We propose a scheme for implementing cross Kerr nonlinearity between two superconducting transmission line resonators (TLR) via their interaction with a coupler which is constructed by two superconducting charge qubits connected to each other via a superconducting quantum interference device. When suitably driven, the coupler can induce very strong cross phase modulation (XPM) between the two TLRs due to its N-type level structure and the consequent electromagnetically induced transparency in its lowest states. The flexibility of our design can lead to various inter-TLR coupling configurations. The obtained cross Kerr coefficient is large enough to allow many important quantum operations in which only few photons are involved. We further show that this scheme is very robust against the fluctuations in solid state circuits. Our numerical calculations imply that the absorption and dispersion resulted from the decoherence of the coupler are very small compared with the strength of the proposed XPM.
Entangled microwave photons form a fundamental resource for quantum information processing and sensing with continuous variables. We use a low-loss Josephson metamaterial comprising superconducting, non-linear, asymmetric inductive elements to generate frequency-entangled photons from vacuum fluctuations at a rate of 2 giga entangled bits per second spanning over 4 GHz bandwidth. The device is operated as a traveling wave parametric amplifier under Kerr-relieving biasing conditions. Furthermore, we realize the first successfully demonstration of single-mode squeezing in such devices -- $3.1\pm…
Nonlinear Feedback in Josephson Circuit Optimization: Application to a Kerr-Reversal JTWPA
Department of Applied Science and Technology, Politecnico di Torino（都灵理工大学应用科学与技术系）；Quantum Metrology and Nanotechnology Division, Istituto Nazionale di Ricerca Metrologica（意大利国家计量科学研究院量子计量与纳米技术部）；Department of Engineering, University of Palermo（巴勒莫大学工程学院）
Josephson-junction based parametric amplifiers have become a ubiquitous component in superconducting quantum machines. Although parametric amplifiers regularly achieve near-quantum limited performance, they have many limitations, including low saturation powers, lack of directionality, and narrow bandwidth. The first is believed to stem from the higher order Hamiltonian terms endemic to Josephson junction circuits, and the latter two are direct consequences of the nature of the parametric interactions which power them. In this work, we attack both of these issues. First, we have designed a new…
We propose a scheme for enhancing the optomechanical coupling between microwave and mechanical resonators by up to seven orders of magnitude to the ultrastrong coupling limit in a circuit optomechanical setting. The tripartite system considered here consists of a Josephson junction Cooper-pair box that mediates the coupling between the microwave cavity and the mechanical resonator. The optomechanical coupling can be modified by tuning the gate charge and the magnetic flux bias of the Cooper-pair box which in turn affect the Josephson capacitance of the Cooper-pair box. We additionally show tha…
While the theoretical studies in waveguide quantum electrodynamics predominate with single-photon and two-photon Fock state (photon number states) input, the experiments are primarily carried out using a faint coherent light. We create a theoretical toolbox to compare and contrast linear and nonlinear light scattering by a two-level or a three-level emitter embedded in an open waveguide carrying Fock state or coherent state inputs. We identify rules to compare light transport properties, the Kerr, and cross-Kerr nonlinearities of the medium for the two types of inputs. A generalized descriptio…
We present a detailed experimental and theoretical analysis of the dispersion and non-linear Kerr frequency shifts of plasma modes in a one-dimensional Josephson junction chain containing 500 SQUIDs in the regime of weak nonlinearity. The measured low-power dispersion curve agrees perfectly with the theoretical model if we take into account the Kerr renormalisation of the bare frequencies and the long-range nature of the island charge screening by a remote ground plane. We measured the self- and cross-Kerr shifts for the frequencies of the eight lowest modes in the chain. We compare the measur…
Josephson meta-materials have recently emerged as very promising platform for superconducting quantum science and technologies. Their distinguishing potential resides in ability to engineer them at sub-wavelength scales, which allows complete control over wave dispersion and nonlinear interaction. In this article we report a versatile Josephson transmission line with strong third order nonlinearity which can be tuned from positive to negative values, and suppressed second order non linearity. As an initial implementation of this multipurpose meta-material, we operate it to demonstrate reversed…
Continuous-variable systems realized in high-coherence microwave cavities are a promising platform for quantum information processing. While strong dynamic nonlinear interactions are desired to implement fast and high-fidelity quantum operations, static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Here we study theoretical models of nonlinear oscillators describing superconducting quantum circuits with asymmetric Josephson-junctions loops. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff…
In this proposal, we present an experimental setup based on superconducting circuits and Josephson junctions to explore the modification of Josephson coefficient in the presence of external magnetic field due to vacuum polarization of quantum electrodynamics. This robust experiment can be considered as one of the few possible chances to observe the fine quantum field theory corrections in the low energy regimes in condensed matter systems. It can also be a new check for the universality of Josephson constant which is important in metrology. We will expect the signal to noise ratio of the read-…
Quantum computers with Kerr-nonlinear parametric oscillators (KPOs) have recently been proposed by the author and others. Quantum computation using KPOs is based on quantum adiabatic bifurcations of the KPOs, which lead to quantum superpositions of coherent states, such as Schrodinger cat states. Therefore, these quantum computers are referred to as "quantum bifurcation machines (QbMs)." QbMs can be used for qauntum adiabatic optimization and universal quantum computation. Superconducting circuits with Josephson junctions, Josephson parametric oscillators (JPOs) in particular, are promising fo…
