Injection locking of a semiconductor double-quantum-dot micromaser

Y.-Y. Liu, J. Stehlik, M. J. Gullans, J. M. Taylor, and J. R. Petta

Phys. Rev. A 92, 053802 – Published 2 November 2015

Abstract

The semiconductor double-quantum-dot (DQD) micromaser generates photons through single-electron tunneling events. Charge noise couples to the DQD energy levels, resulting in a maser linewidth that is 100 times larger than the Schawlow-Townes prediction. We demonstrate linewidth narrowing by more than a factor of 10 using injection locking. The injection locking range is measured as a function of input power and is shown to be in excellent agreement with the Adler equation. The position and amplitude of distortion sidebands that appear outside of the injection locking range are quantitatively examined. Our results show that this unconventional maser, which is impacted by strong charge noise and electron-phonon coupling, is well described by standard laser models.

Received 17 August 2015

DOI:https://doi.org/10.1103/PhysRevA.92.053802

Authors & Affiliations

Y.-Y. Liu¹, J. Stehlik¹, M. J. Gullans^2,3, J. M. Taylor^2,3, and J. R. Petta¹

¹Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
²Joint Quantum Institute, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
³Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA

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Vol. 92, Iss. 5 — November 2015

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Images

Figure 1
Schematic of the DQD micromaser. Two DQDs are coupled to a high-quality factor microwave cavity with input (output) coupling rates $κ_{in}$ ( $κ_{out}$ ). A source-drain bias voltage $V_{SD}$ results in single-electron tunneling through the DQDs and leads to photon emission into the cavity mode.
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Figure 2
Power gain $G = C P_{out} / P_{in}$ plotted as a function of $f_{in}$ with the DQDs configured in Coulomb blockade with no current flow (off state) and with current flowing through the DQDs (on state). In the on state, the peak gain $G_{p} \sim 1000$ and the linewidth is dramatically narrowed, suggestive of a transition to a masing state. Inset: $I Q$ histogram of the output field measured in the on state and with no input tone applied to the cavity. The donut shape is indicative of above-threshold maser action [12, 21].
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Figure 3
(a) Power spectrum of the emitted radiation $S (f)$ plotted as a function of $P_{in}$ . The cavity input frequency $f_{in} = 7880.25$ MHz is close to the free-running maser emission frequency $f_{e} = 7880.25 \pm 0.03$ MHz. Note the significant fluctuations in $f_{e}$ for $P_{in} < - 120 dBm$ . The maser linewidth narrows with increasing $P_{in}$ due to injection locking. The upper panel shows $S (f)$ for $P_{in} = - 125$ dBm (blue) and $P_{in} = - 100$ dBm (black), indicated by the dashed lines in the main panel. (b) Phasor diagram of the maser output in the unlocked configuration. Here the cavity field is a combination of the free-running maser emission at frequency $f_{e}$ and the cavity input tone at $f_{in}$ . In this configuration the phase of the maser is fluctuating relative to the input tone. (c) Schematic illustration of the cavity field in the injection locked state. To within a relative phase $ϕ$ , the maser emission is locked to the input tone.
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Figure 4
$S (f)$ plotted as a function of $P_{in}$ with $f_{in} = 7880.6$ MHz far detuned from $f_{e}$ . (Note the change in the $x$ -axis scale relative to Fig. 3) The maser is injection locked when $P_{in} > - 102 dBm$ . Distortion sidebands are clearly visible in the emission spectrum. Upper panel: $S (f)$ for $P_{in} = - 115$ dBm (red) and $P_{in} = - 100$ dBm (black), indicated by the dashed lines in the main panel.
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Figure 5
The frequency range over which the maser is injection locked, $Δ f_{in}$ , increases with $P_{in}$ . The blue line is a fit to the power law $Δ f_{in} \propto \sqrt{P_{in}}$ prediction of the Adler equation. Insets: $S (f)$ measured as a function of $f_{in}$ with $P_{in} = - 110$ dBm (upper left) and $P_{in} = - 100$ dBm (lower right).
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Figure 6
(a) $S (f)$ measured as a function of $f_{in}$ with $P_{in} = - 105$ dBm. The black line overlaid on the data is the pulled frequency ${\bar{f}}_{e}$ predicted by Adler's injection locking theory. The white dashed lines are the predicted sideband locations. (b) $S (f)$ for $f_{in} = 7880.92$ MHz (upper panel) and $f_{in} = 7880.60$ MHz (lower panel), indicated by the dashed lines in (a). Solid lines are fits to $S (f)$ .
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