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arXiv:1307.2495 · Physical Review Letters

From Coulomb-Blockade to Nonlinear Quantum Dynamics in a Superconducting Circuit with a Resonator

Vera Gramich, Björn Kubala, Selina Rohrer, Joachim Ankerhold

Published Dec 9, 2013• 87 citations
arXivHTMLPDF

Abstract

Motivated by recent experiments on superconducting circuits consisting of a dc-voltage-biased Josephson junction in series with a resonator, quantum properties of these devices far from equilibrium are studied. This includes a crossover from a domain of incoherent to a domain of coherent Cooper pair tunneling, where the circuit realizes a driven nonlinear oscillator. Equivalently, weak photon-charge coupling turns into strong correlations captured by a single degree of freedom. Radiated photons offer a new tool to monitor charge flow and current noise gives access to nonlinear dynamics, which allows us to analyze quantum-classical boundaries.

DOI
10.1103/physrevlett.111.247002

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Motivated by recent experiments on superconducting circuits consisting of a dc-voltage-biased Josephson junction in series with a resonator, quantum properties of these devices far from equilibrium are studied. This includes a crossover from a domain of incoherent to a domain of coherent Cooper pair tunneling, where the circuit realizes a driven nonlinear oscillator. Equivalently, weak photon-charge coupling turns into strong correlations captured by a single degree of freedom. Radiated photons offer a new tool to monitor charge flow and current noise gives access to nonlinear dynamics, which allows us to analyze quantum-classical boundaries.
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.
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.
Photon emission by tunneling electrons can be encouraged by locating a resonator close to the tunnel junction and applying an appropriate voltage bias. However, studies of normal metals show that the resonator also affects how the charges flow, facilitating processes in which correlated tunneling of two charges produces one photon. We develop a theory to analyze this kind of behavior in Josephson junctions by deriving an effective Hamiltonian describing processes where two Cooper pairs generate a single photon. We determine the conditions under which the transport is dominated by incoherent tunneling of two Cooper pairs, while also uncovering a regime of coherent double Cooper-pair tunneling. We show that the system can also display an unusual form of photon blockade and hence could serve as a single-photon source.
We explore the photonic (bright) side of the dynamical Coulomb blockade (DCB) by measuring the radiation emitted by a dc voltage-biased Josephson junction embedded in a microwave resonator. In this regime Cooper pair tunneling is inelastic and associated with the transfer of an energy 2eV into the resonator modes. We have measured simultaneously the Cooper pair current and the photon emission rate at the resonance frequency of the resonator. Our results show two regimes, in which each tunneling Cooper pair emits either one or two photons into the resonator. The spectral properties of the emitted radiation are accounted for by an extension to DCB theory.
Abstract We propose to generate photon-pair blockade in a Josephson-photonics circuit that consists of a dc voltage-biased Josephson junction in series with a superconducting charge qubit and two nondegenerate microwave resonators. The two-level charge qubit is utilized to create anticorrelations of the charge transport; that is, the simultaneous Cooper pair tunneling events are inhibited. When the Josephson frequency matches the sum of resonance frequencies of the charge qubit and the two resonators, we demonstrate that the two resonators can release their energies in the form of antibunched pairs of two strongly correlated photons. The present work provides a practical way for producing a bright microwave source of antibunched photon pairs, with potential applications ranging from spectroscopy and metrology to quantum information processing.
The quantum-mechanical effects typical for single atoms or molecules can be reproduced in micrometer-scale electric devices. In these systems the essential component is a small Josephson junction (JJ) consisting of two superconductors separated by a thin insulator. The quantum phenomena can be controlled in real time by external signals and have a great potential for novel applications. However, their fragility on uncontrolled disturbance caused by typical nearby environments is a drawback for quantum information science, but a virtue for detector technology. Motivated by this we have theoretically studied transistor kind of devices based on single-charge tunneling through small JJs. A common factor of the research is the analysis of the interplay between the coherent Cooperpair (charge carriers in the superconducting state) tunneling and incoherent environmental processes. In the first work we calculate the current due to incoherent Cooper-pair tunneling through a voltage-biased small JJ in series with large JJs and compare the results with recent experiments. We are able to reproduce the main experimental features and interpret these as traces of energy levels and energy bands of the mesoscopic device. In the second work we analyze a similar circuit (asymmetric single-Cooper-pair transistor) but under the assumption that the Cooper-pair tunneling is mainly coherent. This predicts new resonant transport voltages in the circuit due to higher-order processes. However, no clear traces of most of them are seen in the experiments, and similar discrepancy is present also in the case of the symmetric circuit. We continue to study this problem by modeling the interplay between the coherent and incoherent processes more accurately using a density-matrix approach. By this we are able to demonstrate that in typical conditions most of these resonances are indeed washed out by strong decoherence caused by the environment. We also analyze the contribution of three typical weakly interacting dissipative environments: electromagnetic environment, spurious charge fluctuators in the nearby insulating materials, and quasiparticles. In the last work we model the dynamics of a currentbiased JJ perturbed by a smaller JJ using a similar density-matrix approach. We demonstrate that the small JJ can be used also as a detector of the energy-band dynamics in a current biased JJ. The method is also used for modeling the charge transport in the Bloch-oscillating transistor.