Abstract
We show experimentally that a dc-biased Josephson junction in series with two microwave resonators emits entangled beams of microwaves leaking out of the resonators. In the absence of a stationary phase reference for characterizing the entanglement of the outgoing beams, we measure second-order coherence functions for proving entanglement up to an emission rate of 2.5 billion photon pairs per second. The experimental results are found in quantitative agreement with theory, proving that the low frequency noise of the dc bias is the main limitation for the coherence time of the entangled beams. This agreement allows us to evaluate the entropy of entanglement of the resonators, and to identify the improvements that could bring this device closer to a useful bright source of entangled microwaves for quantum-technological applications.
Highlights
The link between electrical transport and emission of radiation has been understood since the invention of electrical lamps, its complete description in the context of quantum conductors requires a comprehensive treatment of the conductor itself, of the charge reservoirs connected to it, and of the electromagnetic modes of the environment that sustain radiation
The two emitted beams are available at the capacitive outputs A and B of the bias tees. They are routed through filters and isolators to a −3 dB hybrid coupler that sends both of them to two nominally identical amplification chains 1 and 2, each equipped with a high electron mobility transistor (HEMT) amplifier
The nonlinearity of Hamiltonian (3) is of a different nature and is always easy to push to higher photon numbers, allowing for a higher entanglement brightness: in our experiment, the Gaussian character of the emitted light was ensured up to only 1–1.5 photons in the resonators, but lowering by a factor 10 the impedance of the two-modes, while increasing the Josephson energy EJ by the same factor, one could make our entangled microwave source 10 times brighter
Summary
The link between electrical transport and emission of radiation has been understood since the invention of electrical lamps, its complete description in the context of quantum conductors requires a comprehensive treatment of the conductor itself, of the charge reservoirs connected to it, and of the electromagnetic modes of the environment that sustain radiation. A voltage-biased Josephson junction connected to a small number of modes originally in the vacuum state provides a simple model system for this physics. For a dc bias V smaller than the gap voltage 2Δ=e, no quasiparticle excitation can absorb the energy 2 eV provided by the biasing circuit upon the tunneling of a Cooper pair. A dc current flows through the junction only if this energy can be absorbed by creating photons in the environmental modes [8,9,10,11].
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