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We have investigated the values of the Rashba spin-orbit coupling constant a in In 0.52 Al 0.48 As͞In 0.53 Ga 0.47 As͞In 0.52 Al 0.48 As quantum wells using the weak antilocalization (WAL) analysis as a function of the structural inversion asymmetry (SIA) of the quantum wells. We have found that the deduced a values have a strong correlation with the degree of SIA of the quantum wells as predicted theoretically. The good agreement between the theoretical and experimental values of a suggests that our WAL approach for deducing a values provides a useful tool in designing future spintronics devices that utilize the Rashba spin-orbit coupling. DOI: 10.1103/PhysRevLett.89.046801 PACS numbers: 72.25.Dc, 72.25.Rb, 73.20.Fz, 73.63.Hs There has been growing interest in the field of "spintronics" [1], which involves exploration of the extra degrees of freedom provided by electron spin, in addition to those due to electron charge, with a view to realizing new functionalities in future electronic devices. One key to realizing such a spin device is the utilization of the spin-orbit (SO) interaction caused by structural inversion asymmetry (SIA) (Rashba term) in quantum wells (QWs) [2], which can be artificially controlled by controlling the applied gate voltages [3 -6] and/or by the specific design of the heterostructure [7]. However, it still remains controversial whether or not the Rashba term really exists in asymmetric QWs from both the theoretical [8][9][10] and the experimental standpoints [11,12]. From the experimental point of view, the controversy arises from the difficulties in the experimental determination of the Rashba SO coupling constant a. While the existence of a spin splitting D at the Fermi energy suggests beating in the Shubnikov -de Haas (SdH) oscillations [3 -6], the D value deduced from the position of the beating node is usually different from the value of the zero-field spin splitting D 0 since D includes the effect of the Zeeman spin splitting in a finite magnetic field [13]. In addition, in order for the beating to be observed, the value of D has to be sufficiently large so that the SdH oscillation is visible at magnetic fields where the beating nodes are supposed to occur. One should also be careful about the beatinglike patterns in the SdH oscillations that are not really related to D. When the position of the Fermi energy is sufficiently close to the second lowest subband edge (within an order of k B T) and significant intersubband scattering is taking place, beatinglike patterns can be observed in the SdH oscillations [14,15]. Also a slight occupation of the second lowest subband itself may produce a beatinglike pattern as well [16]. Therefore, it is essential to develop some other independent experimental techniques for the determination of a values, that are more reliable and reproducible than the SdH beating pattern analysis, in order to clarify the fundamental issues on the Rashba SO coupling. A quantitative understanding of the Rashba mechanism is also important for realizing future ...

We propose a spin-interference device which works even without any ferromagnetic electrodes and any external magnetic field. The interference can be expected in the Aharonov-Bohm ͑AB͒ ring with a uniform spin-orbit interaction, which causes the phase difference between the spin wave functions traveling in the clockwise and anticlockwise direction. The gate electrode, which covers the whole area of the AB ring, can control the spin-orbit interaction, and therefore, the interference. A large conductance modulation effect can be expected due to the spin interference.

We propose an electronic spin-filter device that uses a nonmagnetic triple barrier resonant tunneling diode (TB-RTD). This device combines the spin-split resonant tunneling levels induced by the Rashba spin-orbit interaction and the spin blockade phenomena between two regions separated by the middle barrier in the TB-RTD. Detailed calculations using the InAlAs/InGaAs material system reveal that a splitting of a peak should be observed in the I-V curve of this device as a result of the spin-filtering effect. The filtering efficiency exceeds 99.9% at the peak positions in the I-V curve. DOI: 10.1103/PhysRevLett.88.126601 PACS numbers: 72.25.Hg, 72.25.Mk, 73.40.Ei, 73.40.Gk Experimental realization of a spin-polarized current source and manipulation of electron spin in a semiconductor are among the most important issues in "spintronics" research [1]. In this research area, extra degrees of freedom provided by electron spins, in addition to those provided by electron charges, are expected to play important roles in realizing new functions in future electronic devices, which include spin-FET [2], spin interference devices [3], and a readout device for the qubit information [4]. In order to explore the roles of spin degrees of freedom in a semiconductor, it is essential to realize a spin-polarized current source from which spin-polarized electrons are injected. The properties of electron spins, including their dynamical motions in the pertinent materials are then studied using the injected spin-polarized electrons. Thus far, various magnetic materials, including ferromagnetic metals [5][6][7] and diluted magnetic semiconductors [8 -13], have been used as spin injection sources. Besides the successes in these approaches, it is also important to develop a spin-polarized current source, or a spin filter, that uses only nonmagnetic semiconductors from the viewpoints of both the attainability of high-quality heterostructures and the absence of the stray magnetic field that may cause some undesirable effects on the spin-filtered electrons.In this Letter, we propose a spin-filter device that uses a triple barrier (TB) resonant tunneling diode (RTD) which can generate a spin-polarized current without using magnetic properties of materials. Instead, we utilize the Rashba spin-orbit coupling effect [14-16] (Rashba effect) to induce spin-split resonant tunneling levels (RTL) in the proposed device even in the absence of magnetic field. So far, the Rashba effect in a double barrier (DB) RTD has been discussed from both theoretical [17] and experimental points of view [18], and is predicted to provide some degrees of spin polarization in the transmitted electrons [17]. However, the utilization of Rashba effect alone in a DB-RTD does not produce a high degree of spin polarization ͑.90%͒. To overcome this problem, we propose combining the spin-splitting phenomena caused by the Rashba effect with level-matching between the spindependent RTLs, which is accomplished by adjusting the emitter-collector voltage V EC in the TB-RTD. Thi...

