Bright Side of the Coulomb Blockade

Abstract

We explore the photonic (bright) side of 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 to 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. PACS numbers: 74.50+r, 73.23Hk, 85.25Cp Dynamical Coulomb blockade (DCB) of tunneling is a quantum phenomenon in which tunneling of charge through a small tunnel junction is modified by its electromagnetic environment [1][2][3][4]. This environment is described as an impedance in series with the tunnel element (see Fig. 1a). The sudden charge transfer associated with tunneling can generate photons in the electromagnetic modes of the environment. In a normal metal tunnel junction, biased at voltage V , the energy eV of a tunneling electron can be dissipated both into quasiparticle excitations in the electrodes and into photons. At low temperature energy conservation forbids tunneling processes emitting photons with total energy higher than eV . This suppression reduces the conductance at low bias voltage [1, 2, 4]. In a Josephson junction, DCB effects are more prominent since at bias voltages smaller than the gap voltage 2∆/e quasiparticle excitations cannot take away energy. Therefore, as shown in Fig. 1a, the entire energy 2eV of tunneling Cooper pairs has to be transformed into photons in the impedance for a dc current to flow through the junction [3,4]. Experiments have confirmed the predictions of DCB theory for the tunneling current, both in the normal [5][6][7] and superconducting case [8,9] but the associated emission of photons into the environment has never been investigated. The aim of this work is precisely to fill this gap by exploring the photonic side of DCB. We do so by embedding a Josephson junction into a well controlled electromagnetic environment provided by a microwave resonator. The resonator in turn leaks photons into an amplifier, allowing to measure the rate and spectrum of photons emitted by the junction.The experimental setup is represented in Fig. 1b. A small SQUID acts as a tunable Josephson junction with Josephson energy E J = E J0 | cos(eΦ/ )| adjustable via the magnetic flux Φ threading its loop. The microwave resonator is made of two quarter-wave transformers and its fundamental mode has frequency ν 0 6.0 GHz and quality factor Q 0 9.4. Higher modes of the resonator appear at ν n (2n + 1)ν 0 (n = 1, 2, . . .) with the same lineshape up to small deviations caused by the junction

Microwave quantum optics and electron transport through a metallic dot strongly coupled to a transmission line cavity

“…In particular, the spectral properties of microwaves emitted from a Josephson junction in the dynamical Coulomb blockade regime were investigated in Ref. 29. Also, in a number of very recent experiments, single 31,32 and double 33 quantum dots were coupled to external leads and the electronic transport was investigated via the scattering properties of injected microwaves.…”

“…Refs. 24-26. Lately also systems with mesoscopic or nanoscale conductors, such as Josephson junctions, [27][28][29] superconducting single electrons transistors 18,28,30 and quantum dots, [31][32][33][34] inserted into microwave cavities have been investigated. In particular, the spectral properties of microwaves emitted from a Josephson junction in the dynamical Coulomb blockade regime were investigated in Ref.…”

“…This will introduce new physical effects, beyond what was investigated in earlier works where electronic transport through conductors in the presence of a thermalized electromagnetic environment was at the focus. [27][28][29][36][37][38][39][40][41] The ultrastrong coupling regime in transport corresponds to a coupling strength between the transport electrons and cavity photons of the order of the fre-quency of the fundamental mode of the cavity. In this regime electrons entering the conductor strongly modify the photon states of the cavity and microwave polarons are formed.…”

Double Quantum Dot Floquet Gain Medium

“…n-photon Fock states were generated by repeating this process many times [9]. A second approach utilizes a source-drain bias to drive a current through a Cooper pair box or a double quantum dot (DQD) [10,11]. Here, the source-drain bias continually repumps the excited state of the artificial atom, leading to population inversion and microwave frequency photoemission.…”

Strong back-action of a linear circuit on a single electronic quantum channel

“…The environmental Coulomb blockade was first studied on small, opaque tunnel junctions embedded in linear circuits [2][3][4][5] . The studies were later extended to tunnel junctions of larger conductance 14 and size 15 , and to the high-frequency domain 16 . To go beyond tunnel junctions, a major theoretical difficulty is that a general coherent conductor, with electronic channels of arbitrary transmission probabilities, cannot be handled as a small perturbation to the circuit.…”