# Microwave Photon Detectors Based on Semiconducting Double Quantum Dots

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## Abstract

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## 1. Introduction

## 2. State of the Art

## 3. Detection of Sub-Millimeter Wave Photons by DQDs

## 4. DQD Broadband Microwave Photon Detectors

#### 4.1. DQD Noise Detectors

#### 4.2. Charge Sensing of DQDs

#### 4.3. Detection of Microwave Photons by Conductivity Measurements

## 5. Photon Detectors Based on DQDs Coupled to a Microwave Cavity

#### 5.1. Coupling of DQD to a Single Mode Resonator

#### 5.2. Photon Detection by DQD Coupled to a Microwave Resonator

#### 5.3. Experimental Realization of DQD-Resonator Microwave Photon Detectors

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

MW | Microwave |

QD | Quantum dot |

DQD | Double quantum dot |

QPC | Quantum point contact |

SET | Single electron transistor |

cQED | Circuit quantum electrodynamics |

dc | Direct current |

rf | Radio frequency |

NW | Nanowire |

CNT | Carbon nanotube |

Res | Resonator |

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**Figure 1.**Schematic diagram showing the frequency working range of different photon detectors based on quantum dots (red), superconducting circuits (cyan), and opto-electro-mechanical systems (green). Solid regions show the frequency range of experimentally tested detectors, whereas striped regions indicate possible developments and theoretical proposals.

**Figure 2.**Capacitively coupled systems made by two quantum dots (QDs)—or a QD and a quantum point contact (QPC)—are used to detect photon absorption events. In this scheme, the two systems are individually tuned by external gates. The left dot works as the absorber, the second device is tuned in a configuration where its conductance is strongly dependent on the electrostatic environment. The transition induced by the absorption of the photon results in a conductance change for the sensing (QPC) device.

**Figure 3.**(

**a**) Noise detection scheme based on quantum dots (QDs). The quantum point contact (QPC), which is capacitively coupled to the double quantum dot, acts both as a source of microwave photons and as a charge sensor that probes the configuration of the DQD. (

**b**) Scheme of the different paths that the DQD system can take after photon absorption. ${\mathsf{\Gamma}}_{rel}$ shows the relaxation path, where the electron returns to the ground state, emitting a phonon/photon in the process. ${\mathsf{\Gamma}}_{S}$ followed by ${\mathsf{\Gamma}}_{D}$ shows the charging with an additional electron through tunneling from the source contact. In the two-electron state, tunneling out of the device is permitted: this returns the system to the initial configuration. (

**c**) Typical time trace of the detector signal. The peaks correspond to entering and leaving of the additional electron in the DQD.

**Figure 4.**Schematics of two different reflectometry techniques. Panel (

**a**) shows the rf-SET setup. A read-out quantum dot (QDR) is capacitively coupled to the double quantum dot, with different couplings to each dot. The single-electron transistor (SET) is highly sensitive to the charge configuration of the DQD thanks to the sharpness of the tunneling resonances. Configuration changes due to DQD tunneling events result in a strong change in the SET conductance. This can be observed by monitoring the signal reflected by the resonating circuit. Panel (

**b**) shows the gate reflectometry configuration. In this case, the resonating circuit is directly connected to one of the gates controlling the DQD. Tunnel coupling between the QDs determine a change of the quantum capacitance that can be resolved as a frequency shift of the resonating circuit. This approach results in a simplified and more compact device, but is less performant as a readout technique. In both approaches a bias tee can be used to dc bias the rf lines, so that they can provide a source-drain bias or configure the QD (substituting ${V}_{gQD1}$ in this case). Panels (

**c**,

**d**) show the expected change in the reflected signal amplitude and phase in different configurations (dashed and non-dashed lines) for these readout schemes.

**Figure 5.**Schematics of the hybrid DQD-resonator circuit. A transmission line with incident photon flux $\dot{N}{\omega}_{in}$ is capacitively coupled to a high-quality factor coplanar waveguide resonator that behaves like an ideal quantum harmonic oscillator, with low average photon occupation. The resonator is also capacitively coupled (${g}_{c}$) to the DQD. The level spacing of the DQD can be tuned to match the resonator frequency. When a photon is absorbed, the excited electron can tunnel to the drain contact and be detected as a current flow.

**Table 1.**Summary of the typical parameters reported for different DQD devices coupled to superconducting planar resonators.

DQD | Res. | $\frac{{\mathit{\omega}}_{0}}{2\mathit{\pi}}$ (GHz) | ${\mathit{Q}}_{\mathit{L}}$ | $\frac{2{\mathit{t}}_{\mathit{c}}}{\mathit{h}}$ (GHz) | $\frac{{\mathit{g}}_{\mathit{c}}}{2\mathit{\pi}}$ (MHz) | $\frac{{\mathit{\gamma}}_{\mathit{c}}}{2\mathit{\pi}}$ (MHz) | $\frac{{\mathit{g}}_{\mathit{s}}}{2\mathit{\pi}}$ (MHz) | $\frac{{\mathit{\gamma}}_{\mathit{s}}}{2\mathit{\pi}}$ (MHz) | Ref. |
---|---|---|---|---|---|---|---|---|---|

GaAs | Al | 6.755 | 2630 | 9 | 50 | 900 | - | - | [66] |

InAs NW | Nb | 6.2 | 2000 | 1.8–7 | 30 | 5100 | - | - | [65] |

CNT | Al | 6.72 | 3500 | 5.5 | 3.3 | 550 | - | - | [93] |

Graphene | Al | 6.23896 | 3100 | 6.4 | 6 | 400 | - | - | [94] |

CNT | Nb | 6.75 | 9650 | - | - | - | 1.3 | 2.5 | [91] |

GaAs | Al | 6.852 | 2058 | 7.4 | 11 | 250 | - | - | [95] |

InSb NW | Nb | 6.0749 | 8000 | 7 | 14 | 1000–4000 | - | - | [96] |

Si | Nb | 7.684 | 7460 | 7.68 | 6.7 | 2.6 | - | - | [92] |

GaAs | SQUID | 5.03 | 401 | 4.13 | 119 | 20 | - | - | [85] |

Si | Nb | 5.846 | 4700 | 4.9, 7.4 | 40 | 35 | 5.3 | 2.4 | [68] |

Si | NbTiN | 6.051 | 1120 | 12.6 | 200 | 52 | 13 | 2.5 | [86] |

GaAs | SQUID | 5.07 | 169 | 3.3 | 57 | 3.3 | - | - | [67] |

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**MDPI and ACS Style**

Ghirri, A.; Cornia, S.; Affronte, M.
Microwave Photon Detectors Based on Semiconducting Double Quantum Dots. *Sensors* **2020**, *20*, 4010.
https://doi.org/10.3390/s20144010

**AMA Style**

Ghirri A, Cornia S, Affronte M.
Microwave Photon Detectors Based on Semiconducting Double Quantum Dots. *Sensors*. 2020; 20(14):4010.
https://doi.org/10.3390/s20144010

**Chicago/Turabian Style**

Ghirri, Alberto, Samuele Cornia, and Marco Affronte.
2020. "Microwave Photon Detectors Based on Semiconducting Double Quantum Dots" *Sensors* 20, no. 14: 4010.
https://doi.org/10.3390/s20144010