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The reconfigurable Josephson circulator/directional amplifier

K. M. Sliwa, M. Hatridge, A. Narla, S. Shankar, L. Frunzio, R. J. Schoelkopf, M. H. Devoret

arXiv:1503.00209v4quant-ph

TL;DR

Commercial non-reciprocal microwave devices introduce losses and integration challenges important for superconducting quantum information. This paper experimentally realizes a Josephson circuit that switches between directional-amplifier and circulator operation through parametric couplings. The construction provides nearly quantum-limited amplifier noise performance and an essentially noiseless dispersive circulator, while remaining reconfigurable.

  • Problem

    Commercial circulators and amplifiers suffer losses, and strong magnetic fields hinder circulator integration with superconducting qubits.

  • Method

    The paper establishes simultaneous pairwise gain and conversion processes among three modes of a Josephson-junction superconducting microwave circuit.

  • Results

    The same circuit experimentally performs both directional amplification and circulation, with nearly quantum-limited amplifier noise performance and an essentially noiseless dispersive circulator.

  • Takeaways & Limitations

    Changing pump conditions dynamically switches the device between the two non-reciprocal functions, supporting reconfigurable directional circuits and on-chip integration.

  • Takeaways & Limitations

    The implementation can be optimized by eliminating the cascaded hybrids used to address the modes.

Abstract

from arXiv · show

Circulators and directional amplifiers are crucial non-reciprocal signal routing and processing components involved in microwave readout chains for a variety of applications. They are particularly important in the field of superconducting quantum information, where the devices also need to have minimal photon losses to preserve the quantum coherence of signals. Conventional commercial implementations of each device suffer from losses and are built from very different physical principles, which has led to separate strategies for the construction of their quantum-limited versions. However, as recently proposed theoretically, by establishing simultaneous pairwise conversion and/or gain processes between three modes of a Josephson-junction based superconducting microwave circuit, it is possible to endow the circuit with the functions of either a phase-preserving directional amplifier or a circulator. Here, we experimentally demonstrate these two modes of operation of the same circuit. Furthermore, in the directional amplifier mode, we show that the noise performance is comparable to standard non-directional superconducting amplifiers, while in the circulator mode, we show that the sense of circulation is fully reversible. Our device is far simpler in both modes of operation than previous proposals and implementations, requiring only three microwave pumps. It offers the advantage of flexibility, as it can dynamically switch between modes of operation as its pump conditions are changed. Moreover, by demonstrating that a single three-wave process yields non-reciprocal devices with reconfigurable functions, our work breaks the ground for the development of future, more-complex directional circuits, and has excellent prospects for on-chip integration.

INTRODUCTION

Microwave circulators and directional amplifiers are important for superconducting-qubit signal processing, but commercial devices introduce losses and integration challenges. The paper demonstrates both non-reciprocal functions in one Josephson-junction circuit using parametric couplings.

  • Losses and associated added noise in commercial devices harm the quantum properties of flying microwave photons.
  • Strong magnetic fields used by conventional circulators prevent easy on-chip integration with superconducting qubits.
  • Commercial circulators and amplifiers use different physical principles, motivating separate approaches to improving them.
  • The circuit produces both non-reciprocal functions through interference between parametric couplings among multiple resonant structures.
  • Changing pump conditions switches the device between a directional amplifier and a minimal ferrite-free circulator, linking the two functions physically.

THE JOSEPHSON PARAMETRIC CONVERTER (JPC)

The JPC uses a flux-tunable three-wave interaction to implement pairwise gain and conversion processes among three modes. Combining these processes yields either circulation or directional amplification, with directionality requiring near-ideal conversion.

  • Fluxing the Josephson Ring Modulator near half a flux quantum makes a tri-linear three-body interaction the leading nonlinear Hamiltonian term.
  • Off-resonant pumping of one mode produces either photon gain or unity-gain photon conversion between the other two modes.
  • At zero detuning, conversion follows C = (4|g_ab|^2/κ_aκ_b)/(1 + |g_ab|^2/κ_aκ_b)^2 and reaches full conversion when |g_ab| = √κ_aκ_b.
  • Circulator: Three simultaneous unity-gain conversion processes produce a circulator whose pump-phase sum acts as an artificial gauge flux controlling circulation.
  • Directional amplifier: Two gain processes and one full conversion produce directional amplification with a matched signal input and amplified transmission toward the designated outputs.
  • Directional amplifier: For gains of approximately 12 dB, input matching degrades as conversion decreases, and directionality is lost below C = 0.95.

EXPERIMENTAL APPARATUS AND RESULTS

The experiment uses a tunable three-mode JPC with independently addressable microwave modes and pumps. The apparatus verifies mode orthogonality and operates probes at powers chosen to avoid saturation in each device mode.

