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arXiv:2301.11633 · Physical review. B./Physical review. B

Quantum interferometer for quartets in superconducting three-terminal Josephson junctions

R. Mélin, D. Feinberg

Published Apr 10, 2023• 14 citations
arXivHTMLPDF

Abstract

An interferometric device is proposed in order to analyze the quartet mode in biased three-terminal Josephson junctions (TTJs), and to provide experimental evidence for the emergence of a single stationary phase, the so-called quartet phase. In such a quartet superconducting quantum interference device (quartet SQUID), the flux sensitivity exhibits period $hc/4e$, which is the fingerprint of a transient intermediate state involving two entangled Cooper pairs. The quartet SQUID provides two pieces of information: an amplitude that measures a total ``quartet critical current,'' and a phase lapse coming from the superposition of the following two current components: the quartet supercurrent which is odd in the quartet phase, and the phase-sensitive multiple Andreev reflection (phase MAR) quasiparticle current, which is even in the quartet phase. This makes a TTJ a generically ``$\ensuremath{\theta}$ junction.'' Evidence for phase MARs plays against conservative scenarios involving synchronization of AC Josephson currents, based on ``adiabatic'' phase dynamics and resistively shunted junction--like models.

DOI
10.1103/physrevb.107.l161405

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An interferometric device is proposed in order to analyze the quartet mode in biased three-terminal Josephson junctions (TTJs), and to provide experimental evidence for the emergence of a single stationary phase, the so-called quartet phase. In such a quartet superconducting quantum interference device (quartet SQUID), the flux sensitivity exhibits period hc/4ehc/4ehc/4e, which is the fingerprint of a transient intermediate state involving two entangled Cooper pairs. The quartet SQUID provides two pieces of information: an amplitude that measures a total quartet critical current,'' and a phase lapse coming from the superposition of the following two current components: the quartet supercurrent which is odd in the quartet phase, and the phase-sensitive multiple Andreev reflection (phase MAR) quasiparticle current, which is even in the quartet phase. This makes a TTJ a generically \ensuremathθ\ensuremath{\theta}\ensuremathθ junction.'' Evidence for phase MARs plays against conservative scenarios involving synchronization of AC Josephson currents, based on ``adiabatic'' phase dynamics and resistively shunted junction--like models.
A dc superconducting quantum interference device (SQUID) consisting of a symmetric ring circuit with four Josephson junctions and two independent external currents I1{I}_{1}I1​ and I2{I}_{2}I2​, which enter the circuit at different points, has a phase boundary between the fully superconducting and the normal states that is different from that of a conventional SQUID. The control current I2{I}_{2}I2​ modifies the magnetic flux (\ensuremath{\varphi}) periodicity and the value of the maximum measuring current I1m{I}_{1m}I1m​(\ensuremath{\varphi}). For values of I2{I}_{2}I2​>Ic{I}_{c}Ic​ (critical current of Josephson junction) the fully resistive state exists over flux intervals centered around (n+(1/2)${\ensuremath{\varphi}}_{0}$, where n is an integer and ${\ensuremath{\varphi}}_{0}$ is the fluxoid quantum. A superconducting circuit without Josephson junctions is suggested which should have a phase boundary similar to that found here. Minimization procedures which are usually employed in analyzing SQUID's are discussed.
Superconducting quantum interference devices (SQUIDs) that incorporate two superconductor/insulator/superconductor (SIS) Josephson junctions in a closed loop form the core of some of the most sensitive detectors of magnetic and electric fields currently available. SQUIDs in these applications are typically operated with a finite voltage which generates microwave radiation through the ac Josephson effect. This radiation may impact the system being measured. We describe here a SQUID in which the Josephson junctions are formed from strips of normal metal (N) in good electrical contact with the superconductor (S). Such SNS SQUIDs can be operated under a finite voltage bias with performance comparable or potentially better than conventional SIS SQUIDs. However, they also permit a mode of operation that is based on the unusual interplay of quasiparticle currents and supercurrents in the normal metal of the Josephson junction. The method allows measurements of the flux dependence of the critical current of the SNS SQUID without applying a finite voltage bias across the SNS junction, enabling sensitive flux detection without generating microwave radiation.
A three-terminal Josephson junction biased at opposite voltages can sustain a phase-sensitive dc current carrying three-body static phase coherence, known as the ``quartet current.'' We calculate the zero-frequency current noise cross correlations and answer the question of whether this current is noisy (like a normal current in response to a voltage drop) or noiseless (like an equilibrium supercurrent in response to a phase drop). A quantum dot with a level at energy ${\ensuremath{\epsilon}}_{0}$ is connected to three superconductors Sa,Sb{S}_{a},\phantom{\rule{0.16em}{0ex}}{S}_{b}Sa​,Sb​, and Sc{S}_{c}Sc​ with gap $\mathrm{\ensuremath{\Delta}}$, biased at ${V}_{a}=V,\phantom{\rule{0.16em}{0ex}}{V}_{b}=\ensuremath{-}V$, and Vc=0{V}_{c}=0Vc​=0, and with intermediate contact transparencies. At zero temperature, nonlocal quartets (in the sense of four-fermion correlations) are noiseless at subgap voltage in the nonresonant dot regime ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\gg}1$, which is demonstrated with a semianalytical perturbative expansion of the cross correlations. Noise reveals the absence of granularity of the superflow splitting from Sc{S}_{c}Sc​ towards (Sa,Sb)({S}_{a},{S}_{b})(Sa​,Sb​) in the nonresonant dot regime, in spite of finite voltage. In the resonant dot regime ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\lesssim}1$, cross correlations measured in the (Va,Vb)({V}_{a},{V}_{b})(Va​,Vb​) plane should reveal an ``anomaly'' in the vicinity of the quartet line Va+Vb=0{V}_{a}+{V}_{b}=0Va​+Vb​=0, related to an additional contribution to the noise, manifesting the phase sensitivity of cross correlations under the appearance of a three-body phase variable. Phase-dependent effective Fano factors ${F}_{\ensuremath{\varphi}}$ are introduced, defined as the ratio between the amplitudes of phase modulations of the noise and the currents. At low bias, the Fano factors ${F}_{\ensuremath{\varphi}}$ are of order unity in the resonant dot regime ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\lesssim}1$, and they are vanishingly small in the nonresonant dot regime ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\gg}1$.
Abstract The progressive miniaturization of superconducting quantum interference devices (SQUIDs) used, e.g. for magnetic imaging on the nanoscale or for the detection of the magnetic states of individual magnetic nanoparticles causes increasing problems in realizing a proper flux-bias scheme for reading out the device. To overcome the problem, a multi-terminal, multi-junction layout has been proposed and realized recently for the SQUID-on-tip configuration, which uses constriction-type Josephson junctions (JJ). This geometry is also interesting for SQUIDs based on overdamped superconductor—normal metal—superconductor (SNS) JJ. We fabricated four-terminal, four-junction SQUIDs based on a trilayer Nb/HfTi/Nb process and study their static and dynamic transport properties in close comparison with numerical simulations based on the resistively and capacitively shunted junction model. Simulations and measurements are in very good agreement. However, there are large differences to the transport properties of conventional two-junction SQUIDs, including unusual phase-locked and chaotic dynamic states which we describe in detail. We further extract the current-phase relation of our SNS junctions, which turns out to be purely sinusoidal within the experimental error bars.
The research work discussed in this thesis deals with the study of superconducting Josephson qubits. Superconducting qubits are solid-state artificial atoms which are based on lithographically defined Josephson tunnel junctions properties. When sufficiently cooled, these superconducting devices exhibit quantized states of charge, flux or junction phase depending on their design parameters. This allows to observe coherent evolutions of their states. The results presented can be divided into two parts. In a first part we investigate operations of superconducting qubits based on the quantum coherence in superconducting quantum interference devices (SQUID). We explain experimental data which has been observed in a SQUID subjected to fast, large-amplitude modifications of its effective potential shape. The motivations for this work come from the fact that in the past few years there have been attempts to interpret the supposed quantum behavior of physical systems, such as Josephson devices, within a classical framework. Moreover, we analyze the possibility of generating GHZ states, namely maximally entangled states, in a quantum system made out of three Josephson qubits. In particular, we investigate the possible limitations of the GHZ state generation due to coupling to bosonic baths. In the second part of the thesis we address a particular cause of decoherence of flux qubits which has been disregarded until now: thermal gradients, which can arise due to accidental non equilibrium quasiparticle distributions. The reason for these detrimental effects is that heat currents flowing through Josephson tunnel junctions in response to a temperature gradient are periodic functions of the phase difference between the electrodes. The phase dependence of the heat current comes from Andreev reflection, namely an interplay between the quasiparticles which carry heat and the superconducting condensate which is sensitive to the superconducting phase difference. Generally speaking, the flux qubit states are characterized by different values of the phase difference through their Josephson junctions. Consequently, the phase-dependent thermal current through a device subject a temperature gradient is related to the phase-dependent qubit states. We study how the thermal currents change according to the state of the qubits hence yielding a measurement of the qubit state. This in turn leads to an impact of temperature gradient on the dynamics of the system. We show that flux qubits in the Delft qubit design can have limitations of the decoherence time to the order of microseconds as a result of this newly discovered source of decoherence. In contrast, the fluxonium qubit is found to be well protected due to its superinductance.
We have calculated the dc Josephson current through multi-barrier superconducting junctions (MBSJs). The current-phase relationship of the MBSJs has been obtained numerically from the probability amplitude of the process in which an electron-like quasiparticle is reflected as a hole-like quasiparticle (Andreev reflection) in the junctions. Moreover, using the obtained current-phase relationship of MBSJs, the characteristics of superconducting quantum interference devices containing MBSJs have also been analyzed.