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Physical Review A

Experimental study of microwave photon statistics under parametric amplification from a single-mode thermal state in a cavity

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

Published Nov 6, 2013• 5 citations
Publisher

Abstract

In this paper we present theoretical and experimental studies of the modifications of the thermal spectrum inside a microwave resonator due to a parametric amplification process. Both the degenerate and nondegenerate amplifiers are discussed. Theoretical calculations are compared with measurements performed with a microwave cavity parametric amplifier.

DOI
10.1103/physreva.88.053806

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In this paper we present theoretical and experimental studies of the modifications of the thermal spectrum inside a microwave resonator due to a parametric amplification process. Both the degenerate and nondegenerate amplifiers are discussed. Theoretical calculations are compared with measurements performed with a microwave cavity parametric amplifier.
We present the results of an experimental effort to generate squeezed microwave radiation using the phase-sensitive gain of a Josephson parametric amplifier. To facilitate the interpretation of the experimental results, we first present a discussion of the theory of microwave squeezing via Josephson parametric amplifiers. This is followed by a detailed description of the device fabricated for our experiment. Experimental results are then presented for the device used in both the doubly degenerate or four-photon mode and for the degenerate or three-photon mode. We have observed parametric deamplification of signals by more than 8 dB. We have demonstrated squeezing of 4.2-K thermal noise. When operated at 0.1 K, the amplifier exhibits an excess noise of 0.28 K when referred to the input. This is smaller than the vacuum fluctuation noise level \ensuremath{\Elzxh}\ensuremath{\omega}/2k=0.47 K. The amplifier is thus quieter than a linear phase-insensitive amplifier in principle can be.
In this paper we investigate the absorptive and dispersive properties in the phase-sensitive optical parametric amplification inside a cavity. First, we study the single-resonant optical parametric amplifier theoretically and experimentally. In this case, the mode splitting in the transmission spectra and the M shape in the reflection spectra are observed. However, the shape of the phase shift of the reflected field is unchanged. Then, the double-resonant optical parametric amplifier is studied theoretically, in which electromagnetically induced transparency-like effect may be emulated when the cavity linewidth for the harmonic wave is narrower than for the subharmonic field. The narrow transparency window appears in the absorption spectrum and is accompanied by a very steep variation of the dispersive profile.
We introduce an implementation of a non-degenerate parametric amplifier in which the signal and idler modes, respectively, a microwave mode and an ensemble of spins (e.g., nitrogen-vacancy centers in diamond), are operated in their linear regime. This paramp, which amplifies signals in both parts at room and cryogenic temperatures, can be used to generate both the two-mode and single-mode squeezing of either system. It requires merely modulating the frequency of the spin ensemble at the sum of the cavity and spin frequencies (providing the classical pump) with the two systems sufficiently detuned. This effect is remarkable given that modulating a spin ensemble by itself produces neither amplification nor squeezing, unlike modulating an oscillator, and that an off-resonant perturbative analysis would suggest that modulating the spin ensemble merely parametrically drives the cavity mode. With typical cavity parameters including a cavity quality factor~Q=104Q=10^4Q=104, and a 1 GHz modulation amplitude, the microwave signal can be amplified by approximately $18~\mbox{dB}$ in $1.7~\mbox{$μ$s}$, with a resonant bandwidth of about $0.5~\mbox{MHz}$. At $10~\mbox{mK}$ with the same modulation amplitude and a cavity and spin Q=5×104Q=5\times 10^4Q=5×104 it generates approximately $5~\mbox{dB}$ of squeezing. We also examine the experimental requirements for implementation.
The theory of a parametric amplifier in a cavity is given for both the degenerate and the nondegenerate modes of operation. Previous work on the degenerate case is extended to include the effects of a coherent input and to derive the degrees of coherence and photodetection statistics of the output. Analogous calculations are performed for the nondegenerate parametric amplifier, and particular attention is given to the effects of correlations between the light beams formed from the two frequency components. These are contrasted with the analogous effects for the parametric media in free space often used in experimental studies.
Abstract We introduce an implementation of a non-degenerate parametric amplifier in which the signal and idler modes, respectively, a microwave mode and an ensemble of spins (e.g., nitrogen-vacancy centers in diamond), are operated in their linear regime. This paramp, which amplifies signals in both parts at room and cryogenic temperatures, can be used to generate both the two-mode and single-mode squeezing of either system. It requires merely modulating the frequency of the spin ensemble at the sum of the cavity and spin frequencies (providing the classical pump) with the two systems sufficiently detuned. This effect is remarkable given that modulating a spin ensemble by itself produces neither amplification nor squeezing, unlike modulating an oscillator, and that an off-resonant perturbative analysis would suggest that modulating the spin ensemble merely parametrically drives the cavity mode. With typical cavity parameters including a cavity quality factor Q = 10<4/sup>, and a 1 GHz modulation amplitude, the microwave signal can be amplified by approximately 18 dB in 1.7 μs, with a resonant bandwidth of about 0.5 MHz. At 10 mK with the same modulation amplitude and a cavity and spin Q = 5×10<4sup> it generates approximately 5 dB of squeezing. We also examine the experimental requirements for implementation.