Achieving control over light−matter interaction in custom-tailored nanostructures is at the core of modern quantum electrodynamics. In strongly and ultrastrongly coupled systems, the excitation is repeatedly exchanged between a resonator and an electronic transition at a rate known as the vacuum Rabi frequency Ω R . For Ω R approaching the resonance frequency ω c , novel quantum phenomena including squeezed states, Dicke superradiant phase transitions, the collapse of the Purcell effect, and a population of the ground state with virtual photon pairs are predicted. Yet, the experimental realization of optical systems with Ω R /ω c ≥ 1 has remained elusive. Here, we introduce a paradigm change in the design of light−matter coupling by treating the electronic and the photonic components of the system as an entity instead of optimizing them separately. Using the electronic excitation to not only boost the electronic polarization but furthermore tailor the shape of the vacuum mode, we push Ω R /ω c of cyclotron resonances ultrastrongly coupled to metamaterials far beyond unity. As one prominent illustration of the unfolding possibilities, we calculate a ground state population of 0.37 virtual photons for our best structure with Ω R /ω c = 1.43 and suggest a realistic experimental scenario for measuring vacuum radiation by cutting-edge terahertz quantum detection. KEYWORDS: Quantum electrodynamics, ultrastrong coupling, terahertz, metamaterials I n the strong coupling regime of quantum electrodynamics (QED), where the vacuum Rabi frequency Ω R exceeds the dissipation rates of the electronic excitation and the resonator, new eigenmodes called cavity polaritons emerge. This universal principle is found in a large variety of systems, ranging from atoms 1 to excitons in semiconductors, 2,3 molecules, 4 mid-IR plasmonic structures, 5−9 circuit QED systems at GHz frequencies, 10−13 and structures in the THz spectral range. 14−16 In ultrastrongly coupled structures, Ω R becomes comparable to the resonance frequency ω c itself; the rotating-wave approximation of light−matter interaction falters, and antiresonant coupling terms describing the simultaneous creation of correlated light and matter excitations become relevant. 17−19 Most prominently, the ground state is theorized to be a modified squeezed quantum vacuum with a finite population of correlated virtual photon pairs. 17,19 For sufficiently large values of the relative coupling strength Ω R /ω c ≳1, subcycle switching of Ω R 6,9 may release these photons 17,19,20 in analogy to Unruh− Hawking radiation emerging at the event horizon of black holes. 21 These spectacular perspectives have fuelled the quest of the QED community for ever greater relative coupling strengths, ultimately aiming for Ω R /ω c beyond unity.The key strategy for boosting Ω R /ω c , also referred to as g/ω c , comprises increasing the dipole moment of the electronic transition, decreasing the resonator mode volume and ω c , or enhancing the overlap of the photonic mode and the electroni...

We present the first study relating structural parameters of precipitate-free Ge 0:95 Mn 0:05 films to magnetization data. Nanometer-sized clusters -areas with increased Mn content on substitutional lattice sites compared to the host matrix -are detected in transmission electron microscopy analysis. The films show no overall spontaneous magnetization at all down to 2 K. The TEM and magnetization results are interpreted in terms of an assembly of superparamagnetic moments developing in the dense distribution of clusters. Each cluster individually turns ferromagnetic below an ordering temperature which depends on its volume and Mn content. DOI: 10.1103/PhysRevLett.97.237202 PACS numbers: 75.50.Pp, 68.37.Lp, 75.75.+a, 81.15.Hi The development of a novel class of materials combining standard semiconductors with magnetic elements has recently been driven by considerable technological as well as fundamental scientific interest. While the possibility of a seamless combination of magnetic and semiconducting systems using spins as an additional degree of freedom opens stimulating perspectives in the field of electronics [1,2], reports on materials displaying both semiconducting and ferromagnetic properties have induced great theoretical and experimental efforts in the understanding of the underlying physics [3]. Ga(Mn)As today represents one of the best understood ferromagnets. This material is one example of a diluted magnetic semiconductor (DMS), meaning a dispersion of the magnetic elements without affecting the semiconducting properties of the matrix [4]. The realization of DMS with maximized ferromagnetic ordering temperatures T C represents the ultimate objective in this field.Special attention has been given to technologically important group IV semiconductor based magnetic materials, with a prominent position for GeMn. Since the first claim of the realization of a Ge based DMS [5], most publications [5][6][7][8] have concentrated on reporting high T C ranging from 116 [5] to 285 K [6] and on interpreting the observed ferromagnetism in terms of DMS theories [9]. It is only recently that several of the former GeMn reports have been questioned by structural proofs [10] and hints [11] for the formation of intermetallic ferromagnetic compounds through phase separation in single crystals and lowtemperature molecular beam epitaxy (MBE) fabricated films, respectively. Up to now, only Li et al.[11] presentindirect -indications for the realization of precipitate-free GeMn. Considering the current discussion on the magnetic properties of GeMn, a study of the crystal structure, exploring the degree of Mn dispersion that can be reached in Ge, would obviously be beneficial for the field.In this Letter, we present the first study relating structural parameters of precipitate-free Ge 0:95 Mn 0:05 films to magnetization data, providing new insights into the interpretation of the magnetic properties of GeMn. Although the incorporation of Mn does not induce explicit phase separation, nanometer-sized areas with increased Mn cont...

