The microwave phase locking in Bloch transistor

TL;DR

The work demonstrates gate-tunable, non-dissipative current quantization in a Bloch transistor formed by two Josephson junctions in a coherent quantum phase slip regime. Microwave excitation locks the Bloch oscillations to an oscillating island charge, producing current plateaus at $I_n=2efn$ that can be modulated by a static gate charge through the Aharonov-Casher effect, with a maximum observed current of about $6.6$ nA at $f\approx 6.9$ GHz. The quantization can be controlled via four knobs—gate, bias, MW amplitude, and MW frequency—via a Bessel-function dependence on the island charge and an $E_S$-dependent modulation, and is constrained by quasiparticle poisoning and thermal noise. This BT setup offers a pathway to a scalable, low-dissipation quantum current source suitable for metrology and integration into superconducting quantum circuits.

Abstract

We report on observation of two coherent quantum phenomena, the current quantization in the Josephson Junction (JJ) and the Aharonov-Casher effect. The synergy of two effects is seen as the phase locking of the JJ with the oscillating charge engaged by the microwaves (the current quantization), and a control of the phase locking phenomenon with the static charge of the gate electrode (the Aharonov-Casher effect). The experimental system consists of two coupled JJs in the regime of coherent quantum phase slip. When the microwave is applied, the quantized current plateaus appear on the I - V curve. The effect is dual to the Shapiro voltage steps in JJs. We modulate the quantized current with the static charge induced by the gate electrode. Conceptually, the system has the functionality of the Bloch Transistor: it can deliver gate-controlled quantized non-dissipative current to the quantum circuit.

Figures (4)

• Figure 1: Overview of the experimental sample(a) Focused Ion Beam image of the BT circuit. Two identical Al JJs separated by a small island embedded in the circuit with the super-inductors $L_1$+ $L_2$$\sim$1.5 $\mu$H, resistors $R$= 6.3 k$\Omega$ and quasiparticle traps QP. The MW is delivered to JJs by the gate electrode with capacitance $C_{g}$; (b) Equivalent electric circuit of the device; (c) Interference of the fluxons tunneling through the JJs; (d) Cartoon of the Bloch Transistor with four controls: the gate/bias voltage and the frequency/amplitude of the microwave
• Figure 2: Experimental $I-V$ curve without and with the MW:(a)$I-V$ curve has current blockade below critical voltage $V_C^*=2.5\,\mu\text{V}$. The apparent critical current is $I_C^*\sim 14\,\text{nA}$; (b) Current quantization under the MW of 6.91 GHz. The horizontal lines indicate the current corresponding to $I=2efn$, $n=0,\pm1,\pm2$. One can tune the BT to different $n$ by varying $V_{b}$.
• Figure 3: Gate control of the BT. (a) The intensity graph of the differential resistance $dV/dI$ vs normalized current $I_{\text{dc}}/2ef$ and gate voltage. The peaks of $dV/dI$ are at the centres of the quantized plateaus $I_{\text{dc}}=2efn$. They are periodically modulated with the charge $e=V_\text{g}C_\text{g}$ induced at the island between the JJs; (b) Cross section of the intensity graph taken at fixed $I_{\text{dc}}/2ef$ corresponding to different $n$. The curves are shifted by 1.2 k$\Omega$ for clarity. There is a phase shift of the gate modulation between different $n$.
• Figure 4: MW control of the BT:(a) Intensity plot of the differential resistance $dV/dI$ at different bias and $\delta Q/2e$. The bright peaks are located at the quantized current plateaus, $I_{\text{dc}}=2efn$; (b) Cross section of $dV/dI$ at $I_{\text{dc}}=2ef$ (green dots). The solid blue line is a fit of the experimental data with the square of Bessel function $J_n^2(\delta Q_{\text{g}}/2e$) with $n$= 1.