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arXiv:1903.11529 · Physical review. B./Physical review. B

Statistics of radiation due to nondegenerate Josephson parametric down-conversion

Lisa Arndt, Fabian Hassler

Published Jul 8, 2019• 12 citations
arXivHTMLPDF

Abstract

In a process called parametric down-conversion, a dc-biased Josephson junction coupled to two microwave resonators emits photon pairs when the Josephson frequency matches the sum of the two resonance frequencies. Recent experiments have shown that such a setup permits analyzing the correlation of the radiation. Motivated by these results, we study theoretically the full counting statistics of a nondegenerate parametric oscillator below the threshold of instability. Furthermore, we analyze the second-order coherences of the radiation and discuss thermal effects on the radiation statistics. We provide results for the driving strength at which the Cauchy-Schwarz inequality is most strongly violated. Additionally, we study the impact of asymmetry in the linewidth of the modes---a distinctive property of the nondegenerate resonance effect. In particular, we find that the radiation from the mode with the larger linewidth preferably takes the total detuning, while the other mode emits photons at its resonance frequency.

DOI
10.1103/physrevb.100.014505

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In a process called parametric down-conversion, a dc-biased Josephson junction coupled to two microwave resonators emits photon pairs when the Josephson frequency matches the sum of the two resonance frequencies. Recent experiments have shown that such a setup permits analyzing the correlation of the radiation. Motivated by these results, we study theoretically the full counting statistics of a nondegenerate parametric oscillator below the threshold of instability. Furthermore, we analyze the second-order coherences of the radiation and discuss thermal effects on the radiation statistics. We provide results for the driving strength at which the Cauchy-Schwarz inequality is most strongly violated. Additionally, we study the impact of asymmetry in the linewidth of the modes---a distinctive property of the nondegenerate resonance effect. In particular, we find that the radiation from the mode with the larger linewidth preferably takes the total detuning, while the other mode emits photons at its resonance frequency.
We study a voltage-biased Josephson junction coupled to two resonators of incommensurate frequencies. Using a density matrix approach to analyze the cavity fields and an input-output description to analyze the emitted photonic fluxes and their correlation functions, we have shown, both for infinite- and finite-bandwidth detectors, that the emitted radiation is nonclassical in the sense that the correlators violate Cauchy-Schwarz inequalities. We have also studied the time dependence of the photonic correlations and showed that their linewidth becomes narrower with the increase of the emission rate approaching from below the threshold limit.
Motivated by recent experiments, we study theoretically the full counting statistics of radiation emitted below the threshold of parametric resonance in a Josephson-junction circuit. In contrast to most optical systems, a significant part of emitted radiation can be collected and converted to an output signal. This permits studying the correlations of the radiation. To quantify the correlations, we derive a closed expression for full counting statistics in the limit of long measurement times. We demonstrate that the statistics can be interpreted in terms of uncorrelated bursts, each encompassing 2N2N2N photons; this accounts for the bunching of the photon pairs produced in the course of the parametric resonance. We present the details of the burst rates. In addition, we study the time correlations within the bursts and discuss experimental signatures of the statistics deriving the frequency-resolved cross-correlations.
We investigate electromagnetic radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. At frequencies below the well-known emission peak at the Josephson frequency (2eV/h), extra radiation is triggered by quantum fluctuations in the transmission line. For weak tunneling couplings and typical Ohmic transmission lines, the corresponding photon-flux spectrum is symmetric around half the Josephson frequency, indicating that the photons are predominately created in pairs. By establishing an input-output formalism for the microwave field in the transmission line, we give further evidence for this nonclassical photon pair production, demonstrating that it violates the classical Cauchy-Schwarz inequality for two-mode flux cross correlations. In connection to recent experiments, we also consider a stepped transmission line, where resonances increase the signal-to-noise ratio.
We study microwave radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. An input-output formalism for the radiation field is established, using a perturbation expansion in the junction's critical current. Using output field operators solved up to the second order, we estimate the spectral density and the second-order coherence of the emitted field. For typical transmission line impedances and at frequencies below the main emission peak at the Josephson frequency, radiation occurs predominantly due to two-photon emission. This emission is characterized by a high degree of photon bunching if detected symmetrically around half of the Josephson frequency. Strong phase fluctuations in the transmission line make related nonclassical phase-dependent amplitude correlations short lived, and there is no steady-state two-mode squeezing. However, the radiation is shown to violate the classical Cauchy-Schwarz inequality of intensity cross-correlations, demonstrating the nonclassicality of the photon pair production in this region.
We study microwave radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. An input-output formalism for the radiation field is established, using a perturbation expansion in the junction's critical current. Using output field operators solved up to the second order, we estimate the spectral density and the second-order coherence of the emitted field. For typical transmission line impedances and at frequencies below the main emission peak at the Josephson frequency, radiation occurs predominantly due to two-photon emission. This emission is characterized by a high degree of photon bunching if detected symmetrically around half of the Josephson frequency. Strong phase fluctuations in the transmission line make related nonclassical phase-dependent amplitude correlations short lived, and there is no steady-state two-mode squeezing. However, the radiation is shown to violate the classical Cauchy-Schwarz inequality of intensity cross-correlations, demonstrating the nonclassicality of the photon pair production in this region.
We analyze the quantum dynamics of two electromagnetic oscillators coupled in series to a voltage-biased Josephson junction. When the applied voltage leads to a Josephson frequency across the junction which matches the sum of the two mode frequencies, tunneling Cooper pairs excite photons in both modes simultaneously leading to far-from-equilibrium states. These states display highly nonclassical features including strong antibunching, violation of Cauchy-Schwartz inequalities, and number squeezing. We obtain approximate analytic results for both the regimes of low and high photon occupancies which are supported by a full numerical treatment. The impact of asymmetries between the two modes is explored, revealing a pronounced enhancement of number squeezing when the modes are damped at different rates.