. We showed that the joint action of ac and dc fields leads to the strong mutual
more » ... rong mutual influence of Rabi-and Bloch oscillations, one to another. We focused on the regime of ultrastrong coupling, for which Bloch-and Rabi-frequencies are significant values of the frequency of interband transition. The Hamiltonian was solved numerically, with account of anti-resonant terms. It manifests by the appearance of a great number of narrow high-amplitude resonant lines in the spectra of tunneling current and dipole moment. We proposed the new concept of terahertz (THz) spectroscopy, which is promising for different applications in future nanoelectronics and nano-photonics. Appl. Sci. 2017, 7, 721 2 of 24 spectra became the attribute of nano-objects of various spatial configurations, but the same chemical composition. In this context, the future of spectroscopy development would probably be associated with the spectroscopy of a whole range of electronic devices, or their rather large components. This trend will provide tools of the tunable spectroscopy adapted for such types of tasks. The promising examples from this point of view are based on the strong and ultrastrong interactions of condensed matter with EM-field. The strong-coupling field-matter interaction is defined as a regime, in which the EM-field does not correspond to the small perturbation [1]. It leads to the periodical transitions of a two-level quantum system between its stationary states under the action of ac driving field (Rabi-oscillations-RO) [1]. The phenomenon was theoretically predicted by Rabi on nuclear spins in radio-frequency magnetic field [2], and afterwards, discovered in various physical systems, such as electromagnetically driven atoms [3], semiconductor quantum dots [4], and different types of solid-state qubits [5][6] [7] [8] [9] . The simplest physical picture of the Rabi effect is given by the model of a single atom [1]. It can be essentially modified by a set of additional features, such as broken inversion symmetry [10], spatial RO propagation in the arrays of coupled Rabi-oscillators (Rabi-waves), and local field depolarization effects [11] [12] [13] [14] [15] [16] . The early quantum theory of electrical conductivity in crystal lattices by Bloch, Zener and Wannier [17] [18] [19] [20] , led to the prediction that a homogeneous dc field induces an oscillatory, rather than uniform, motion of the electrons. These so-called Bloch-oscillations (BO) have never been observed in natural crystals because the scattering time of the electrons by the lattice defects is much shorter than the Bloch period [21] . In semiconductor superlattices, the larger spatial period leads to a much shorter Bloch period, and BO have been observed through the THz radiation of the electrons [22] . BO in dc biased lattices is due to wave interference, and have been observed in a number of quite different physical systems: a few interacting atoms in optical lattices [23, 24] , ultracold atoms [25-30], light intensity oscillations in waveguide arrays [31] [32] [33] [34] [35] [36] [37] , acoustic waves in layered and elastic structures [38], atomic oscillations in Bose-Einstein condensates [39], among others. Several recent studies have investigated the dynamics of cold atoms in optical lattices subject to ac forcing; the theoretically predicted renormalization of the tunneling amplitudes has been verified experimentally. Recent observations include global motion of the atom cloud, such as giant "super-Bloch oscillations" [40] . As a result, BO was transformed from a partial physical effect, to the universal phenomenon of oscillatory motion of wave packets placed in a periodic potential, when driven by a constant force [24, 41] . Recently, there have been several theoretical studies of the ultrastrong light-matter interaction regime [42] [43] [44] [45] , where the Rabi frequency becomes comparable with the frequency of the inter-zone quantum transition [43] . This regime has been realized experimentally with intersubband transitions coupled with plasmon waveguides in the infrared frequency range [46] , and metallic microcavities in the THz [47] [48] [49] , magnetoplasmons of two-dimensional electron gas [50], superconducting qubits [51], and molecular transitions [52] . It was shown that the system behaves like a multi-level quantum bit with non-monochromatic energy spacing, owing to the inter-particle interactions. One of the general tendencies in modern physics consists of the synthesis of different physical mechanisms in the network of one physical process, with their strong mutual influence. One of such examples have been demonstrated in [53] , where the quantum chain of the coupled two-level fermion systems driven simultaneously by ac and dc fields was considered. It was shown that in the case of resonant interaction with an ac-component, the particle dynamics exhibits itself in the oscillatory regime, which may be interpreted as a combination of RO and BO, with their strong mutual influence. This type of quantum dynamics was named in [53] as Rabi-Bloch oscillations (RBO). Such a scenario dramatically differs from the individual picture of both types of oscillations due to the interactions. This novel effect is counterintuitive because of the strongly different frequency ranges for two such types of oscillation existences. In this paper, we consider the RBO in the regimes of strong and ultrastrong coupling. We present the approximate analytical solution, and results of the numerical modelling. We study both Appl. Sci. 2017, 7, 721 3 of 24 the temporal dynamics and spectra, identify the spectral lines, and compare the spectra behavior in the strong and ultrastrong regimes. Conclusively, we discuss the promising applications of our results in the novel types of spectroscopy.
doi:10.3390/app7070721 fatcat:3sgevkk4hzdejfganocxhsjmie