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New Journal of Physics

The measurement of a single-mode thermal field with a microwave cavity parametric amplifier

C. Braggio, G. Carugno, F. Della Valle, Giuseppe Galeazzi, Augusto Lombardi, G. Ruoso, Dino Zanello

Published Jan 18, 2013• 8 citations
Publisher

Abstract

In this paper, we present the experimental study of a single-mode thermal field carried out using a microwave parametric amplifier tuned at 1.5 GHz and working at room temperature. The parametric amplifier is based on a variable capacitance diode placed inside a microwave resonant cavity. The measured distribution of the thermal photons inside the resonator follows the expected Bose–Einstein distribution probability.

DOI
10.1088/1367-2630/15/1/013044

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In this paper, we present the experimental study of a single-mode thermal field carried out using a microwave parametric amplifier tuned at 1.5 GHz and working at room temperature. The parametric amplifier is based on a variable capacitance diode placed inside a microwave resonant cavity. The measured distribution of the thermal photons inside the resonator follows the expected Bose–Einstein distribution probability.
Low-noise amplifiers are of great significance in the field of quantum technologies. We study a thermally driven parametric amplifier based on a superconductor-insulator-graphene-insulator-superconductor (SSS-III-GGG-III-SSS) junction coupled to a superconducting microwave cavity. The strong nonlinearity in the temperature dependence of our device leads to thermal self-modulation that produces impedance oscillations at frequencies around twice the angular cavity resonance frequency ${\ensuremath{\omega}}_{\mathrm{r}}$. In particular, reactance modulation of the effective capacitance yields a gain of 18.6 dB over a frequency span of 125 kHz with a minimum noise temperature of TN=1.4K{T}_{\mathrm{N}}=1.4\phantom{\rule{0.2em}{0ex}}\mathrm{K}TN​=1.4K. Our theoretical modeling gives insight into the exact mixing processes, confirmation of the electron-phonon coupling parameter and possible improvements of the studied system.
A fundamental result of quantum mechanics is that the fluctuations of a bosonic field are given by its temperature TTT. An electromagnetic mode with frequency ωωω in the microwave band has a significant thermal photon occupation at room temperature according to the Bose-Einstein distribution nˉ=kBT/ℏω\bar{n} = k_BT / \hbarωnˉ=kB​T/ℏω. The room temperature thermal state of a 3 GHz mode, for example, is characterized by a mean photon number nˉ∼2000\bar{n} \sim 2000nˉ∼2000 and variance Δn2≈nˉ2Δn^2 \approx \bar{n}^2Δn2≈nˉ2. This thermal variance sets the measurement noise floor in applications ranging from wireless communications to positioning, navigation, and timing to magnetic resonance imaging. We overcome this barrier in continuously cooling a ∼3{\sim} 3∼3 GHz cavity mode by coupling it to an ensemble of optically spin-polarized nitrogen-vacancy (NV) centers in a room-temperature diamond. The NV spins are pumped into a low entropy state via a green laser and act as a heat sink to the microwave mode through their collective interaction with microwave photons. Using a simple detection circuit we report a peak noise reduction of −2.3±0.1 dB-2.3 \pm 0.1 \, \textrm{dB}−2.3±0.1dB and minimum cavity mode temperature of 150±5K150 \pm 5 \textrm{K}150±5K. We present also a linearized model to identify the important features of the cooling, and demonstrate its validity through magnetically tuned, spectrally resolved measurements. The realization of efficient mode cooling at ambient temperature opens the door to applications in precision measurement and communication, with the potential to scale towards fundamental quantum limits.
Low-noise amplifiers are of great importance in the field of quantum technologies. We study a thermally driven parametric amplifier based on a superconductor-insulator-graphene-insulator-superconductor (SIGIS) junction coupled to a superconducting microwave cavity. The strong non-linearity in the temperature dependence of our device leads to thermal self-modulation that produces impedance oscillations at frequencies around twice the angular cavity resonance frequency ωrω_\mathrm{r}ωr​. In particular, reactance modulation of the effective capacitance yields a gain of 18.6 dB over a frequency span of 125 kHz with a minimum noise temperature of TN=1.4T_\mathrm{N} = 1.4TN​=1.4 K. Our theoretical modelling gives insight into the exact mixing processes, confirmation of the electron-phonon coupling parameter and possible improvements of the studied system.
In this Master thesis, I present a theoretical description and experimental measurements of a tunable microwave resonator operated as a parametric amplifier. Superconducting parametric amplifiers have attracted great interest in recent years as it has been demonstrated that they can operate with a noise performance at the standard quantum limit. \nParametric amplification is achieved in the devices by modulating the electrical length of the resonator at twice the resonance frequency. The device measured in this thesis consists of a quarter-wavelength microwave resonator fabricated in a thin-film aluminum coplanar waveguide geometry. With a termination to ground through a Superconducting Quantum Interference Device (SQUID), the boundary condition of the resonator becomes sensitive to an applied magnetic field. This enables the tuning of the resonance frequencies, using a DC magnetic field, over a wide frequency range of 670MHz. Similarly, an AC magnetic field then allows for the modulation of the resonator electrical length at microwave frequencies. \nWe characterized the device by first measuring the DC tuning curves of the 2nd and 3rd harmonics of the resonator, around 4 GHz and 6 GHz respectively. We then studied parametric amplification in the device when the electrical length was modulated at approximately twice the resonance frequency of one of the modes. We scanned the pump frequency and pump power over a wide range to study the region in parameters which gives parametric gain. We performed an in-depth parameter sweep over this region, identifying pump parameters that provided maximum gain and maximum system noise improvements compared the following HEMT amplifier. \nWe find that the use of the parametric amplifier can improve the system noise temperature by more than 10 dB compared to a start-of-the-art commercial HEMT amplifier. This implies a performance near the standard quantum limit.
Parametric amplifiers are known to squeeze the vacuum state of the electromagnetic field, thus the statistics of the photocounts at their output should be that of squeezed vacuum. However, several theoretical works predict a very different statistical distribution. We have measured the photocount statistics of a Josephson parametric amplifier and recover the expected squeezed vacuum statistics. We explain this discrepancy by showing theoretically how the photocount statistics is dictated by the detection process. Namely, most experiments will naturally measure a single mode of the electromagnetic field, while the aforementioned theoretical works implicitly describe massively multimode detection.