The Josephson ring modulator (JRM) is a device, based on Josephson tunnel junctions, capable of performing nondegenerate mixing in the microwave regime without losses. The generic scattering matrix of the device is calculated by solving coupled quantum Langevin equations. Its form shows that the device can achieve quantum-limited noise performance both as an amplifier and a mixer. Fundamental limitations on simultaneous optimization of performance metrics like gain, bandwidth, and dynamic range (including the effect of pump depletion) are discussed. We also present three possible integrations of the JRM as the active medium in a different electromagnetic environment. The resulting circuits, named Josephson parametric converters (JPC), are discussed in detail, and experimental data on their dynamic range are found to be in good agreement with theoretical predictions. We also discuss future prospects and requisite optimization of JPC as a preamplifier for qubit readout applications.
The Josephson ring modulator (JRM) is a device, based on Josephson tunnel junctions, capable of performing nondegenerate mixing in the microwave regime without losses. The generic scattering matrix of the device is calculated by solving coupled quantum Langevin equations. Its form shows that the device can achieve quantum-limited noise performance both as an amplifier and a mixer. Fundamental limitations on simultaneous optimization of performance metrics like gain, bandwidth, and dynamic range (including the effect of pump depletion) are discussed. We also present three possible integrations of the JRM as the active medium in a different electromagnetic environment. The resulting circuits, named Josephson parametric converters (JPC), are discussed in detail, and experimental data on their dynamic range are found to be in good agreement with theoretical predictions. We also discuss future prospects and requisite optimization of JPC as a preamplifier for qubit readout applications.
Nondegenerate Josephson mixers (JMs), formed by coupling two different transmission-line resonators to Josephson ring modulators (JRMs), are vital and versatile devices capable of processing microwave signals at the quantum limit. Owing to the lossless nondegenerate three-wave mixing process enabled by the JRM, JMs can perform phase-preserving amplification of quantum signals, generate two-mode squeezed states, and perform noiseless frequency conversion. However, due to their limited bandwidth and saturation power, such resonator-based JMs are generally unable to simultaneously process frequency-multiplexed signals required in large quantum processors. To overcome this longstanding dual challenge, we redesign the JRM parameters by optimizing its inductances to suppress higher order mixing products and engineer its electromagnetic environment by incorporating lumped-element coupled-mode networks between the JRM and the two distinct ports of the JM. By implementing these strategies, we measure for JMs realized with four coupled modes per port, operated in amplification (conversion), bandwidths of about 400 MHz (700 MHz) with power reflections above 10 dB (below − 10 dB) and saturation powers of about − 110 dBm at 15 dB ( − 91 dBm at − 26 dB). Similarly, we demonstrate for a low external quality factor resonant-mode JM operated in conversion, a maximum bandwidth of about 670 MHz with power reflections below − 10 dB and a maximum saturation power of about − 86 dBm at − 17 dB. Such nondegenerate JMs with enhanced bandwidths and saturation powers could serve in a variety of frequency-multiplexed settings ranging from high-fidelity qubit readout and unidirectional routing of quantum signals to the generation of remote entanglement with continuous variables.
Josephson parametric amplifiers (JPA) are nonlinear devices that are used for quantum sensing and qubit readout in the microwave regime. While JPAs regularly operate near the quantum limit, their gain saturates for very small (few-photon) input power. In a previous work, we showed that the saturation power of JPAs is not limited by pump depletion, but instead by the fourth-order nonlinearity of Josephson junctions, the nonlinear circuit elements that enables amplification in JPAs. Here, we present a systematic study of the nonlinearities in JPAs, show which nonlinearities limit the saturation power, and present a strategy for optimizing the circuit parameters for achieving the best possible JPA. For concreteness, we focus on JPAs that are constructed around a Josephson ring modulator (JRM). We show that by tuning the external and shunt inductors, we should be able to take the best experimentally available JPAs and improve their saturation power by $\ensuremath{\approx}15\phantom{\rule{0.16em}{0ex}}\mathrm{dB}$. Finally, we argue that our methods and qualitative results are applicable to a broad range of cavity-based JPAs.
Non-linear microwave devices based on Josephson tunnel junctions and operating near the quantum limit have so far been based on SQUIDS and degenerate parametrically pumped oscillators, or related systems. This chapter addresses a new type of Josephson device operation that performs quantum analog signal processing, namely that of non-degenerate three-wave mixing. Both quantum-limited amplification and frequency conversion are possible with such devices, and their characteristics are entirely calculable analytically. The chapter in particular discusses the relationships between photon number gain, bandwidth, and dynamic range.
Two-mode squeezed vacuum states are a crucial component of quantum technologies. In the microwave domain, they can be produced by the Josephson ring modulator that acts as a three-wave mixing nondegenerate parametric amplifier. Here, we numerically solve the full master equation of three bosonic modes describing the Josephson ring modulator to compute squeezing of output fields and gain at low signal power. We show that the third-order interaction from the three-wave mixing process intrinsically limits squeezing and reduces gain. Since our results are related to other general cavity-based three-wave mixing processes, these imply that any nondegenerate parametric amplifier will have an intrinsic squeezing limit in the output fields.
Three-wave mixing devices, i.e. non-linear circuits converting power among three microwave signals, are key elements of analog information processing in the microwave domain. However, they are based on dissipative components such as semiconductor diodes, or SIS tunnel junctions biased near the superconducting gap. The loss of signal limits their operation and also introduces noise above the minimum required by quantum mechanics. By using Josephson junctions and superconducting resonators, we've been able to build such a quantum device. In its amplification mode, this device can be used as a preamplifier in many experiments where a few photon wide microwave signals must be measured by commercial instruments, which are sensitive to powers several orders of magnitude larger. The price to pay for this amplification is the necessary degradation of information. Indeed, an extension of the no-cloning theorem imposes that a linear phase preserving amplifier adds at least half a quantum of noise to the signal. By amplifying the finite frequency noise emitted by an NIN tunnel junction, we demonstrated that the total measurement chain adds less than 2.3 quanta to this limit thanks to our device. The operating principle of this device is based on Josephson parametric amplification. I will explain this mechanism and show preliminary results which illustrate that it can generate quantum correlated pairs of spatially separated photons with different wavelengths known as two-mode squeezed states. This experiment exploits the tunability of our device and the ease-of-use inherent to micro-wave circuits to perform a quantum optics experiment demonstrating this entanglement.
Josephson parametric converters (JPCs) are superconducting devices capable of performing nondegenerate, three-wave mixing in the microwave domain without losses. One drawback limiting their use in scalable quantum architectures is the large footprint of the auxiliary circuit needed for their operation, in particular, the use of off-chip, bulky, broadband hybrids and magnetic coils. Here, we realize a JPC that eliminates the need for these bulky components. The pump drive and flux bias are applied in the Hybrid-Less, Coil-Less (HLCL) device through an on-chip, lossless, three-port power divider and an on-chip flux line, respectively. We show that the HLCL design considerably simplifies the circuit and reduces the footprint of the device while maintaining a comparable performance to state-of-the-art JPCs. Furthermore, we exploit the tunable bandwidth property of the JPC and the added capability of applying alternating currents to the flux line in order to switch the resonance frequencies of the device, hence demonstrating time-multiplexed amplification of microwave tones that are separated by more than the dynamical bandwidth of the amplifier. Such a measurement technique can potentially serve to perform a time-multiplexed, high-fidelity readout of superconducting qubits.