Transmon Qubit in a Magnetic Field: Evolution of Coherence and Transition Frequency

We report on spectroscopic and time-domain measurements on a fixed-frequency concentric transmon qubit in an applied in-plane magnetic field to explore its limits of magnetic field compatibility. We demonstrate quantum coherence of the qubit up to field values of $B={40}\,\mathrm{mT}$, even without an optimized chip design or material combination of the qubit. The dephasing rate $\Gamma_\varphi$ is shown to be not affected by the magnetic field in a broad range of the qubit transition frequency. For the evolution of the qubit transition frequency, we find the unintended second junction created in the shadow angle evaporation process to be non-negligible and deduce an analytic formula for the field-dependent qubit energies. We discuss the relevant field-dependent loss channels, which can not be distinguished by our measurements, inviting further theoretical and experimental investigation. Using well-known and well-studied standard components of the superconducting quantum architecture, we are able to reach a field regime relevant for quantum sensing and hybrid applications of magnetic spins and spin systems.Comment: 9 pages, 8 figure

Two-level system hyperpolarization with a quantum Szilard engine

In the last decades, superconducting circuits have made important contributions to the study of quantum mechanical phenomena. Their performance approaches the threshold allowing for fault tolerant quantum computation. However, the innate complexity of solid-state physics exposes superconducting quantum circuits to interactions with uncontrolled degrees of freedom degrading their coherence. Although tremendous progress has been made to improve the coherence of superconducting circuits, they still have to cope with various loss and decoherence mechanisms, and with further improvements, it becomes increasingly challenging to track down individual decoherence mechanisms. By implementing a quantum Szilard engine with an active feedback control loop, we show that a superconducting granular aluminum fluxonium qubit is coupled weakly to a two-level system (TLS) environment of unknown physical origin, with a relatively long intrinsic energy relaxation time exceeding 50ms. As part of the hyperpolarization with the quantum Szilard engine, the TLSs can be cooled down, resulting in a four times lower qubit population, or they can be heated up to manifest themselves as a negative-temperature environment. We show that the TLSs and the qubit are each other\u27s dominant loss mechanism and that the qubit relaxation is independent of the TLS populations. Since the TLSs are much longer lived than the qubit, non-exponential relaxation and non-Poissonian quantum jumps can be observed. The incoherent relaxation dynamics of the system is described by the Solomon equations, for which a rigorous derivation is presented starting from a general Lindblad equation for the qubit and an arbitrary number of TLSs. In the limit of large numbers of TLSs, the relaxation is likely to follow a power law, which is deduced from the Solomon equations and confirmed experimentally. Moreover, the measured non-Poissonian quantum jump statistics can be reproduced by a diffusive stochastic Schrödinger equation. With increasing number of TLSs, entanglement and measurement back action can be ignored, and the quantum jump statistics can also be reproduced by the Solomon equations. The transition from a stochastic Schrödinger equation model to the Solomon equations hints at a quantum-to-classical transition

The Bragg demagnifier: X-ray imaging with kilometer propagation distance within a meter

We introduce a new X-ray imaging technique to facilitate propagation-based phase contrast of large, centimeter-sized samples. The diffracted X-ray wavefield behind the sample is demagnified by asymmetric Bragg crystal optics, thereby virtually increasing the propagation distance and thus enhancing the image contrast. We demonstrate the significant increase in image contrast compared to conventional phase contrast imaging at the same short physical propagation distance. Additionally, the Bragg demagnifier enables the reduction of image blur caused by the finite X-ray source size. In combination with a subsequent Bragg magnifier, the method will allow for an even higher dose efficiency, rendering this technique a potential candidate for, e.g., low-dose (bio)medical diagnostics

The Threat of Capital Drain: A Rationale for Public Banks?

