Coupling artificial molecular spin states by photon-assisted tunnelling

ARTICLE Received 8 Jul 2011 | Accepted 20 Oct 2011 | Published 22 Nov 2011 DOI: 10.1038/ncomms1561 Coupling artificial molecular spin states by photon-assisted tunnelling L.R. Schreiber1, F.R. Braakman1, T. Meunier1,2, V. Calado1, J. Danon3, J.M. Taylor4, W. Wegscheider5,6 & L.M.K. Vandersypen1 Artificial molecules containing just one or two electrons provide a powerful platform for studies of orbital and spin quantum dynamics in nanoscale devices. A well-known example of these dynamics is tunnelling of electrons between two coupled quantum dots triggered by microwave irradiation. So far, these tunnelling processes have been treated as electric-dipoleallowed spin-conserving events. Here we report that microwaves can also excite tunnelling transitions between states with different spin. We show that the dominant mechanism responsible for violation of spin conservation is the spin–orbit interaction. These transitions make it possible to perform detailed microwave spectroscopy of the molecular spin states of an artificial hydrogen molecule and open up the possibility of realizing full quantum control of a two-spin system through microwave excitation. 1 Kavli Institute of Nanoscience, TU Delft, 2600 GA Delft, The Netherlands. 2 Institut Néel, CNRS and Université Joseph Fourier, 38042 Grenoble, France. Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany. 4 Joint Quantum Institute of Standards and Technology, University of Maryland, 20899 Gaithersburg, USA. 5 Institute for Experimental and Applied Physics, University of Regensburg, 93053 Regensburg, Germany. 6 Solid State Physics Laboratory, ETH 8093 Zurich, Switzerland. Correspondence and requests for materials should be addressed to L.R.S. (email: ). 3 NATURE COMMUNICATIONS | 2:556 | DOI: 10.1038/ncomms1561 | www.nature.com/naturecommunications © 2011 Macmillan Publishers Limited. All rights reserved. 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms1561 Results Device and excitation protocol. Figure 1a displays a scanning electron micrograph of a sample similar to that used in the experiments. It shows the metal gate pattern that electrostatically defines a DD and a quantum point contact (QPC) within a GaAs/ (Al,Ga)As two-dimensional electron gas. An on-chip Co micromagnet (μ magnet) indicated in blue in Figure 1a generates an inhomogeneous magnetic field across the DD, which adds to the homogeneous external in-plane magnetic field B (Methods), but is not needed for the molecular spin spectroscopy. The sample was mounted in a dilution refrigerator equipped with high-frequency lines. The gate voltages are set so that the DD can be considered as a closed system (the interdot tunnelling rates are 104 times larger than the dot-to-lead tunnelling rates), and the tilt of the DD potential is tuned by the dc-voltages VL and VR, applied to the left and right side gates. Working near the turn-on of the first conductance plateau, the current through the QPC, IQPC, depends upon the local charge configuration and provides a sensitive meter for the absolute number of electrons (nL, nR) in the left and right dot, respectively13,14. First, we excite the DD as indicated in the top panel of Figure 1b, by adding to VR continuous-wave microwave excitation at fixed frequency ν = 11 GHz. When the photon energy of the microwaves matches the energy splitting between the ground state and a state with a different charge configuration, a new steady-state charge configuration results, which is visible as a change in the QPC current, ΔIQPC. The excitation is on–off modulated at 880 Hz and lockin detection of ΔIQPC reveals the microwave-induced change of the charge configuration (see Methods for further experimental details). The lower panel of Figure 1b shows ΔIQPC as a function of VL and VR near the (1,1) to (0,2) boundary of the charge stability diagram. Sharp red (blue) lines indicate microwave-induced tunnelling of an electron from the right to the left dot (left to right), labelled as Δn = + 1 (Δn = − 1), respectively (Fig. 1c). Sidebands can result from multi-photon absorption. At the boundaries with the (0,1) and (1,2) 2 0.57 ms 0.57 ms Ac-VR Ac-VL 0V y B (1, 1) (1, 2) ε z x –595 ΔIQPC (a. u.) 5 VL VR (0, 1) 0 (0, 2) –1185 –1180 Dc-bias VR (mV) 5 μs 200 ns 0.57 ms F >0 Δn = +1 –5 (1, 1) –600 F Ac-VR Ac-VL h ( 0, 2) –595 (0, 2) <0 Δn = –1 (1, 1) Dc-bias VL (mV) IQPC –600 h –1185 Dc-bias VL (mV) I n recent years, artificial molecules in mesoscopic systems have drawn much attention owing to a fundamental interest in their quantum properties and their potential for quantum information applications. Arguably, the most flexible and tunable artificial molecule consists of coupled semiconductor quantum dots that are defined in a two-dimensional electron gas using a set of patterned electrostatic depletion gates. Electron spins in such quantum dots exhibit coherence times up to 200 μs (ref. 1), about 104–106 times longer than the relevant quantum gate operations2–4, making them attractive quantum bit (qubit) systems.5 The molecular orbital structure of these artificial quantum objects can be probed spectroscopically by microwave modulation of the voltage applied to one of the gates that define the dots6. In this way, the delocalized nature of the electronic eigenstates of an artificial hydrogen-like molecule was observed7,8. More recently, electrical microwave excitation was used for spectroscopy of single spins9–11 and coherent single-spin control9,11, through electric-dipole spin resonance. Here we perform microwave spectroscopy7,8,12 on molecular spin states in an artificial hydrogen molecule formed by a double quantum dot (DD) which contains exactly two electrons. In contrast to all previous photon-assisted tunnelling (PAT) experiments, we observe not only the usual spin-conserving tunnel transitions, but also transitions between molecular states with different spin quantum numbers. We discuss several possible mechanisms and conclude from our analysis that these transitions become allowed predominantly through spin–orbit (SO) interaction. The possibility to excite spinflip tunnelling transitions lifts existing restrictions in our thinking about quantum control and detection of spins in quantum dots, and allows universal control of spin qubits without gate-voltage pulses. –1180 Dc-bias VR (mV) Figure 1 | Photon-assisted tunnelling in a 2-electron double quantum dot. (a) Scanning-electron micrograph top view of the double-dot gate structure with Co micromagnet (blue). The voltages applied to the left VL and right VR side gates (red) control the detuning ε of the double-dot potential. The double-dot charge state is read out by means of the current IQPC running through a nearby quantum point contact (white arrow). (b) Charge stability diagram around the 2-electron regime at B = 1.5 T. (nL,nR) indicate the absolute numbers of electrons in the left and right dot (...truncated)