Raman phonon emission in a driven double quantum dot

ARTICLE Received 15 Feb 2014 | Accepted 20 Mar 2014 | Published 23 Apr 2014 DOI: 10.1038/ncomms4716 Raman phonon emission in a driven double quantum dot J.I. Colless1,*, X.G. Croot1,*, T.M. Stace2, A.C. Doherty1, S.D. Barrett3, H. Lu4, A.C. Gossard4 & D.J. Reilly1 The compound semiconductor gallium–arsenide (GaAs) provides an ultra-clean platform for storing and manipulating quantum information, encoded in the charge or spin states of electrons confined in nanostructures. The absence of inversion symmetry in the zinc-blende crystal structure of GaAs however, results in a strong piezoelectric interaction between lattice acoustic phonons and qubit states with an electric dipole, a potential source of decoherence during charge-sensitive operations. Here we report phonon generation in a GaAs double quantum dot, configured as a single- or two-electron charge qubit, and driven by the application of microwaves via surface gates. In a process that is a microwave analogue of the Raman effect, phonon emission produces population inversion of the two-level system and leads to rapid decoherence of the qubit when the microwave energy exceeds the level splitting. Comparing data with a theoretical model suggests that phonon emission is a sensitive function of the device geometry. 1 ARC Centre of Excellence for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia. 2 ARC Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia. 3 Blackett Laboratory and Institute for Mathematical Sciences, Imperial College London, London SW7 2PG, UK. 4 Materials Department, University of California, Santa Barbara, California 93106, USA. * These authors contributed equally to the work. Correspondence and requests for materials should be addressed to D.R. (email: ). NATURE COMMUNICATIONS | 5:3716 | DOI: 10.1038/ncomms4716 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4716 D evices based on gallium–arsenide (GaAs) are advantageous for hosting qubits because the electron’s small effective mass in this material produces a large level splitting, the lack of valley degeneracy in the band structure simplifies operation, and the clean epitaxial interface used to confine electrons leads to inherently low charge noise1,2. A potential drawback of GaAs and other group III–V compounds3 is the presence of nuclear spins in the host lattice, which can rapidly dephase electron spin states4. Dynamical-decoupling techniques5 however, have recently addressed dephasing from nuclei, demonstrating6 that spin coherence can be preserved for times long enough that it is now important to address alternate decoherence mechanisms such as residual charge noise and processes that incoherently couple electrons to phonons7,8, either directly9, or via the spin orbit interaction10–12. In this respect, the piezoelectric nature of GaAs, while advantageous for shuttling electrons long distances13,14, also opens a channel for enhanced relaxation and dephasing, in particular, for qubit states with a charge dipole15–19. Such phonon generation mechanisms have recently been examined in the context of readout backaction19 and compared with transport measurements of InAs nanowires20,21 and graphene21. Here we investigate a phonon emission process, distinct from the usual phonon-mediated spontaneous relaxation (T1-type) that leads to the qubit decaying to the ground state. This alternate mechanism additionally limits charge coherence in GaAs and complicates microwave control, even in ideal structures at zero temperature. In a microwave version of the well-known optical technique of Raman spectroscopy, this mechanism provides a means of detecting the phonon spectral density created by the unique nanoscale device geometry. Our experimental results are in qualitative agreement with a theoretical model based on a nonMarkovian master equation and we suggest approaches to suppress the electron–phonon coupling, which could further improve coherence times and controllability of these qubit systems. Results Microwave spectroscopy. Our system is a charge qubit with one or two electrons in a double quantum dot, controlled by resonant microwaves22–24, which drive Rabi oscillations of the electron between the ground and excited states, as shown schematically in Fig. 1a. In the detuned regime where the microwave energy exceeds the qubit level splitting (see Fig. 1b), we suggest that this system undergoes driven phonon emission, a process which interrupts coherent oscillations and leads to population inversion, as predicted theoretically25,26. A micrograph of our double quantum dot device is shown in Fig. 1c, including a proximal rfquantum point contact27 (rf-QPC), which is used as a sensor to read out the charge state of the system (see Fig. 1d and Methods). Gate voltages VL and VR control the detuning e of energy levels between the two dots. For e 44 0 the ground and excited states of the qubit correspond to localizing the electron mostly in the a b E Phonon Phonon (0,1) Microwaves |e〉 h |g〉 (1,0) (1,0) (0,1) 0 c d 0  4 Vrf (arb. units) GQPC –820 (2,0) –840 (1,0) (2,1) (2,2) 0.6 pF VL (mV) Prf (0,0) –860 (1,2) (1,1) (0,1) (0,2) 200 nH –880 L ~10–31 GHz microwaves C P R –780 –760 –740 –720 –700 VR (mV) Figure 1 | Few-electron double quantum dot under microwave excitation. (a) Cartoon of the double dot potential showing a single-electron wavefunction coherently tunnelling between the ground |gS and excited state |eS under microwave excitation. In a microwave analogue of the Raman effect, photon-stimulated emission of phonons (ripples) is modulated by the mode spectrum set by the intra-dot spacing, which for our device is B280 nm. (b) Energy-level diagram for the single-electron charge qubit showing the stimulated-phonon emission process (light blue) that leads to asymmetric line shapes and population inversion. At a later time, spontaneous emission of a phonon (orange) leads to qubit relaxation. Grey shading depicts virtual states. (c) Micrograph of the double dot device showing surface gates and ohmic contacts to the electron gas (crossed squares). Scale bar, 300 nm. Microwaves are applied to the plunger (P) or centre (C) gate. The conductance GQPC of a proximal rf-QPC detects the average charge state of the dot and modulates the amount of reflected-rf power, Prf, from a resonant-tank circuit, enabling fast readout (see Methods for details). (d) Charge-stability diagram of the double dot, detected using the rf-QPC. Labels (n,m) denote the number of electrons in the left and right quantum dots, respectively. The demodulated signal Vrf is proportional to the QPC conductance and thus the double dot charge configuration. Gate voltages VL and VR are applied to gates (...truncated)