  • The three modes are tunable over a 400 MHz span by varying the external magnetic flux through the ring.
  • The experiment uses modes near 9.167, 5.241, and 7.174 GHz with decay rates of 44, 19, and 50 MHz, respectively.
  • Cascaded 180° hybrids separately address the three modes, allowing pumps and probe tones to be applied through directional couplers.
  • Circulator-mode probing used −55 dBm near saturation, whereas directional-amplifier probing used −75 dBm well outside the saturated regime.
  • Without pumps, the modes were completely orthogonal; probing one mode produced no response at the frequencies of the other two.

Circulator

The circuit realizes a Josephson circulator by pairwise coupling three modes through conversion processes. With three microwave pumps, it achieves low-loss, broadband circulation whose direction reverses when the total pump phase changes.

  • Three pairwise conversion processes couple all modes to realize the Josephson circulator.The conversion coefficients are jointly optimized for input matching and reverse isolation across all three ports.
  • Changing the total pump phase reverses circulation direction without other pump-parameter changes or degraded overall performance.The measured scattering parameters agree well with theory in both circulation directions.
  • On resonance, reflection is better than −10 dB, reverse isolation exceeds 18.5 dB, and insertion loss is below 0.5 dB.Insertion loss is calibrated relative to the individual conversion processes.
  • 11 MHz bandwidth provides input matching better than −10 dB at all ports and insertion loss better than 1 dB.The bandwidth results from the combined bandwidths of the individual conversion processes.
  • Performance is limited by imperfections in pairwise conversion, pump-phase drift, and spatial-mode mismatch, while higher-order nonlinearities remain insufficiently characterized.The latter uncertainty affects the number of probe photons the device can process without degradation.
  • Circulation alternates direction at three working points separated by π in pump phase, with smooth scattering-parameter transitions between them.The working points occur at −3π/2, −π/2, and π/2.

Directional amplifier

The same three-mode circuit operates as a phase-preserving directional amplifier when its pairwise processes are configured for gain and conversion. It provides directional gain with near-quantum-limited noise, but requires highly efficient conversion to preserve matching.

  • The directional-amplifier configuration uses two conjugating photon-gain processes and one unity-gain conversion process among the three modes.The physical ports can assume different signal, idler, and vacuum roles depending on pump conditions.
  • Signals at S are amplified and transmitted to I and V with 14 dB gain, while signals incident on I are isolated from S by 8 dB.S and V have reflection coefficients of −16 dB or better, whereas the third port shows reflection gain.
  • Signals incident on V are transmitted with near-unity photon gain, and the directional gain has an 11 MHz 3-dB bandwidth.Other bandwidth definitions can instead use input matching or reverse isolation.
  • Directional-amplifier noise agrees within 1 dB with the corresponding single pairwise gain process and is essentially quantum-limited like the JPC phase-preserving amplifier.Noise visibility is observed at the gain outputs I and V, but not at isolated input S.
  • As the conversion coefficient decreases, scattering magnitudes rise; below C = 0.95, input matching is lost and reflection gain appears.The threshold rises with amplifier gain, so 14 dB was selected to retain sufficient input matching.
  • High forward gain with a matched input requires a nearly perfect converter, while phase drift and higher-order nonlinearities constrain performance and dynamic range.Cascaded low-gain stages are proposed as one practical route to high net gain with less extreme pump precision.

DISCUSSION AND CONCLUSIONS

The Josephson circuit implements both circulator and directional-amplifier functions, with reconfigurable operation, low-loss noise performance, and prospects for integration into cryogenic microwave systems.

  • Reconfigurable operation: The same Josephson circuit performs both circulator and directional-amplifier functions, with each function selected by a specific pump configuration.The implementation uses three pump frequencies, amplitudes, and phases.
  • Circulator: This work reports the first successful implementation of a Josephson microwave circulator.The device operates as a purely dispersive, ferrite-free circulator.
  • Noise and simplicity: The circuit's purely dispersive construction is expected to be essentially noiseless and produces nearly quantum-limited noise performance in directional-amplifier operation.The authors compare its noise performance favorably with previous Josephson-junction proposals and standard superconducting amplifiers.
  • Limitations: Experimental results agree qualitatively with theory, although discrepancies remain because of neglected higher-order terms and imperfect control of pump phases.Further work is needed on dynamic range, off-resonant response, and higher-order mixing products.
  • Integration: Eliminating cascaded microwave hybrids could make the device fully planar while removing potential sources of loss and mismatch.The authors identify this as an optimization of the present implementation.
  • Integration: The absence of large magnetic fields gives the methodology prospects for on-chip integration with standard circuit QED systems and other cryogenic microwave measurements.The paper identifies applications including kinetic inductance detectors, dispersive magnetometers, and quantum nanomechanical resonators.
  • Physical principle: Directionality arises from a non-reciprocal phase shift acquired through a parametric two-mode interaction, linking different non-reciprocal devices.The work also points toward directional phase-sensitive amplification using the same three modes with different pumps.
  • Reconfigurable operation: The device's in-situ switching can support more complicated signal-routing schemes and potentially quantum switch matrices or gain media.The switching time is limited by the device bandwidth.

