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arXiv:cond-mat/9601011 · Europhysics Letters (EPL)

Single Cooper-pair tunnelling induced by non-classical microwaves

A. A. Odintsov, Apostol Vourdas

Published May 10, 1996• 20 citations
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Abstract

A mesoscopic Josephson junction interacting with a mode of non-classical microwaves with frequency ω is considered. Squeezing of the electromagnetic field drastically affects the dynamics of Cooper tunnelling. In particular, Bloch steps can be observed even when the microwaves are in the squeezed vacuum state with zero average amplitude of the field ⟨ E ( t )⟩ = 0. The interval between these steps is double in size in comparison to the conventional Bloch steps.

DOI
10.1209/epl/i1996-00468-4

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A mesoscopic Josephson junction interacting with a mode of non-classical microwaves with frequency ω is considered. Squeezing of the electromagnetic field drastically affects the dynamics of Cooper tunnelling. In particular, Bloch steps can be observed even when the microwaves are in the squeezed vacuum state with zero average amplitude of the field ⟨ E ( t )⟩ = 0. The interval between these steps is double in size in comparison to the conventional Bloch steps.
We study scattering of propagating microwave fields by a DC-voltage-biased Josephson junction. At sub-gap voltages, a small Josephson junction works merely as a non-linear boundary that can absorb, amplify, and diversely convert propagating microwaves. We find that in the leading-order perturbation theory of the Josephson coupling energy, the spectral density and quadrature fluctuations of scattered thermal and coherent radiation can be described in terms of the well-known P(E)P(E)P(E) function. Applying this, we show how thermal and coherent radiation can be absorbed and amplified in a circuit with a resonance frequency. We also show when a coherent input can create a two-mode squeezed output. In addition, we evaluate scattering amplitudes between arbitrary photon-number (Fock) states, describing individual photon multiplication and absorption processes occuring at the junction.
Mesoscopic Josephson devices, interacting with non-classical microwaves, are studied. The phase difference in Josephson's equations is a quantum mechanical operator, whose expectation value with respect to the density matrix describing the microwaves, determines the current. Dual phenomena with vortex condensates in Josephson array insulators are also considered. Dual Josephson junctions for vortices, made from two insulators separated by a weak link through which the vortices tunnel, are described by dual Josephson equations.
We report the observation of photon pairs in the photoassisted shot noise of a tunnel junction in the quantum regime at very high frequency and very low temperature. We have measured the fluctuations of the noise power generated by the junction at two different frequencies, f(1) = 4.4 and f(2) = 7.2 GHz, while driving the junction with a microwave excitation of frequency f(0) = f(1) + f(2). We observe clear correlations between the fluctuations of the two noise powers even when the mean photon number per measurement is much smaller than one. This is strong evidence for photons being emitted in pairs. We also demonstrate that the electromagnetic field generated by the junction exhibits two-mode amplitude squeezing, a proof of its nonclassicality. The data agree very well with predictions based on the fourth cumulant of the current fluctuations generated by the junction.
The interplay of the tunneling transfer of charges and the emission and absorption of light can be investigated in a set-up, where a voltage-biased Josephson junction is placed in series to a microwave cavity. Here, we concentrate on the emission process and show that due to the inherent nonlinearity of the Josephson junction tunneling Cooper-pairs can create a variety of non-classical states of light. Depending on experimental parameters and tuning the device can be described by effective Hamiltonians, indicating specific photon creation mechanisms which lead to strongly bunched or anti-bunched light emission. We derive explicit analytical expressions for the photon correlation function g(2)(τ=0)g^{(2)}(τ=0)g(2)(τ=0) for these different processes and investigate their full crossover numerically. Photon distribution functions show squeezing and other interesting non-Poissonian behavior.