We have observed the coherent exchange of a single energy quantum between a flux qubit and a superconducting LC circuit acting as a quantum harmonic oscillator. The exchange of an energy quantum is known as the vacuum Rabi oscillation: the qubit is oscillating between the excited state and the ground state and the oscillator between the vacuum state and the first excited state. We also show that we can detect the state of the oscillator with the qubit and thereby obtained evidence of level quantization of the LC circuit. Our results support the idea of using oscillators as couplers of solid-state qubits.

† authors with equal contribution to this work Superconducting qubits 1,2 behave as artificial two-level atoms and are used to investigate fundamental quantum phenomena. In this context, the study of multi-photon excitations 3,4,5,6,7 occupies a central role. Moreover, coupling superconducting qubits to on-chip microwave resonators has given rise to the field of circuit QED 8,9,10,11,12,13,14,15 . In contrast to quantum-optical cavity QED 16,17,18,19 , circuit QED offers the tunability inherent to solid-state circuits. In this work, we report on the observation of key signatures of a two-photon driven Jaynes-Cummings model, which unveils the upconversion dynamics of a superconducting flux qubit 20 coupled to an on-chip resonator. Our experiment and theoretical analysis show clear evidence for the coexistence of one-and two-photon driven level anticrossings of the qubit-resonator system. This results from the symmetry breaking of the system Hamiltonian, when parity becomes a not well-defined property 21 . Our study provides deep insight into the interplay of multiphoton processes and symmetries in a qubit-resonator system.In cavity QED, a two-level atom interacts with the quantized modes of an optical or microwave cavity. The information on the coupled system is encoded both in the atom and in the cavity states. The latter can be accessed spectroscopically by measuring the transmission properties of the cavity 16 , whereas the former can be read out by suitable detectors 18,19 . In circuit QED, the solid-state counterpart of cavity QED, the first category of experiments was implemented by measuring the microwave radiation emitted by a resonator (acting as a cavity) strongly coupled to a charge qubit 8 . In a dual experiment, the state of a flux qubit was detected with a DC superconducting quantum interference device (SQUID) and vacuum Rabi oscillations were observed 10 . More recently, both approaches have been exploited to extend the toolbox of quantum optics on a chip 11,12,13,14,15,22 . Whereas all these experiments employ one-photon driving of the coupled qubit-resonator system, multi-photon studies are available only for sideband transitions 15 or bare qubits 3,4,5,6,7 . The experiments discussed in this work explore, to our knowledge for the first time, the physics of the two-photon driven Jaynes-Cummings dynamics in circuit QED. In this context, we show that the dispersive interaction between the qubit and the two-photon driving enables real level transitions. The nature of our experiment can be understood as an upconversion mechanism, which transforms the two-photon coherent driving into single photons of the Jaynes-Cummings dynamics. This process requires energy conservation and a not well-defined parity 21 of the interaction Hamiltonian due to the symmetry breaking of the qubit potential. Our experimental findings reveal that such symmetry breaking can be obtained either by choosing a suitable qubit operation point or by the presence of additional spurious fluctuators 23 .The main elements of our setup, ...

In order to gain a better understanding of the origin of decoherence in superconducting flux qubits, we have measured the magnetic field dependence of the characteristic energy relaxation time (T(1)) and echo phase relaxation time (T(2)(echo)) near the optimal operating point of a flux qubit. We have measured T(2)(echo) by means of the phase cycling method. At the optimal point, we found the relation T(2)(echo) approximately 2T(1). This means that the echo decay time is limited by the energy relaxation (T(1) process). Moving away from the optimal point, we observe a linear increase of the phase relaxation rate (1/T(2)(echo)) with the applied external magnetic flux. This behavior can be well explained by the influence of magnetic flux noise with a 1/f spectrum on the qubit.

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