Microwave spectroscopy on a double quantum dot with an on-chip Josephson oscillator

We present measurements on microwave spectroscopy on a double quantum dot with an on-chip microwave source. The quantum dots are realized in the two-dimensional electron gas of an AlGaAs/GaAs heterostructure and are weakly coupled in series by a tunnelling barrier forming an `ionic' molecular state. We employ a Josephson oscillator formed by a long Nb/Al-AlOx /Nb junction as a microwave source. We find photon-assisted tunnelling sidebands induced by the Josephson oscillator, and compare the results with those obtained using an externally operated microwave source.

Here we present an on-chip microwave oscillator integrated in a single low-temperature set-up with a coupled quantum dot structure. Integrating on-chip microwave sources has the advantage of easily combining advanced spectrometers with mesoscopic devices. Furthermore, the influence of black-body radiation is minimized, since all the electrical connections to the outside world are essentially dc lines and so can be heavily filtered [12,13]. As a microwave source we employ a long Josephson tunnel junction (JTJ) with well-defined emission characteristics. These junctions commonly radiate in the range from a few GHz up to 600 GHz [14]. Their typical radiation linewidth can be as small as 10 −6 relative to the emission frequency [15]. Recently, this has triggered rapid progress in the use of these devices in integrated submillimetre wave superconducting receivers [16]. The quantum dots are defined in a two-dimensional electron gas (2DEG) by electron-beam-written lateral Schottky gates. The versatility of these devices lies in their ability to tune the tunnel contacts over a wide range. This permits the straightforward fabrication of tunnel-coupled quantum dots ('covalent artificial molecules') or decoupled dots ('ionic artificial molecules') [11]. In contrast to the excitation spectra of real atoms or molecules, the spectra of single or even coupled quantum dots reveal a striking difference in their discrete level structures. It has been shown in a whole variety of experiments that Kohn's theorem [17] prevails for quantum dots [18,19]. The theorem states that only the centre-of-mass (CM) degree of freedom couples to a spatially homogeneous electromagnetic field. In previous studies of excitations in quantum dots by coupling radiation via antennas, only CM excitations were found [11,19,20]. Here we 'move' the radiation source close to the quantum dots in an attempt to verify whether the inhomogeneity of the near-field radiation affects the electronic excitations. This is in close analogy to the probing of single molecules by scanning near-field microscopy [21].
Our set-up is shown in figure 1: the Si chip with the Nb/Al-AlO x /Nb Josephson junction is glued on top of the quantum dot AlGaAs/GaAs chip with photoresist. The inset of figure 1 shows the quantum dot gate structure used in this work: the application of an appropriate negative gate voltage defines two quantum dots in the 2DEG of the AlGaAs/GaAs heterostructure with an electron density of 1. varying the voltages V gA and V gB applied to the plunger gates shown in the inset of figure 1, the electron configuration of the double dot can be changed. Plotting the current through the system as a function of V gA and V gB produces the charging diagram in figure 2. Subsequently, we obtain charging energies of the individual dots of E A C = e 2 /2C Σ = 220 µeV and E B C = 205 µeV. Thus the 'electronic' radii are r A = 400 nm and r B = 430 nm. For the absolute number of electrons in each dot we find that n A = 850 and n B = 980. Hence, the dots are rather classical systems in which we do not expect the resolution of discrete single particle energies because of the confinement potential. In the current measurements, the interdot coupling is chosen to be weak (C A−B = 2 aF), i.e. we see a hexagonal array of points for the charging diagram [22] which corresponds to the 'ionic' coupling limit. All results were obtained in the linear regime (drain/source bias V ds = 19 µV).
In an earlier set-up, we focussed on defining a weak link with a modified atomic force microscope (AFM) tip directly in the Al contacts by nano-ploughing the Al sheet and hence forming the Schottky gates [23,24]. This is of great advantage for probing the microwave response of quantum dots in the absolute near-field limit, since the photon source is located only 100 nm from the tunnel barriers. However, these weak links radiate with a very large radiation linewidth. Hence, we choose here to employ a well characterized JTJ oscillator placed on top of the quantum dots. The JTJ we use in these measurements is an overlap Nb/Al-AlO x /Nb long Josephson junction with dimensions 20 × 400 µm 2 (width × length). In the measurements presented, tuning of the frequency was possible by varying the JTJ critical current with the applied magnetic field and selecting the appropriate bias point at a resonant state. When operated in the flux-flow regime, the JTJ radiation frequencies f = 2 eV/h are on the order of 100-500 GHz. This is above the Coulomb energy for this particular quantum dot. We employ a finite magnetic field to operate the junction at a Fiske step of the current-voltage characteristic, a self-resonant state. The fundamental cavity resonance frequency of the junction is f =c/(2 ), wherec is the Swihart velocity and is the junction length.
In order to characterize the microwave response of the coupled quantum dots, we first studied them with a conventional microwave source. The radiation was then transduced by an antenna on the gate structure of the quantum dots. The charging diagram of the double dot with microwave excitation is shown as a greyscale plot in figure 3. The radiation of the far-field source is fixed at 10 GHz. The sidebands are found on only one side, depending on the tuning of the barrier transmission coefficients. In measurements on a similar two-dot device, we obtained symmetrically as well as asymmetrically induced sidebands in the charging diagram [25]. However, since we are interested in the alteration of the microwave coupling by the JTJ, we deliberately chose to maintain the tuning with only one sideband, which is clearly visible in the inset of figure 3. This ensures finally that we can directly compare the measurements with the conventional microwave source and the on-chip source. The inset shows one of the typical traces from the greyscale plot with the sidebands induced by the frequency-dependent absorption.

2.6
The induced sidebands are marked by arrows-the peak height modulation is due to the specific trace taken out of the charging diagram (marked by the dashed line). A cut along one of the two periodic resonance lines would yield peaks of similar amplitude. The net pumping of electrons leads to a reduction of the absolute current value down to only some 100 fA. Also the noise floor is slightly enhanced by coupling the radiation.
When the on-chip Josephson oscillator is operated as a source with a typical emission frequency of f ∼ = 10 GHz, we observe charging diagrams like the one shown in figure 4. The JTJ emission frequency was determined by taking the I-V characteristics. Biasing the JTJ with a current of I = 1 µA, we are able to detect sidebands which resemble those induced by the far-field source (compare the insets of figures 3 and 4). The power emitted is then on the order of P dc ∼ 20 µV × 1 µA ≈ 20 pW, where 20 µV is the voltage drop over the JTJ at 10 GHz. Moreover, the peak broadening is almost identical to that determined before. As can be seen, the resonances of the current (marked by lines in the plot) and the induced sidebands (marked by arrows) possess a long term stability. Since the observed resonances for the on-chip source as well as for the far-field source are almost identical, we conclude that the photon absorption process only depends on the shape of the local electrostatic potential. Varying the frequency of the radiation for such a tunnel-coupled dot system results in the well-known linear relation between the position of the sideband relative to the ground state and the frequency for the case of weak coupling [11,25].
In summary, we find photon-assisted tunnelling in a weakly coupled double quantum dot, induced by an on-chip source. This source consists of a long Josephson junction placed on top of the chip carrying the double dot. We find nearly identical radiation coupling with the on-chip source and the far-field source. We conclude from this comparison that the photon absorption process depends only on the local electrostatic environment of the quantum dots. Furthermore, this result confirms that Kohn's theorem is valid in the near-field regime, as long as it provides a spatially homogeneous radiation field across the excited electronic system. This we expect to change when a Josephson junction is embedded in the dot's gate structure.