This paper yields a rationale for why subsidized public banks may be desirable from a regional perspective in a financially integrated economy. We present a model with credit rationing and heterogeneous regions in which public banks prevent a capital drain from poorer to richer regions by subsidizing local depositors, for example, through a public guarantee. Under some conditions, cooperative banks can perform the same function without any subsidization; however, they may be crowded out by public banks. We also discuss the impact of the political structure on the emergence of public banks in a political-economy setting and the role of interregional mobility

Solomon equations for qubit and two-level systems

We model and measure the combined relaxation of a qubit, a.k.a. central spin, coupled to a discrete two-level system (TLS) environment. We present a derivation of the Solomon equations starting from a general Lindblad equation for the qubit and an arbitrary number of TLSs. If the TLSs are much longer lived than the qubit, the relaxation becomes non-exponential. In the limit of large numbers of TLSs the populations are likely to follow a power law, which we illustrate by measuring the relaxation of a superconducting fluxonium qubit. Moreover, we show that the Solomon equations predict non-Poissonian quantum jump statistics, which we confirm experimentally

Transmon qubit in a magnetic field: Evolution of coherence and transition frequency

We report on spectroscopic and time-domain measurements on a fixed-frequency concentric transmon qubit in an applied in-plane magnetic field to explore its limits of magnetic field compatibility. We demonstrate quantum coherence of the qubit up to field values of $B=40\,\mathrm{mT}$, even without an optimized chip design or material combination of the qubit. The dephasing rate $\Gamma_\varphi$ is shown to be unaffected by the magnetic field in a broad range of the qubit transition frequency. For the evolution of the qubit transition frequency, we find the unintended second junction created in the shadow angle evaporation process to be non-negligible and deduce an analytic formula for the field-dependent qubit energies. We discuss the relevant field-dependent loss channels, which cannot be distinguished by our measurements, inviting further theoretical and experimental investigation. Using well-known and well-studied standard components of the superconducting quantum architecture, we are able to reach a field regime relevant for quantum sensing and hybrid applications of magnetic spins and spin systems

Thermalization of a flexible microwave stripline measured by a superconducting qubit

With the demand for scalable cryogenic microwave circuitry continuously rising, recently developed flexible microwave striplines offer the tantalizing perspective of increasing the cabling density by an order of magnitude without thermally overloading the cryostat. We use a superconducting quantum circuit to test the thermalization of input flex cables with integrated 60 dB of attenuation distributed at various temperature stages. From the measured decoherence rate of a superconducting fluxonium qubit, we estimate a residual population of the readout resonator of 2.2 $\pm$ 0.9 x 10$^{-3}$ photons and we measure a 0.28 ms thermalization time for the flexible stripline attenuators. Furthermore, we confirm that the qubit reaches an effective temperature of 26:4 mK, close to the base temperature of the cryostat, practically the same as when using a conventional semi-rigid coaxial cable setup

Implementation of a Transmon Qubit Using Superconducting Granular Aluminum

The high kinetic inductance offered by granular aluminum (grAl) has recently been employed for linear inductors in superconducting high-impedance qubits and kinetic inductance detectors. Because of its large critical current density compared to typical Josephson junctions, its resilience to external magnetic fields, and its low dissipation, grAl may also provide a robust source of nonlinearity for strongly driven quantum circuits, topological superconductivity, and hybrid systems. Having said that, can the grAl nonlinearity be sufficient to build a qubit? Here we show that a small grAl volume (10×200×500  nm$^{3}$) shunted by a thin film aluminum capacitor results in a microwave oscillator with anharmonicity α two orders of magnitude larger than its spectral linewidth Γ$_{01}$, effectively forming a transmon qubit. With increasing drive power, we observe several multiphoton transitions starting from the ground state, from which we extract α=2$_{π}$×4.48  MHz. Resonance fluorescence measurements of the |0⟩→|1⟩ transition yield an intrinsic qubit linewidth γ=2$_{π}$×10  kHz, corresponding to a lifetime of 16  μs, as confirmed by pulsed time-domain measurements. This linewidth remains below 2$_{π}$×150  kHz for in-plane magnetic fields up to ∼70  mT