The harmonic oscillator is a foundational concept in both theoretical and experimental quantum mechanics. Here, we demonstrate harmonic oscillators in a semiconductor platform by faithfully implementing continuously graded alloy semiconductor quantum wells. Unlike current technology, this technique avoids interfaces that can hamper the system and allows for the production of multiwell stacks several micrometers thick. The experimentally measured system oscillations are at 3 THz for two structures containing 18 and 54 parabolic quantum wells. Absorption at room temperature is achieved: this is as expected from a parabolic potential and is unlike square quantum wells that require cryogenic operation. Linewidths below 11% of the central frequency are obtained up to 150 K, with a 5.6% linewidth obtained at 10 K. Furthermore, we show that the system correctly displays an absence of nonlinearity despite electronelectron interactions-analogous to the Kohn theorem. These high-quality structures already open up several new experimental vistas.
Scalable architectures characterized by quantum bits (qubits) with low error rates are essential to the development of a practical quantum computer. In the superconducting quantum computing implementation, understanding and minimizing materials losses is crucial to the improvement of qubit performance. A new material that has recently received particular attention is indium, a low-temperature superconductor that can be used to bond pairs of chips containing standard aluminum-based qubit circuitry. In this work, we characterize microwave loss in indium and aluminum/indium thin films on silicon substrates by measuring superconducting coplanar waveguide resonators and estimating the main loss parameters at powers down to the sub-photon regime and at temperatures between 10 and 450 mK. We compare films deposited by thermal evaporation, sputtering, and molecular beam epitaxy. We study the effects of heating in vacuum and ambient atmospheric pressure as well as the effects of pre-deposition wafer cleaning using hydrofluoric acid. The microwave measurements are supported by thin film metrology including secondary-ion mass spectrometry. For thermally evaporated and sputtered films, we find that two-level states (TLSs) are the dominating loss mechanism at low photon number and temperature. Thermally evaporated indium is determined to have a TLS loss tangent due to indium oxide of ∼ 5 × 10 −5 . The molecular beam epitaxial films show evidence of formation of a substantial indium-silicon eutectic layer, which leads to a drastic degradation in resonator performance.
new regime is attained-the strong coupling regime (SCR)-where light and matter exchange energy coherently and periodically. In the frequency domain, this leads to a radical change of the system's spectral response. From the first observation with Rydberg atoms, the SCR has been demonstrated in a plethora of systems spanning excitons, organic molecules, electronic transitions, superconducting qubits and many others. [2] The strength of the light-matter interaction is often gauged by a dimensionless parameter η that is the ratio between the coupling constant Ω R (also called the vacuum Rabi frequency) over the resonant transition frequency ω 0 . [3] Above a value η > 0.1, one enters the ultra-strong coupling (USC) regime where the diamagnetic terms of the interaction Hamiltonian start to play an important role, leading to a deviation from the linear approximation and the formation of a sizeable population of virtual photons in the ground state of the system. [4] The same foundational article by Ciuti et al. [4] also proposed that an abrupt modulation of the system ground state leads to a release of such virtual population as real photons, an approach that could lead to the development of non-classical light emitters at long-wavelengths. Continuously graded parabolic quantum wellswith excellent optical performances are used to overcome the low-frequency and thermal limitations of square quantum wells at terahertz (THz) frequencies. The formation of microcavity intersubband polaritons at frequencies as low as 1.8 THz is demonstrated, with a sustained ultra-strong coupling regime up to a temperature of 200 K. Thanks to the excellent intersubband transition linewidth, polaritons present quality factors up to 17. It is additionally shown that the ultra-strong coupling regime is preserved when the active region is embedded in subwavelength resonators, with an estimated relative strength η = Ω R /ω 0 = 0.12. This represents an important milestone for future studies of quantum vacuum radiation because such resonators can be optically modulated at ultrafast rates, possibly leading to the generation of non-classical light via the dynamic Casimir effect. Finally, with an effective volume of 2 10 6 0 3 λ × × − −, it is estimated that fewer than 3000 electrons per resonator are ultra-strongly coupled to the quantized electromagnetic mode, proving it is also a promising approach to explore few-electron polaritonic systems operating at relatively high temperatures.
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