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arXiv:1503.03640 · Physical Review B

Photon cross-correlations emitted by a Josephson junction in two microwave cavities

Mircea Trif, Pascal Simon

Published Jul 7, 2015• 39 citations
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Abstract

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.

DOI
10.1103/physrevb.92.014503

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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.
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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 creation and emission of pairs of highly nonclassical microwave photons in a setup where a voltage‐biased Josephson junction is connected in series to two electromagnetic oscillators. Tuning the external voltage such that the Josephson frequency equals the sum of the two mode frequencies, each tunneling Cooper pair creates one additional photon in both of the two oscillators. The time‐resolved statistics of photon emission events from the two oscillators is investigated by means of single‐ and cross‐oscillator variants of the second‐order correlation function and the waiting‐time distribution . They provide insight into the strongly correlated quantum dynamics of the two oscillator subsystems and reveal a rich variety of quantum features of light including strong antibunching and the presence of negative values in the Wigner function.
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.