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arXiv:1704.01961 · Physical Review Letters

Threshold Dynamics of a Semiconductor Single Atom Maser

Y.-Y. Liu, J. Stehlik, Christopher Eichler, Xiao Mi, Thomas R. Hartke, Michael J. Gullans, Jacob M. Taylor, J. R. Petta

Published Aug 31, 2017• 36 citations
arXivHTMLPDF

Abstract

We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

DOI
10.1103/physrevlett.119.097702

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We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.
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 experimentally study the phase stabilization of a semiconductor double-quantum-dot (DQD) single-atom maser by injection locking. A voltage-biased DQD serves as an electrically tunable microwave frequency gain medium. The statistics of the maser output field demonstrate that the maser can be phase locked to an external cavity drive, with a resulting phase noise $\mathcal{L}=\ensuremath{-}99$ dBc/Hz at a frequency offset of 1.3 MHz. The injection locking range, and the phase of the maser output relative to the injection locking input tone are in good agreement with Adler's theory. Furthermore, the electrically tunable DQD energy level structure allows us to rapidly switch the gain medium on and off, resulting in an emission spectrum that resembles a frequency comb. The free running frequency comb linewidth is $\ensuremath{\approx}8$ kHz and can be improved to less than 1 Hz by operating the comb in the injection locked regime.
We predict a bistability in the photon emission from a solid-state single-atom laser comprising a microwave cavity coupled to a voltage-biased double quantum dot. To demonstrate that the single-atom laser is bistable, we evaluate the photon emission statistics and show that the distribution takes the shape of a tilted ellipse. The switching rates of the bistability can be extracted from the electrical current and the shot noise in the quantum dots. This provides a means to control the photon emission statistics by modulating the electronic transport in the quantum dots. Our prediction is robust against moderate electronic decoherence and dephasing and is important for current efforts to realize single-atom lasers with gate-defined quantum dots as the gain medium.
Reaching high cavity population with a coherent pump in the strong-coupling regime of a single-atom laser is impossible due to the photon blockade effect. In this work, we experimentally demonstrate that in a single-atom maser based on a transmon strongly coupled to two resonators it is possible to pump over a dozen of photons into the system. The first high-quality resonator plays a role of usual lasing cavity, and the second one presents a controlled dissipation channel, bolstering population inversion, and modifies the energy level structure to lift the blockade. As a confirmation of lasing action, we observe conventional laser features such as the narrowing of emission linewidth and external signal amplification. Additionally, we report unique single-atom features: self-quenching and several lasing thresholds.
We present the theory of a truly microscopic maser consisting of a single-mode high-Q resonator in which a monoenergetic beam of excited two-level atoms is injected at such a low flux that at most one atom at a time is present inside the cavity. Both a microscopic theory and a heuristic Fokker-Planck approach are presented. We show that the micromaser exhibits a number of novel features that are averaged out in usual masers and lasers. First, the field is in general sub-Poissonian, which reflects the quantization of both the field and its sources. Second, the onset of maser oscillations may be followed by a succession of abrupt transitions in the state of the field. Finally, as the atomic flux through the resonator is increased, the maser threshold acquires characteristics of a continuous phase transition, whereas the subsequent changes in the field distribution become analogous to first-order phase transitions.