Artificial cavity photon resonators with ultrastrong light-matter interactions are attracting interest both in semiconductor and superconducting systems, due to the possibility of manipulating the cavity quantum electrodynamic ground state with controllable physical properties. We report here experiments showing ultrastrong light-matter coupling in a terahertz metamaterial where the cyclotron transition of a high mobility two-dimensional electron gas is coupled to the photonic modes of an array of electronic split-ring resonators. We observe a normalized coupling ratio Ω ωc = 0.58 between the vacuum Rabi frequency Ω and the cyclotron frequency ω c . Our system appears to be scalable in frequency and could be brought to the microwave spectral range with the potential of strongly controlling the magnetotransport properties of a highmobility 2DEG.

Interacting fermions on a lattice can develop strong quantum correlations, which lie at the heart of the classical intractability of many exotic phases of matter [1, 2, 3, 4]. Seminal efforts are underway in the control of artificial quantum systems, that can be made to emulate the underlying Fermi-Hubbard models [5, 6, 7, 8,9,10,11]. Electrostatically confined conduction band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical pure-state initialisation and readily adhere to an engineerable Fermi-Hubbard Hamiltonian [12,13,14,15,16,17,18,19,20,21,22,23]. Until now, however, the substantial electrostatic disorder inherent to solid state has made attempts at emulating Fermi-Hubbard physics on solid-state platforms few and far between [24,25]. Here, we show that for gate-defined quantum dots, this disorder can be suppressed in a controlled manner. Novel insights and a newly developed semi-automated and scalable toolbox allow us to homogeneously and independently dial in the electron filling and nearest-neighbour tunnel coupling. Bringing these ideas and tools to fruition, we realize the first detailed characterization of the collective Coulomb blockade transition [26], which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition [1]. As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here show how quantum dots can be used to investigate the physics of ever more complex many-body states.

The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matter-like quantum system to coherently transform an individual excitation into a single photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work we demonstrate strong coupling between the charge degree of freedom in a gate-defined GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quantum interference devices (SQUIDs). In the resonant regime, we resolve the vacuum Rabi mode splitting of size 2g/2π = 238 MHz at a resonator linewidth κ/2π = 12 MHz and a DQD charge qubit dephasing rate of γ2/2π = 80 MHz extracted independently from microwave spectroscopy in the dispersive regime. Our measurements indicate a viable path towards using circuit based cavity QED for quantum information processing in semiconductor nano-structures.In the strong coupling limit, cavity QED realizes the coherent exchange of a single quantum of energy between a nonlinear quantum system with two or more energy levels, e.g. a qubit, and a single mode of a high quality cavity capable of storing individual photons [1]. The distinguishing feature of strong coupling is a coherent coupling rate g, determined by the product of the dipole moment of the multi-level system and the vacuum field of the cavity, which exceeds both the cavity mode linewidth κ, determining the photon life time, and the qubit linewidth γ 2 = γ 1 /2 + γ ϕ , set by its energy relaxation and pure dephasing rates, γ 1 and γ ϕ , respectively.The strong coupling limit of Cavity QED has been reached with a multitude of physical systems including alkali atoms [2], Rydberg atoms [3], superconducting circuits [4,5] and optical transitions in semiconductor quantum dots [6,7]. Of particular interest is the use of this concept in quantum information processing with supercondcuting circuits where it is known as circuit QED [4,8,9].Motivated by the ability to suppress the spontaneous emission of qubits beyond the free space limit [10], to perform quantum non-demolition (QND) qubit read-out [11,12], to couple distant qubits through microwave photons coherently [13,14] and to convert quantum information stored in stationary qubits to photons [15,16], research towards reaching the strong coupling limit of cavity QED is pursued for the charge and spin degrees of freedom in semiconductor nano-structures [17][18][19][20][21][22]. Recently, in parallel with the work discussed here, independent efforts to reach this goal have come to fruition with gate defined DQDs in silicon [23] and carbon nanotubes [24].The essence of our approach to reach the strong coupling limit with individual electronic charges in GaAs DQDs is rooted in the enhancement of the electric component of the vacuum fluctuations ∝ √ Z r [25] by increas-ing the resonator impedance Z r beyond the typical 50 Ω of a standard copl...

The spin-orbit interaction (SOI) in zincblende semiconductor quantum wells can be set to a symmetry point, in which spin decay is strongly suppressed for a helical spin mode. Signatures of such a persistent spin helix (PSH) have been probed using the transient spin grating technique, but it has not yet been possible to observe the formation and the helical nature of a PSH. Here we directly map the diffusive evolution of a local spin excitation into a helical spin mode by a timeand spatially resolved magneto-optical Kerr rotation technique. Depending on its in-plane direction, an external magnetic field interacts differently with the spin mode and either highlights its helical nature or destroys the SU(2) symmetry of the SOI and thus decreases the spin lifetime. All relevant SOI parameters are experimentally determined and confirmed with a numerical simulation of spin diffusion in the presence of SOI.Conduction-band electrons in semiconductors experience SOI from intrinsic [1] and extrinsic sources, leading to spin dephasing, current-induced spin polarization and spin Hall effects [2]. These physical mechanisms are of great fundamental and technological interest, recently also in the context of topolocial insulators [3] and Majorana fermions [4,5]. Intrinsic SOI arises from an inversion asymmetry of the bulk crystal (Dresselhaus term) and of the grown layer structure (Rashba term). In a quantum well (QW), these two components can be tailored by means of the confinement potential [6], and the Rashba SOI can be externally tuned by using gate electrodes [7,8]. In general, SOI leads to precession of electron spins. In the diffusive limit, in which the scattering length is much smaller than the spin-orbit (SO) length λ SO , a random walk of the spins on the Bloch sphere will dephase a non-equilibrium spin polarization [9].Of special interest is the situation in a two-dimensional electron gas (2DEG) with balanced Rashba and Dresselhaus contributions [6,[10][11][12][13]. There, the SOI attains SU(2) symmetry and the spin polarization of a helical mode is preserved. The reason for this conservation of the spin polarization is a unidirectional effective SO magnetic field B SO , which depends linearly on the component of the electron momentum along a specific in-plane direction. This causes the precession angle of a moving electron to vary linearly with the distance traveled along that direction, irrespective of whether the electron path is ballistic or diffusive [10,11]. In such a situation, a local spin excitation is predicted to evolve into a helical spin mode termed PSH [ Fig. 1(a)]. Transient spin grating measurements [6] showed that a spin excitation with a spatially modulated out-of-plane spin component decays with two characteristic lifetimes that correspond to two superposed spin modes of opposite helicity. * Electronic address: gsa@zurich.ibm.comHere we directly measure the diffusive evolution of a local spin excitation into a PSH by time-resolved Kerr rotation microscopy [ Fig. 1(b)]. We employ a pumpprobe appro...