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IEEE Transactions on Applied Superconductivity

Fast Digital Phase Detection of a Coherent Tone At GHz Frequencies

Luigi Di Palma, P. Mastrovito, Alessandro Miano, A. J. Salim, Federico Vittorio Lupo, J. Bernhardt, Laura Di Marino, D. Massarotti, Giovanni Piero Pepe, Francesco Tafuri, Oleg A. Mukhanov, M. Arzeo

Published Jan 17, 2024• 3 citations
Publisher

Abstract

We present a detection technique based on a flux-switchable Josephson Digital Phase Detector (JDPD), which is capable of discriminating between two phase values of a coherent input tone. When suitably flux stimulated, the JDPD switches from a single-minimum to a double-minima potential and, as a result, relaxes in one of two stable configurations depending on the phase sign of the input stimulus. The outcome of this procedure is digitally encoded in the occupation probability of the phase particle in either of the two JDPD wells. In this manuscript, we demonstrate the working principle of the JDPD by discriminating the phase of a 5 GHz tone with a protocol of 300 ns of time duration. This result supports the future implementation of the JDPD to readout the state of a qubit.

DOI
10.1109/tasc.2024.3354681

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We present a detection technique based on a flux-switchable Josephson Digital Phase Detector (JDPD), which is capable of discriminating between two phase values of a coherent input tone. When suitably flux stimulated, the JDPD switches from a single-minimum to a double-minima potential and, as a result, relaxes in one of two stable configurations depending on the phase sign of the input stimulus. The outcome of this procedure is digitally encoded in the occupation probability of the phase particle in either of the two JDPD wells. In this manuscript, we demonstrate the working principle of the JDPD by discriminating the phase of a 5 GHz tone with a protocol of 300 ns of time duration. This result supports the future implementation of the JDPD to readout the state of a qubit.
We propose a new phase detection technique based on a flux-switchable superconducting circuit, the Josephson digital phase detector (JDPD), which is capable of discriminating between two phase values of a coherent input tone. When properly excited by an external flux, the JDPD is able to switch from a single-minimum to a double-minima potential and, consequently, relax in one of the two stable configurations depending on the phase sign of the input tone. The result of this operation is digitally encoded in the occupation probability of a phase particle in either of the two JDPD wells. In this work, we demonstrate the working principle of the JDPD up to a frequency of 400 MHz with a remarkable agreement with theoretical expectations. As a future scenario, we discuss the implementation of this technique to superconducting qubit readout. We also examine the JDPD compatibility with the single-flux-quantum architecture, employed to fast-drive and measure the device state.
Quantum computation requires high-fidelity qubit readout, preserving the quantum state. In the case of superconducting (SC) qubits, readout is typically performed using a complex analog experimental setup operated at room temperature, which poses significant technological and economic barriers to large system scalability. An alternative approach is to perform a cryogenic on-chip qubit readout based on a Josephson Digital Phase Detector (JDPD): a flux switchable device capable of digitizing the phase sign of a coherent input. The readout operation includes the flux excitation of the JDPD to evolve from a single to a double-minima potential. In this work, the effect of the flux bias characteristics on the JDPD performances is studied numerically. To meet the identified requirements that maximize detection fidelity and tackle the engineering challenges, a cryogenic on-chip Single Flux Quantum based flux bias driver is proposed and discussed.
Josephson junction qubits are promising candidates for a scalable quantum processor. Such qubits are commonly manipulated by means of sequences of rf-pulses and different methods are used to determine their quantum state. The readout should be able to distinguish the two qubit states with high accuracy and be faster than the relaxation time of the qubit. We discuss and experiment with a readout method based on the switching of a Josephson junction from the zero voltage state to a finite voltage state. The Josephson junction circuit has a non-linear dynamics and when it is brought to a bifurcation point, it can be made arbitrarily sensitive to small perturbations. This extreme sensitivity at a bifurcation point can be used to distinguish the two quantum states if the topology of the phase space of the circuit leads to a quick separation into the final states where re-crossings of the bifurcation point are negligible. We optimize a switching current detector by analyzing the phase space of a Josephson junction circuit with frequency dependent damping. A pulse and hold technique is used where an initial current pulse brings the junction close to its bifurcation point and the subsequent hold level is used to give the circuit enough time to evolve until the two states can be distinguished by the measuring instrument. We generate the pulse and hold waveform by a new technique where a voltage step with following linear voltage rise is applied to a bias capacitor. The frequency dependent damping is realized by an on-chip RC-environment fabricated with optical lithography. Josephson junction circuits are added on by means of e-beam lithography. Measurements show that switching currents can be detected with pulses as short as 5 ns and a resolution of 2.5% for a sample directly connected to the measurement leads of the cryostat. Detailed analysis of the switching currents in the RC-environment show that pulses with a duration of 20 us can be explained by a generalization of Kramers' escape theory, whereas switching the same sample with 25 ns pulses occurs out of thermal equilibrium, with sensitivity and speed adequate for qubit readout.
We perform two-tone spectroscopy on quantum circuits, where high-frequency radiation is generated by a voltage-biased superconductor-normal-superconductor Josephson junction and detection is carried out by an ancillary microwave resonator. We implement this protocol on two different systems, a transmon qubit and a $\ensuremath{\lambda}/4$ resonator. We demonstrate that this two-tone Josephson spectroscopy operates well into the millimeter-wave band, reaching frequencies larger than 80 GHz, and is well suited for probing highly coherent quantum systems.
We present a technique for linewidth measurement and phase-locking of Josephson oscillators using digital rapid single-flux-quantum (RSFQ) circuits. The oscillator consists of a resistively shunted 6 /spl mu/m/spl times/6 /spl mu/m Nb/AlO/sub x//Nb Josephson tunnel junction that is integrated with RSFQ input and output circuits. A cascade of RSFQ T flip-flops is used to directly monitor the output of the Josephson oscillator. Spectral characteristics have been measured directly for oscillator frequencies ranging from 10-50 GHz. The linewidth can be reduced by over 100 times by phase-locking the oscillator to an RSFQ pulse train generated by an external sinusoidal signal. These Josephson oscillators can be used as on-chip stable high frequency clocks for RSFQ circuits.
In this Letter, we experimentally demonstrated that Josephson threshold detectors (JTDs) could be developed to implement the sensitive detection of broadband microwave photons. Beginning with the numerical simulations of the damped dynamics for the macroscopic phase particle generated by a Josephson junction (JJ), we showed that the time-domain threshold voltage state switched measurements of the JJ driven by a low-frequency triangular wave current, which could be utilized to implement the sensitive microwave photons detection. The detectable signal power can be determined by using the Kumar–Caroll index to quantify the distinguishability between two statistical distributions on the measured threshold switched durations of the JJ with and without the signal input. Experimentally, we fabricated the Al/AlOx/Al JJ and measured its threshold responses, at 50 mK temperature, to the input microwave photons at the frequency of ∼5 GHz. The experimental results indicated that the weak microwave signals, which are phenomenologically threatened by the additional thermal noise that modifies the damped phase dynamics of the JJ, can be detected by the fabricated JTD. The detectable power of the microwave signals demonstrated here was calibrated as about −92 dBm (corresponding to the photons rate of ∼2×108 photons/ms). Based on the numerical simulations for optimizing the relevant performance indicators of the detectors, we further argue that the JTDs could be utilized to achieve the sensitive detection of broadband microwave photons at the single-photon level.