JPC Fabrication

The JPC was fabricated on silicon using a conventional Dolan-bridge process and combines microstrip resonators with a tunable Josephson Ring Modulator.

  • Fabrication: The JPC was fabricated on 300 µm silicon using electron-beam lithography and double-angle aluminum deposition.The process uses the conventional Dolan bridge technique.
  • Resonators: The device contains two perpendicular 300 µm-wide λ/2 microstrip resonators with lengths of 4.68 mm and 9 mm.Each resonator is terminated by a microstrip gap-coupling capacitor.
  • Coupling: The coupling capacitors are 28 fF for mode a and 32 fF for mode b, setting the energy decay rates κ_a, κ_b, and κ_c.
  • Josephson Ring Modulator: The Josephson Ring Modulator has four 1.7 µA Al/AlOx/Al junctions in a loop, shunted by four 3.6 µA junctions.The shunt junctions lift hysteretic behavior and allow frequency tuning with an external magnetic field.

Pairwise gain and conversion characteristics

The experiments characterize the pairwise conversion and gain processes used to configure the three-mode circuit as either a circulator or directional amplifier.

  • Pump tuning: The pumps were individually tuned to minimize frequency offsets in shared modes while preserving the required frequency-summation conditions.
  • Circulator: The circulator uses three pairwise conversion processes, with pump powers tuned for large and well-matched conversion coefficients.
  • Circulator: Simultaneously activating and fine-tuning the three processes optimizes the full circulator's input match and reverse isolation.
  • Circulator: C_ab = 0.97 and C_bc = 0.98 were achieved for two pairwise conversion processes in the circulator.The supplied passage ends before reporting the remaining coefficient.
  • Directional amplifier: The directional amplifier combines one pairwise conversion process with two pairwise gain processes.Maximizing conversion also limits the achievable directional gain.
  • Directional amplifier: The conversion process reached C_ab = 0.998, while higher-order terms produced a slight double dip in S_aa.
  • Directional amplifier: The pairwise gain processes were set to G_ac = 12 dB and G_bc = 13 dB to avoid overwhelming C_ab.

rectional amplifier

The analysis calculates scattering parameters from individual gain and conversion processes and identifies the condition at which directionality is lost.

  • Directionality threshold: The analysis treats directionality as a function of the individual gain and conversion processes that form the device.
  • Scattering analysis: The model assigns conversion to the a–b process and gain to the b–c and a–c processes, then calculates the resulting scattering parameters.
  • Scattering analysis: The on-resonance input match S_bb is calculated from the individual pump coupling strengths g_ab, g_bc, and g_ac.
  • Directionality threshold: The threshold for loss of directionality occurs when S_bb = 1, yielding a relation involving the conversion coefficient and gain-coupling term.The supplied passage states the relation begins with (1−C) and includes |g_ab|^2/(κ_aκ_b).
  • Parameter mapping: The single-pump coupling strengths are expressed in terms of the corresponding gain and conversion coefficients.For example, the supplied expression relates √G_bc to the normalized coupling strength |g_bc|^2/(κ_bκ_c).

Detailed experimental configuration

The experiment uses a three-mode Josephson Parametric Converter with separately pumped pairwise conversion and gain processes, embedded in a broadband microwave measurement setup. Pump parameters are matched across processes, while cascaded hybrids and directional couplers route inputs and outputs.

  • Readout chain: The base-temperature components are arranged in the dilution refrigerator, and frequency-converted outputs are mixed back to the input frequency when needed.Unconnected switch ports are terminated in 50 Ω.
  • Mode-specific processes: The circuit implements pairwise conversion processes between modes for circulator operation and pairwise gain plus conversion processes for directional-amplifier operation.The conversion coefficient and center frequency are matched for processes involving each mode, while the two photon gains are matched and conversion is set near unity.
  • Experimental nonideality: The measured s_cc response is smaller than expected for both pumps, which is attributed to mismatches in the cascaded hybrid structure.This is an implementation-specific deviation from the intended response.
  • Pump conditions: Pump parameters are chosen to match the center frequencies of both processes involving each port, with matched photon gains and near-unity conversion.These conditions define the intended operating balance among the three modes.
  • Cryogenic circuit: The JPC is connected to cascaded 180° hybrids addressing modes a, b, and c, with directional couplers separating input from output.Directional couplers were selected for their 4–20 GHz operating bandwidth rather than using circulators in the setup.
  • Room-temperature instrumentation: Three separate generators apply the pumps at room temperature, locked to a common 10 MHz rubidium atomic clock, while switches select addressed inputs and measured outputs.Probe and pump tones are combined before entering the dilution refrigerator and outputs pass through filtering, isolation, and amplification stages.
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