Abstract
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.
Highlights
In a resistive environment, charge tunneling across a voltage-biased Josephson junction (JJ) triggers simultaneous microwave emission [1, 2], that carries away all or some of the gained electrostatic energy
We study microwave radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line
We investigate microwave radiation produced in a dc-voltage-biased superconducting transmission line that is terminated by a small JJ
Summary
Charge tunneling across a voltage-biased Josephson junction (JJ) triggers simultaneous microwave emission [1, 2], that carries away all or some of the gained electrostatic energy. We establish an input–output formalism for the field operators in the transmission line In this formalism, the electric current across the JJ acts as a nonlinear and time-dependent boundary condition for the microwave field [11, 12]. The photon flux has been studied recently experimentally in this regime, [6] and it was shown that the radiation at voltages below the Josephson frequency, for typical transmission-line impedances, is due to simultaneous two-photon emission. We derive an equivalent inequality but expressed in terms of P(E)-functions This is used to show that the emitted photons below the Josephson frequency violate the inequality, demonstrating the nonclassicality of the photon pair production in this region.
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