The physics and operating principles of hybrid superconductor-semiconductor devices rest ultimately on the magnetic properties of their elementary subgap excitations, usually called Andreev levels. Here we report a direct measurement of the Zeeman effect on the Andreev levels of a semiconductor quantum dot with large electron g-factor, strongly coupled to a conventional superconductor with a large critical magnetic field. This material combination allows spin degeneracy to be lifted without destroying superconductivity. We show that a spin-split Andreev level crossing the Fermi energy results in a quantum phase transition to a spin-polarized state, which implies a change in the fermionic parity of the system. This crossing manifests itself as a zero-bias conductance anomaly at finite magnetic field with properties that resemble those expected for Majorana modes in a topological superconductor. Although this resemblance is understood without evoking topological superconductivity, the observed parity transitions could be regarded as precursors of Majorana modes in the long-wire limit.

In this review we focus on electronic transport through semiconductor nanostructures which are driven by ac fields. Along the review we describe the available experimental information on different nanostructures, like resonant tunneling diodes, superlattices or quantum dots, together with the theoretical tools needed to describe the observed features. These theoretical tools such as, for instance, the Floquet formalism, the non-equilibrium Green's function technique or the density matrix technique, are suitable for tackling with photon-assisted transport problems where the interplay of different aspects like nonequilibrium, nonlinearity, quantum confinement or electron-electron interactions gives rise to many intriguing new phenomena. Along the review we give many examples which demonstrate the possibility of using appropriate ac fields to control/manipulate coherent quantum states in semiconductor nanostructures.

A double quantum dot device is a tunable two-level system for electronic energy states. A dc electron current was used to directly measure the rates for elastic and inelastic transitions between the two levels. For inelastic transitions, energy is exchanged with bosonic degrees of freedom in the environment. The inelastic transition rates are well described by the Einstein coefficients, relating absorption with stimulated and spontaneous emission. The most effectively coupled bosons in the specific environment of the semiconductor device used here were acoustic phonons. The experiments demonstrate the importance of vacuum fluctuations in the environment for quantum dot devices and potential design constraints for their use for preparing long-lived quantum states.

We propose a measurement setup for detecting quantum noise over a wide frequency range using inelastic transitions in a tunable two-level system as a detector. The frequency-resolving detector consists of a double quantum dot which is capacitively coupled to the leads of a nearby mesoscopic conductor. The inelastic current through the double quantum dot is calculated in response to equilibrium and nonequilibrium current fluctuations in the nearby conductor, including zero-point fluctuations at very low temperatures. As a specific example, the fluctuations across a quantum point contact are discussed. PACS numbers: 73.50.Td, 73.20.Dx, Two-level systems (TLS) coupled to a dissipative environment are canonical model systems to study dephasing in quantum mechanics [1]. The reversed problem is a TLS that measures the characteristics of a specific environment. The transition rate for levels separated by an energy e is a measure of the spectral density of the fluctuations in the environment at a frequency f e͞h. Transitions are allowed when energy can be exchanged with the environment. Recently, two device structures were realized that can be used as tunable TLS. In a superconducting single electron transistor a Cooper pair [2] and in a double quantum dot (DQD) an electron [3] can make inelastic transitions between two discrete energy states. In this work we calculate the rate for inelastic transitions in a DQD coupled to an environment formed by a second mesoscopic device.Small electronic devices have interesting equilibrium and nonequilibrium noise properties which are nonlinear in frequency [4]. In equilibrium, a transition occurs going from low frequencies, where Johnson-Nyquist noise due to thermal fluctuations dominates, to high frequencies where quantum noise due to zero-point fluctuations (ZPF) prevails. When the device is voltage biased, nonequilibrium fluctuations can become dominant. These lead to shot noise in the current, which has been measured near zero frequency [5] and at several high-frequency values where ZPF become dominant [6]. The idea of using a mesoscopic device, quantum point contact (QPC), as an environment for another device, quantum dot, has successfully been used in the so-called "which-path" detector [7]: the dc shot-noise of the QPC modifies the transport properties of the dot, leading to dephasing. Here we propose a setup for studying the effect of broadband fluctuations on the inelastic rate in a TLS. This setup provides a frequencyresolved detection over a large frequency range of the fluctuations in mesoscopic systems. A wide frequency range requires that the frequency dependent impedance of the whole circuit is taken into account. Below, we first describe the basic properties of a DQD, then formulate transition probabilities in terms of the noise spectrum, followed by calculations where the specific environment is formed by a QPC.A DQD is a fully controllable TLS. The separation between levels e ϵ E L 2 E R , the tunnel rates across the left and right barriers, G L , G R , and the tu...