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arXiv:2610.24391

Quantum state tomography through multi-frequency Josephson effect

Xian-Peng Zhang, Ting-Rui Hu, Zhen-Biao Yang, Rubén Seoane Souto, Yugui Yao

Published Oct 17, 2026• 0 citations
arXivHTMLPDF

Abstract

Macroscopic quantum effects emerge when the coherent behavior of countless microscopic quantum states manifests collectively at a visible scale, as exemplified by the supercurrent carried by innumerable finite-momentum Cooper pairs. By rigorously analyzing the time evolution of superconducting nanodevices including finite-momentum superconductors and quantum-dot Josephson junctions, we analytically derive the ubiquitous macroscopic supercurrent that originates from quantum interference between distinct many-body eigenstates, which we term as the dynamic interference supercurrent. The dynamic interference supercurrent in a system of two Andreev spin qubits exhibits multi-frequency Josephson effect in the absence of external voltage and is governed by the response of the many-body eigenfunctions ($\vert r\rangle$) to variations in the superconducting phase $ϕ$, determined by the $ϕ$-space Berry connection $C_{rr'}=\langle r|\partial_ϕ|r'\rangle$. The macroscopic dynamic interference supercurrent, an inherent property of the superposition state itself, enables an advanced quantum entanglement measurement of the Andreev spin qubits. These findings open new avenues for investigating superconducting nanodevice properties from a wave-function level, with substantial implications for advancing quantum science and technology in solid-state superconducting devices, such as quantum computer, communication, memory, and sensor.

DOI
10.48550/arxiv.2610.24391

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In this thesis we present theoretical investigations of the effects of Andreev bound states on the current transport in superconducting interferometers. We also investigate the slow dynamics of the Andreev states in a superconducting point contact, and the possible application as a quantum bit. We consider superconductor-normal metal-superconductor (SNS) and normal metalsuperconductor (NS) interferometers, where the contact region is a Y-shaped normal metal wave guide, and the two connection points to the same superconducting electrode can have different phases. The electric current in the interferometer is calculated as a function of the applied voltage and the phase difference . Andreev reflection in SNS and NS interferometers incorporates two features: interference in the arms of the Y-shaped normal region, and interplay with Andreev resonances. The latter feature yields rich phase dependent current structures in the subgap voltage region. The interference effect leads to a suppression of the current structures at . We investigate the effects on the Josephson current in NS interferometers due to current injection from the normal electrode. The two main effects of the nonequilibrium situation are: nonequilibrium population of the Andreev levels, which can result in enhancement, suppression, or even sign reversal of the Josephson current, and an anomalous interference Josephson effect, which gives rise to a long range Josephson effect, increasing with the voltage up to the superconducting gap . The two Andreev states in a superconducting quantum point contact can be accessed for manipulation and measurement by embedding the point contact in a superconducting loop. We calculate an effective Hamiltonian for the slow dynamics of the Andreev two-level system in the ring. Furthermore, we discuss methods of manipulation of the Andreev levels, and coupling of qubits. The state of the Andreev two-level system can be read out by monitoring the macroscopic quantum tunneling in a current biased Josephson junction, which is embedded in the superconducting ring of the qubit. We discuss the effects on the qubit, the readout scheme and the signal-to-noise ratio. THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Coherent processes in Superconducting quantum interferometers and qubits
We report on measurements of macroscopic quantum states in superconducting Josephson circuits using a highly sensitive hybrid quantum interferometer as the readout probe. The investigated Josephson circuit is one of the leading candidates as solid-state qubits (persistent current qubit), which are known to exhibit macroscopic quantum states with atomic-like properties. The readout device is a modified Andreev interferometer with semi-metallic normal segment in a “folded" geometry, and is designed to reduce the back action during measurement, as well as minimising the electromagnetic coupling between the circuit and the environment.\n A pulsed lock-in technique has been developed to perform continuous readout of the superconductor phase difference using pulse lengths down to 10 ns. The technique enables to control the energy of the probing quasiparticles in the normal segment of the interferometer, which in turn allows to control of the supercurrent owing in the SNS junction and prevents electron heating of the normal segment.\n An experimental set-up was designed and installed in a dilution fridge consisting of shielded wiring, magnetic screens, RF tight sample holder and printed circuit board to allow the injection of high frequency excitation signals, while minimising the environment effect on the qubit through careful electrical filtering. The effect of strong RF irradiation on Andreev interferometers allowed us to estimate the response time of the readout device to be less than 40 ps.\n The measurements show that two macroscopically distinct metastable states exist when the device is biased at the qubit degeneracy point, between which the system makes transitions that can be continuously monitored. Real time kinetics of the system has been investigated at different magnetic fluxes, pulse parameters, temperature and RF radiation. Based on statistical analysis of the transitions, we argue that the metastability is connected with macroscopic quantum tunnelling effects rather than thermal excitation. The experimental data support the hypothesis of a large low frequency noise causing low transition rates.
We have analyzed and measured the quantum coherent dynamics of a circuit containing two coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Two qubits are coupled electrostatically by a small island overlapping both Cooper pair boxes. Quantum state manipulation ofthe qubit circuit is done by applying non-adiabatic voltage pulses to the common gate. We read out each qubit by means of probe electrodes connected to Cooper pair boxes through high-Ohmic tunnel junctions. With such a setup the measured pulse-induced probe currents are proportional to the probability for each qubit to have an extra Cooper pai1r after the manipulation. As expected from theory and observed experimentally the measured pulse-induced current in each probe has two frequency components whose position on the frequency axis can be externally controlled. This is a result ofthe inter-qubit coupling which is also responsible for the avoided level crossing that we observed in the qubits' spectra. Our simulations show that in the absence of decoherence and with a rectangular pulse shape the system remains entangled most ofthe time reaching maximally entangled states at certain instances.
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 observed coherent time evolution between two quantum states of a superconducting flux qubit comprising three Josephson junctions in a loop. The superposition of the two states carrying opposite macroscopic persistent currents is manipulated by resonant microwave pulses. Readout by means of switching-event measurement with an attached superconducting quantum interference device revealed quantum-state oscillations with high fidelity. Under strong microwave driving, it was possible to induce hundreds of coherent oscillations. Pulsed operations on this first sample yielded a relaxation time of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These results are promising for future solid-state quantum computing.