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arXiv:1409.6696 · Physical Review Letters

Fluctuation-Dissipation Relations of a Tunnel Junction Driven by a Quantum Circuit

Olivier Parlavecchio, Carles Altimiras, J.-R. Souquet, Pascal Simon, Inès Safi A, P. Joyez, D. Vion, P. Roche, D. Esteve, F. Portier

Published Mar 25, 2015• 48 citations
arXivHTMLPDF

Abstract

We derive fluctuation-dissipation relations for a tunnel junction driven through a resonator displaying strong quantum fluctuations. We find that the fluctuation-dissipation relations derived for classical external drives hold, provided the effect of the circuit's quantum fluctuations is incorporated into the modified nonlinear current voltage characteristics. We also demonstrate that all quantities measured under a time dependent bias can be reconstructed from their values measured under a dc bias using photoassisted tunneling relations. We confirm these predictions by implementing the circuit and measuring the dc current through the junction, its high frequency admittance, and its current noise at the frequency of the resonator.

DOI
10.1103/physrevlett.114.126801

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We derive fluctuation-dissipation relations for a tunnel junction driven through a resonator displaying strong quantum fluctuations. We find that the fluctuation-dissipation relations derived for classical external drives hold, provided the effect of the circuit's quantum fluctuations is incorporated into the modified nonlinear current voltage characteristics. We also demonstrate that all quantities measured under a time dependent bias can be reconstructed from their values measured under a dc bias using photoassisted tunneling relations. We confirm these predictions by implementing the circuit and measuring the dc current through the junction, its high frequency admittance, and its current noise at the frequency of the resonator.
In circuit quantum electrodynamical systems, the quasiparticle-related losses in Josephson junctions are suppressed due to the gap in the superconducting density of states which is much higher than the typical energy of a microwave photon. In this work, we show that a strong drive even at a frequency lower than twice the superconductor gap parameter can activate dissipation in the junctions due to photon-assisted breaking of the Cooper pairs. Both the decay rate and noise strength associated with the losses are sensitive to the dc phase bias of the junction and can be tuned in a broad range by the amplitude and the frequency of the external driving field, making the suggested mechanism potentially attractive for designing tunable dissipative elements. We also predict pronounced memory effects in the driven Josephson junctions, which are appealing for both theoretical and experimental studies of non-Markovian physics in superconducting quantum circuits. We illustrate our theoretical findings by studying the spectral properties and the steady-state population of a low-impedance resonator coupled to the driven Josephson junction: we show the emergence of non-Lorentzian spectral lines and broad tunability of effective temperature of the steady state.
The complex energy shifts of the energy levels of a macroscopic system subject to dissipation are calculated as a function of the phenomenological damping parameters describing the classical motion of the system. These results are applied to the energy levels of the zero-voltage state of a current-biased Josephson junction in parallel with an arbitrary dissipative circuit. Following the approach of Leggett, the influence of the same dissipative circuit on the tunneling rate out of the zero-voltage state is also calculated. The dependences of both phenomena, quantization of energy levels, and quantum tunneling, on the admittance of the circuit are compared.
This thesis is concerned with employing the statistics of charge transfer in a conductor as a tool for quantum measurement. The physical systems studied are electronic devices made by nanoscale manufacturing techniques. In this context quantum measurement appears not as a postulate, but as physical process. In this thesis I am considering a quantum system, in particular a qubit or a nanomechanical resonator, interacting with a tunnel junction. The effect of coupling a quantum system to a tunnel junction is twofold: The state of the quantum system will be changed and there will be information about the quantum system in the statistics of charge transfer of the tunnel junction. As the first example a quantum measurement process of a qubit is considered. A common description of the system and charge dynamics is found by introducing a new quantity, the charge specific density matrix. By deriving and solving a Markovian master equation for this quantity the measurement process is analyzed. The measurement is shown to be a dynamical process, where correlations between the initial state of the qubit and the number of charges transferred in the tunnel junction arise on a typical timescale, the measurement time. As another example of a quantum system a nanomechanical oscillator is considered. It is found, that the biased tunnel junction, acting as a non-equilibrium environment to the oscillator, increases the temperature of the oscillator from its thermal equilibrium value. The current in the junction is modulated by the interaction with the oscillator, but the influence vanishes for bias voltages smaller than the oscillator frequency. For an asymmetric junction and non-vanishing oscillator momentum a current is shown to flow through the junction even at zero bias. The current noise spectrum induced by the oscillator in the tunnel junction consists of a noise floor and a peaked structure with peaks at zero frequency, the oscillator frequency and double the oscillator frequency. The peak heights are dependent on the coupling strength between oscillator and junction, the occupation number of the oscillator, the bias voltage and the junction temperature. I show how the peak height can be used as a measure of the oscillator temperature, demonstrating that the noise of a tunnel junction can be used for electronic thermometry of a nanomechanical oscillator.
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.
We consider a biased quantum point contact between two Luttinger liquids measuring a quantum-mechanical system (oscillator). There are three main physical results. First, we find that for voltages higher than the oscillator level spacing, the effect of the measurement is equivalent to coupling to a heat bath, with an effective temperature that only depends on the device $I\ensuremath{-}V$ characteristic. Second, we find that this heating changes the $I\ensuremath{-}V$ characteristics on the junction. Finally, we predict a modulation of the tunneling current at the oscillator frequency. Also, we find that a generalized nonequilibrium fluctuation-dissipation relation connects the decoherence and dissipation of the oscillator to the current-voltage characteristics of the device.
A time-dependent bias voltage on a tunnel junction generates a time-dependent modulation of its current fluctuations, and in particular of its variance. This translates into an excitation at frequency f~\tilde ff~​ generating correlations between current fluctuating at any frequency f and at frequency ±f~\tilde ff~​−f. We report the measurement of such a correlation in the fully quantum regime, i.e. when both frequencies are much greater than kBT/h with T the temperature. Such a correlator, usually referred to as the noise susceptibility, is involved in corrections to the measurements of higher-order moments and in the squeezing of noise.