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arXiv:1606.01922 · Physical review. B./Physical review. B

Giant photon gain in large-scale quantum dot-circuit QED systems

Bijay Kumar Agarwalla, Manas Kulkarni, Shaul Mukamel, Dvira Segal

Published Sep 30, 2016• 20 citations

Abstract

Motivated by recent experiments on the generation of coherent light in engineered hybrid quantum systems, we investigate gain in a microwave photonic cavity coupled to quantum dot structures and develop concrete directions for achieving a giant amplification in photon transmission. We propose two architectures for scaling up the electronic gain medium: (i) $N$-double quantum dot systems and (ii) $M$-quantum dots arranged in series akin to a quantum cascade laser setup. In both setups, the fermionic reservoirs are voltage biased, and the quantum dots are coupled to a single-mode cavity. Optical amplification is explained based on a sum rule for the transmission function, and it is determined by an intricate competition between two different processes: charge-density response in the gain medium and cavity losses to input and output ports. The same design principle is also responsible for the corresponding giant amplification in other photonic observables, mean photon number, and emission spectrum, thereby realizing a quantum device that behaves as a giant microwave amplifier.

DOI: 10.1103/physrevb.94.121305

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Motivated by recent experiments on the generation of coherent light in engineered hybrid quantum systems, we investigate gain in a microwave photonic cavity coupled to quantum dot structures and develop concrete directions for achieving a giant amplification in photon transmission. We propose two architectures for scaling up the electronic gain medium: (i)

N

-double quantum dot systems and (ii)

M

-quantum dots arranged in series akin to a quantum cascade laser setup. In both setups, the fermionic reservoirs are voltage biased, and the quantum dots are coupled to a single-mode cavity. Optical amplification is explained based on a sum rule for the transmission function, and it is determined by an intricate competition between two different processes: charge-density response in the gain medium and cavity losses to input and output ports. The same design principle is also responsible for the corresponding giant amplification in other photonic observables, mean photon number, and emission spectrum, thereby realizing a quantum device that behaves as a giant microwave amplifier.

Coherent photon source is an important element that has been widely used in spectroscopy, imaging, detection, and teleportation in quantum optics. However, it is still a challenge to realize micro-scale coherent emitters in semiconductor systems. We report the observation of gain in a cavity-coupled GaAs double quantum dot system with a voltage bias across the device. By characterizing and analyzing the cavity responses to different quantum dot behaviors, we distinguish the microwave photon emission from the signal gain. This study provides a possibility to realize micro-scale amplifiers or coherent microwave photon sources in circuit quantum electrodynamics (cQED) hybrid systems.

A semiconductor single-atom micromaser consists of a microwave cavity coupled to a gain medium, a double quantum dot driven out of equilibrium by a bias voltage. The masing threshold of this system was recently probed by measuring photon statistics in the cavity [Y-Y. Liu et al., Phys. Rev. Lett. 119, 097702 (2017)]. In this paper, we develop an in-depth, rigorous understanding of this experiment and related works. First, we use a semiclassical theory and study transmission spectroscopy. This approach allows us to derive the masing threshold condition for arbitrary temperature and voltage bias, and expose microscopic principles required for realizing photon gain and thereby a photon amplifier. Next, by employing the quantum master equation approach we extend the Scully-Lamb quantum theory of a laser to the present setup, and investigate the statistics of emitted photons below and above the masing threshold as a function of experimentally tunable parameters. Although our focus is primarily on hybrid quantum dot circuit - quantum electrodynamics systems, our approach is adaptable to other light-matter systems where the gain medium consists of a mesoscopic structure.

We present our recent experiments where we demonstrate a hybrid architecture consisting of a quantum dot circuit coupled to a single mode of the electromagnetic ¯eld. We use single wall carbon nanotube based circuits inserted in superconducting microwave cavities. By probing the nanotube dot using a dispersive readout in the Coulomb blockade and the Kondo regime, we determine an electron-photon coupling strength which should enable circuit QED experiments with more complex quantum dot circuits. We extend our architecture to two quantum dot circuits in a microwave cavity. These circuits are separated by 200 times their own size, but share the same anti-node of the cavity ¯eld. We demonstrate their interaction mediated by the cavity photons.

We demonstrate a hybrid device architecture where the charge states in a double quantum dot (DQD) formed in a Si/SiGe heterostructure are read out using an on-chip superconducting microwave cavity. A quality factor Q = 5400 is achieved by selectively etching away regions of the quantum well and by reducing photon losses through low-pass filtering of the gate bias lines. Homodyne measurements of the cavity transmission reveal DQD charge stability diagrams and a charge-cavity coupling rate gc/2π= 23 MHz. These measurements indicate that electrons trapped in a Si DQD can be effectively coupled to microwave photons, potentially enabling coherent electron-photon interactions in silicon.

We investigate photon-mediated transport processes in a hybrid circuit-QED structure consisting of two double quantum dots coupled to a common microwave cavity. Under suitable resonance conditions, electron transport in one double quantum dot is facilitated by the transport in the other dot via photon-mediated processes through the cavity. We calculate the average current in the quantum dots, the mean cavity photon occupation, and the current cross-correlations with both a full numerical simulation and a recursive perturbation scheme that allows us to include the influence of the cavity order-by-order in the couplings between the cavity and the quantum dot systems. We can then clearly identify the photon-mediated transport processes.

We investigate photon-mediated transport processes in a hybrid circuit-QED structure consisting of two double quantum dots coupled to a common microwave cavity. Under suitable resonance conditions, electron transport in one double quantum dot is facilitated by the transport in the other dot via photon-mediated processes through the cavity. We calculate the average current in the quantum dots, the mean cavity photon occupation, and the current cross-correlations with both a full numerical simulation and a recursive perturbation scheme that allows us to include the influence of the cavity order-by-order in the couplings between the cavity and the quantum dot systems. We can then clearly identify the photon-mediated transport processes.