Charge and Spin State Readout of a Double Quantum Dot Coupled to a Resonator

Abstract

State readout is a key requirement for a quantum computer. For semiconductor-based qubit devices it is usually accomplished using a separate mesoscopic electrometer. Here we demonstrate a simple detection scheme in which a radio-frequency resonant circuit coupled to a semiconductor double quantum dot is used to probe its charge and spin states. These results demonstrate a new non-invasive technique for measuring charge and spin states in quantum dot systems without requiring a separate mesoscopic detector. PACS numbers:State readout is a key requirement for a quantum information processor. For semiconductor-based qubit devices this is usually accomplished using a separate mesoscopic electrometer such as a quantum point contact (QPC) [1]. Non-invasive detection using a QPC has been critical to recent advances in coherent control of few-electron double quantum dots [2], allowing their charge configurations to be mapped in regimes where transport through the double dot itself is not measurable [3]. Furthermore, through spin-to-charge conversion techniques, spin state measurements of single and double dots have been demonstrated using QPCs [4,5].Resonant microwave circuits have played an important role in performing sensitive measurements of mesoscopic devices. In the case of superconducting charge qubits, earlier schemes used a proximal single electron transistor (SET) charge detector to perform state readout [6,7]. This SET was coupled to an impedance matching rf resonant circuit to form an rf-SET which had dramatically improved sensitivity and bandwidth [8]. Similarly, an rf-QPC has also been realised for broadband charge detection of semiconductor quantum dot devices [9,10].More recently, state readout of a superconducting charge qubit has been accomplished by directly coupling it to a microwave resonant circuit [11][12][13]. Working in the dispersive regime where the resonator and qubit bandgap energies are detuned, the qubit has a state-dependent 'quantum capacitance' which causes a shift in the resonator frequency [14]. This frequency shift can then be detected using standard homodyne detection techniques.In this Letter, we demonstrate dispersive detection using a resonant circuit coupled directly to an AlGaAs/GaAs few-electron double quantum dot device. This allows us to probe the charge state of a single electron confined to a double quantum dot. We also perform a spin-state measurement for a pair of electrons using the resonant circuit. These results demonstrate a new and non-invasive technique for measuring charge and spin states in semiconductor quantum dot systems without the need for a separate mesoscopic detector.In using the resonator to probe the state of a double quantum dot we consider the double dot as a charge qubit where a single electron occupies either the ground state of one dot or the other [16]. The Hamiltonian for this two level system is given by H = 1 2 σ z + tσ x , where is the detuning between the two dot chemical potential energies and t is the interdot tunnel coupling energy which m...

Sensitive Radio-Frequency Measurements of a Quantum Dot by Tuning to Perfect Impedance Matching

“…Estimating the difference in quantum capacitance [6] between qubit states as approximately 10 fF, our measured sensitivity S C ¼ 1.6 aF= ffiffiffiffiffiffi Hz p would, at first sight, indicate single-shot readout with the unit SNR in integration time T meas ∼ 13 ns. Crucially, this sensitivity is achieved with a maximum bias V 0 ≈ 170 μV rms , which is smaller than the typical singlet-triplet splitting in a qubit device [32] and, therefore, does not induce charge relaxation in the triplet manifold.…”

“…If the state can be mapped to an electrical impedance, this goal can be achieved using radio-frequency reflectometry of an electrical resonator incorporating the quantum device [1]. This technique permits rapid readout of charge sensors [2,3], spin qubits [4], and nanomechanical resonators [5], as well as complex impedance measurements of quantum-dot circuits [6][7][8][9][10][11]. For optimal sensitivity, which can approach the quantum limit [12], impedance matching between the device and the external circuitry is essential to maximize power transfer between them [13,14].…”

Polaron dynamics and decoherence in an interacting two-spin system coupled to an optical-phonon environment

“…One can readout the charge state non-invasively by various methods such as using a radio frequency resonant circuit coupled to a DQD as demonstrated in Ref. 30; employing quantum point contact charge detector as was done in Ref. 31; transferring quantum information to a quantized cavity field as explained in Ref.…”

Circuit quantum electrodynamics with a spin qubit

“…We observe two resonance conditions corresponding to single spin rotations in the left and right quantum dot, with g-factors of 8.2 and 10.6 [13]. Around = 0, the DQD has a spin state dependent dipole moment that allows spin state readout via the superconducting cavity [30]. We combine quantum control of the spins using EDSR and cavity detection of single spin dynamics using the pulse sequence shown in Figs. 4 (a),(b).…”