The spin-orbit interaction (SOI) of a two-dimensional hole gas in the inversion symmetric semiconductor Ge is studied in a strained-Ge=SiGe quantum well structure. We observe weak antilocalization (WAL) in the magnetoconductivity measurement, revealing that the WAL feature can be fully described by the k-cubic Rashba SOI theory. Furthermore, we demonstrate electric field control of the Rashba SOI. Our findings reveal that the heavy hole (HH) in strained Ge is a purely cubic Rashba system, which is consistent with the spin angular momentum m j ¼ AE3=2 nature of the HH wave function. DOI: 10.1103/PhysRevLett.113.086601 PACS numbers: 72.25.Dc, 73.20.Fz, 73.21.-b The spin-orbit interaction (SOI) in a two-dimensional system is a subject of considerable interest because the SOI induces spin splitting at a zero magnetic field, which is important in both fundamental research and electronic device applications [1]. Recent developments of SOI-induced phenomena in the solid state demonstrate many possibilities utilizing spin current and the emergence of new physics such as the spin interferometer [2,3], persistent spin helix [4,5], spin Hall effect [6][7][8], and quantum spin Hall effect [9,10]. Up to now, there have been two well-known SOIs existing in solids: the Dresselhaus SOI [11] due to bulk inversion asymmetry (BIA) in the crystal structure and the Rashba SOI [12,13] due to spatial inversion asymmetry (SIA).In low-dimensional systems, the Rashba SOI becomes more important because it is stronger at the heterointerface and can be controlled by an external electric field. Many of the pioneering studies on the SOI-induced phenomena mentioned above were performed in two-dimensional electron systems, where the Rashba SOI is described by the k-linear Rashba term. In the Hamiltonian, the k-linear Rashba term can be written aswhere σ AE ¼ 1=2ðσ x AE iσ y Þ denote combinations of Pauli spin matrices, k AE ¼ k x AE ik y , and k x , k y are the components of the in-plane wave vector k ∥ . The effective magnetic field Ω 1 ðk ∥ Þ acting on the transport carrier due to the k-linear Rashba term is illustrated in Fig. 1(a).Recently, a higher-order contribution of the Rashba SOI, the so-called k 3 (k-cubic) Rashba SOI, has received more attention [14,15]. The Hamiltonian for the k-cubic Rashba SOI is expressed asand the effective magnetic field Ω 3 ðk ∥ Þ in k space is illustrated in Fig. 1(b) [15]. There is a significant difference in the effective field symmetry between the k-linear and the k-cubic Rashba SOI with one and three rotations in k space, respectively. The k 3 symmetry of the SOI is an interesting subject because it influences all of the SOI-induced phenomena as opposed to the k-linear Rashba term. For example, in case of the spin Hall effect, the k-cubic Rashba term is predicted to give rise to a larger spin Hall conductivity [17][18][19].

No abstract