Superconducting circuit quantisation conventionally starts from classical Euler-Lagrange circuit equations-of-motion. Invoking the correspondence principle yields a canonically quantisedcircuit description of circuit dynamics over a bosonic Hilbert space. This process has been very successful for describing experiments, but implicitly starts from the classical Ginsberg-Landau (GL) mean field theory for the circuit. Here we employ a different approach which starts from a microscopic fermionic Hamiltonian for interacting electrons, whose ground space is described by the Bardeen-Cooper-Schrieffer (BCS) many-body wavefuction that underpins conventional superconductivity. We introduce the BCS ground-space as a subspace of the full fermionic Hilbert space, and show that projecting the electronic Hamiltonian onto this subspace yields the standard Hamiltonian terms for Josephson junctions, capacitors and inductors, from which standard quantised circuit models follow. Importantly, this approach does not assume a spontaneously broken symmetry, which is important for quantised circuits that support superpositions of phases, and the phase-charge canonical commutation relations are derived from the underlying fermionic commutation properties, rather than imposed. By expanding the projective subspace, this approach can be extended to describe phenomena outside the BCS ground space, including quasiparticle excitations.
Ferrite-free circulators that are passive and readily integratable on a chip are highly sought-after in quantum technologies based on superconducting circuits. In our previous work,we implemented such a circulator using a three-Josephson-junction loop that exhibited unambiguous nonreciprocity and signal circulation, but required junction energies to be within 1% of design values. This tolerance is tighter than standard junction fabrication methods provide, so we propose and demonstrate a design improvement that relaxes the required junction fabrication precision, allowing for higher device performance and fabrication yield. Specifically, we introduce large direct capacitive couplings between the waveguides to create strong Fano scattering interference. We measure enhanced `circulation fidelity‘ above 97%, with optimised on-resonance insertion loss of 0.2~dB, isolation of 18~dB, and power reflectance of −15~dB, in good agreement with model calculations.
Building large-scale superconducting quantum circuits will require miniaturisation and integration of supporting devices including microwave circulators, which are currently bulky,stand-alone components. Here we report the realisation of a passive on-chip circulator which is made from a loop consisting of three tunnel-coupled superconducting islands, with DC-only control fields. We observe the effect of quasiparticle tunnelling, and we dynamically classify the system into different quasiparticle sectors. When tuned for circulation, the device exhibits strongly non-reciprocal 3-port scattering, with average on-resonance insertion loss of 2 dB, isolation of 14 dB, power reflectance of -11 dB, and a bandwidth of 200 MHz.
We present the design of a passive, on-chip microwave circulator based on a ring of superconducting tunnel junctions. We investigate two distinct physical realisations, based on eitherJosephson junctions (JJ) or quantum phase slip elements (QPS), with microwave ports coupled either capacitively (JJ) or inductively (QPS) to the ring structure. A constant bias applied to the center of the ring provides the symmetry breaking (effective) magnetic field, and no microwave or rf bias is required. We find that this design offers high isolation even when taking into account fabrication imperfections and environmentally induced bias perturbations and find a bandwidth in excess of 500 MHz for realistic device parameters.
Single photon detectors are fundamental tools of investigation in quantum optics and play a central role in measurement theory and quantum informatics. Photodetectors based on differenttechnologies exist at optical frequencies and much effort is currently being spent on pushing their efficiencies to meet the demands coming from the quantum computing and quantum communication proposals. In the microwave regime however, a single photon detector has remained elusive although several theoretical proposals have been put forth. In this article, we review these recent proposals, especially focusing on non-destructive detectors of propagating microwave photons. These detection schemes using superconducting artificial atoms can reach detection efficiencies of 90\% with existing technologies and are ripe for experimental investigations.
Detecting an itinerant microwave photon with high efficiency is an outstanding problem in microwave photonics and its applications. We present a scheme to detect an itinerant microwavephoton in a transmission line via the nonlinearity provided by a transmon in a driven microwave resonator. By performing continuous measurements on the output field of the resonator we theoretically achieve an over-unity signal-to-noise (SNR) for a single shot measurement and 84% distinguishability between zero and one microwave photon with a single transmon and 90% distinguishability with two cascaded transmons. We also show how the measurement diminishes coherence in the photon number basis thereby illustrating a fundamental principle of quantum measurement: the higher the measurement efficiency, the greater is the decoherence.
The ability to detect the presence of a single, travelling photon without destroying it has been a long standing project in optics and is fundamental for applications in quantum informationand measurement. The realization of such a detector has been complicated by the fact that photon- photon interactions are very weak at optical frequencies. At microwave frequencies, very strong photon-photon interactions have been demonstrated. Here however, the single-photon detector has been elusive due to the low energy of the microwave photon. In this article, we present a realistic proposal for quantum nondemolition measurements of a single propagating microwave photon. The detector design is built on a of chain of artificial atoms connected through circulators which break time-reversal symmetry, making both signal and probe photons propagate in one direction only. Our analysis is based on the theory of cascaded quantum systems and quantum trajectories which takes the full dynamics of the atom-field interaction into account. We show that a signal-to-noise ratio above one can be realized with current state of the art microwave technology.
We show, in the context of single photon detection, that an atomic
three-level model for a transmon in a transmission line does not support the
predictions of the nonlinear polarisabilitymodel known as the cross-Kerr
effect. We show that the induced displacement of a probe in the presence or
absence of a single photon in the signal field, cannot be resolved above the
quantum noise in the probe. This strongly suggests that cross-Kerr media are
not suitable for photon counting or related single photon applications. Our
results are presented in the context of a transmon in a one dimensional
microwave waveguide, but the conclusions also apply to optical systems.