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arXiv:1301.3788 · Physical Review B

Quantum photovoltaic effect in double quantum dots

Canran Xu, Maxim Vavilov

Published Jan 25, 2013• 29 citations
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Abstract

We analyze the photovoltaic current through a double quantum dot system coupled to a high-quality driven microwave resonator. The conversion of photons in the resonator to electronic excitations produces a current flow even at zero bias across the leads of the double quantum dot system. We demonstrate that due to the quantum nature of the electromagnetic field in the resonator, the photovoltaic current exhibits a double peak dependence on the frequency $\ensuremath{\omega}$ of an external microwave source. The distance between the peaks is determined by the strength of interaction between photons in the resonator and electrons in the double quantum dot. The double peak structure disappears as strengths of relaxation processes increases, recovering a simple classical condition for maximal current when the microwave frequency is equal to the resonator frequency.

DOI
10.1103/physrevb.87.035429

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We analyze the photovoltaic current through a double quantum dot system coupled to a high-quality driven microwave resonator. The conversion of photons in the resonator to electronic excitations produces a current flow even at zero bias across the leads of the double quantum dot system. We demonstrate that due to the quantum nature of the electromagnetic field in the resonator, the photovoltaic current exhibits a double peak dependence on the frequency \ensuremathω\ensuremath{\omega}\ensuremathω of an external microwave source. The distance between the peaks is determined by the strength of interaction between photons in the resonator and electrons in the double quantum dot. The double peak structure disappears as strengths of relaxation processes increases, recovering a simple classical condition for maximal current when the microwave frequency is equal to the resonator frequency.
Motivated by recent interest in implementing circuit quantum electrodynamics with semiconducting quantum dots, we consider a double quantum dot (DQD) capacitively coupled to a superconducting resonator that is driven by the microwave field of a superconducting transmission line. We analyze the DQD current response using input-output theory and show that the resonator-coupled DQD is a sensitive microwave single photon detector. Using currently available experimental parameters of DQD-resonator coupling and dissipation, including the effects of 1/f1/f1/f charge noise and phonon noise, we determine the parameter regime for which incident photons are completely absorbed and near-unit $\ensuremath{\gtrsim}98$% efficiency can be achieved. We show that this regime can be reached by using very high quality resonators with quality factor $Q\ensuremath{\simeq}{10}^{5}$.
The quantum dynamics of a double quantum dot two-level system, coupled to a leaking microwave resonator mode, is theoretically investigated. The double quantum dot is driven by applying a continuous field giving rise to time-dependent modulations of its energy separation between the ground levels of each dot, forming the qubit. Therefore, the cavity resonances occur when the difference between the resonator and the qubit frequencies equals the multiple of the modulation frequency, respectively. In the strong Coulomb interaction limit and the weak couplings of the combined system, i.e. the qubit and the single-mode cavity, to corresponding electronic, phononic or photonic reservoirs, we have demonstrated that the output cavity electromagnetic field is formed of a single-photon flux obeying the sub-Poissonian quantum photon statistics. This was proved via Fano's factor behaviour or by comparing the resonator's second- and third-order photon correlation functions, respectively. The phonon, the cavity mode dephasing or the environmental temperatures influence on the quantum properties of the photons are also discussed.
Self-sustained oscillators play a central role in the stabilization and synchronization of complex dynamical systems. A number of different physical systems are currently being investigated to clarify the importance of such active components in the quantum realm. Here we explore the properties of a driven dissipative electron-photon hybrid system based on superconducting microwave resonators coupled resonantly to a voltage-biased double quantum dot (DQD). First, we establish a Hopf bifurcation at a critical value of the electron-photon coupling, beyond which an effective negative friction sustains steady limit-cycle oscillations of individual resonators. Second, we show that two such limit-cycle resonators coupled via the same voltage-biased DQD synchronize for small enough frequency detuning. A nonlinear photon Keldysh action is derived by perturbation theory in the effective circuit fine-structure constant, and the limit-cycle dynamics is analyzed in terms of resulting saddle-point, and Fokker-Planck equations. In the Markovian limit of infinite bias voltage, these results are shown to agree well with the solution of a corresponding Lindblad master equation for the DQD resonator system.
Semiconductor double quantum dots (DQD) coupled to superconducting microwave resonators offer a promising platform for the detection of single microwave photons. In previous works, the photodetection was studied for a monochromatic source of microwave photons. Here, we theoretically analyze the photodetection of single microwave pulses. The photodetection in this case can be seen as a nonlinear filtering process of an incoming signal, the pulse, to an outgoing one, the photocurrent. This analogy to signal processing motivated the derivation of a Wigner-function formalism which provides a compelling visualization of the time and frequency properties of the photodetector for low intensities. We find a trade-off between detecting the time and the frequency of the incoming photons, in agreement with the time-energy uncertainty relation. As the intensity of the source increases, the photodetection is influenced by coherent Rabi oscillations of the DQD. Our findings give insight into the time-dependent properties of microwave photons interacting with electrons in a DQD-resonator hybrid system and provide guidance for experiments on single microwave pulse detection.
We have realized a hybrid solid-state quantum device in which a single-electron semiconductor double quantum dot is dipole coupled to a superconducting microwave frequency transmission line resonator. The dipolar interaction between the two entities manifests itself via dispersive and dissipative effects observed as frequency shifts and linewidth broadenings of the photonic mode respectively. A Jaynes-Cummings Hamiltonian master equation calculation is used to model the combined system response and allows for determining both the coherence properties of the double quantum dot and its interdot tunnel coupling with high accuracy. The value and uncertainty of the tunnel coupling extracted from the microwave read-out technique are compared to a standard quantum point contact charge detection analysis. The two techniques are found to be consistent with a superior precision for the microwave experiment when tunneling rates approach the resonator eigenfrequency. Decoherence properties of the double dot are further investigated as a function of the number of electrons inside the dots. They are found to be similar in the single-electron and many-electron regimes suggesting that the density of the confinement energy spectrum plays a minor role in the decoherence rate of the system under investigation.
In this study, a model of a double-quantum-dot system driven by two-mode microwave photons is presented. The quantum master equation is derived from the system’s Hamiltonians, and the expression for the steady-state current is obtained. Electronic tunneling properties are then analyzed. The results revealed that different two-mode quantum microwave photons have varying effects on the tunneling current within the double-quantum-dot system, with a steplike current trend emerging. The tunneling current showed pronounced negative differential conductance for both coherent and squeezed microwave photons. Furthermore, the tunneling current was significantly influenced by changing the squeezing coefficient and phase. The asymmetric evolution of the tunneling current under varying bias voltages also depends on the asymmetry in system parameters. These findings are crucial for manipulating the transport properties of double-quantum-dot systems in nanostructured devices.