The use of a Kerr nonlinearity to generate squeezed light is a well-known way to surpass the quantum noise limit along a given field quadrature. Nevertheless, in the most common regime of weak nonlinearity, a single Kerr resonator is unable to provide the proper interrelation between the field amplitude and squeezing required to induce a sizable deviation from Poissonian statistics. We demonstrate experimentally that weakly coupled bosonic modes allow exploration of the interplay between squeezing and displacement, which can give rise to strong deviations from the Poissonian statistics. In par…
Microwave parametric amplifiers based on Josephson junctions have become a key component of many quantum information experiments. One key limitation which has not been well predicted by theory is the gain saturation behavior which determines its ability to process large amplitude signals. The typical explanation for this behavior in phase-preserving amplifiers based on three-wave mixing is pump depletion, in which the consumption of pump photons to produce amplification results in a reduction in gain. However, in this work we present experimental data and theoretical calculations showing that …
We explore amplification and cross-Kerr nonlinearity by a three-level emitter (3LE) embedded in a waveguide and driven by two light beams. The coherent amplification and cross-Kerr nonlinearity were demonstrated in recent experiments, respectively, with a V and a ladder-type 3LE coupled to an open superconducting transmission line carrying two microwave fields. Here, we consider $Λ$, V, and ladder-type 3LE, and compare the efficiency of coherent and incoherent amplification as well as the magnitude of the cross-Kerr phase shift in all three emitters. We apply the Heisenberg-Langevin equations …
We propose a deterministic scheme for teleporting an unknown qubit through continuous-variable entangled states in superconducting circuits. The qubit is a superconducting two-level system and the bipartite quantum channel is a photonic entangled coherent state between two cavities. A Bell-type measurement performed on the hybrid state of solid and photonic states brings a discrete-variable unknown electronic state to a continuous-variable photonic cat state in a cavity mode. This scheme further enables applications for quantum information processing in the same architecture of circuit-QED suc…
The coupling between a superconducting qubit and a control line inevitably results in radiative decay of the qubit into the line. We propose a Josephson quantum filter (JQF), which protects the data qubit (DQ) from radiative decay through the control line without reducing the gate speed on DQ. JQF consists of a qubit strongly coupled to the control line to DQ, and its working principle is a subradiance effect characteristic to waveguide quantum electrodynamics setups. JQF is a passive circuit element and is therefore suitable for integration in a scalable superconducting qubit system.
Photon-pressure coupling between two superconducting circuits is a promising platform for investigating radiation-pressure coupling in novel parameter regimes and for the development of radio-frequency (RF) quantum photonics and quantum-limited RF sensing. So far, the intrinsic Josephson nonlinearity of photon-pressure coupled circuits has not been considered a potential resource for enhanced devices or novel experimental schemes. Here, we implement photon-pressure coupling between a RF circuit and a microwave cavity containing a superconducting quantum interference device (SQUID) which can be…
We study the effect of Kerr nonlinearity in quantum thermal machines having a Kerr-nonlinear oscillator as working substance and operating under the ideal quantum Otto cycle. We first investigate the efficiency of a Kerr-nonlinear heat engine and show that by varying the Kerr-nonlinear strength the efficiency surpasses in up to 2.5 times the efficiency of a quantum harmonic oscillator Otto engine. Moreover, the Kerr-nonlinearity makes the coefficient of performance of the Kerr-nonlinear refrigerator to be as large as 3 times the performance of quantum harmonic oscillator Otto refrigerators. Th…
Non-linearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA), the only device in which the quantum limit has so far been achieved at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) non-linearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type non-linearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction non-linearity in the linear response regim…
Two-photon coupling via Josephson element II: Interaction dressing, cross-Kerr coupling, and limits of low-energy bosonic model
Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine（乌克兰国家科学院博戈留博夫理论物理研究所）；Institute of Physics of the National Academy of Sciences（乌克兰国家科学院物理研究所）
High quality factors, strong nonlinearities, and extensive design flexibility make superconducting circuits an ideal platform to investigate synchronization phenomena deep in the quantum regime. Recently~\cite{Loerch-2017}, it was predicted that energy quantization and conservation can block the synchronization of two identical, weakly coupled nonlinear self-oscillators. Here we propose a Josephson junction circuit realization of such a system along with a simple homodyne measurement scheme to observe this effect. We also show that at finite detuning, where phase synchronization takes place, t…
While coherently-driven Kerr microcavities have rapidly matured as a platform for frequency comb formation, such microresonators generally possess weak Kerr coefficients; consequently, triggering comb generation requires millions of photons to be circulating inside the cavity. This suppresses the role of quantum fluctuations in the comb's dynamics. In this paper, we realize a minimal version of coherently-driven Kerr-mediated microwave frequency combs in the circuit QED architecture, where the quantum vacuum's fluctuations are the primary limitation on comb coherence. We achieve a comb phase c…
A Tunable, Modeless, and Hybridization-free Cross-Kerr Coupler for Miniaturized Superconducting Qubits
Kavli Nanoscience Institute and Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology（加州理工学院卡尔弗纳米科学研究所和托马斯·J·沃森Sr.应用物理实验室）；Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）
Circuit quantum electrodynamics (QED) studies the interaction of artificial atoms, open transmission lines and electromagnetic resonators fabricated from superconducting electronics. While the theory of an artificial atom coupled to one mode of a resonator is well studied, considering multiple modes leads to divergences which are not well understood. Here, we introduce a first-principles model of a multimode resonator coupled to a Josephson junction atom. Studying the model in the absence of any cutoff, in which the coupling rate to mode number $n$ scales as $\sqrt{n}$ for $n$ up to $\infty$, …
In recent years, superconducting qubits show great potential in quantum computation. Hence, microwave photons become very interesting qubits for quantum information processing assisted by superconducting quantum computation. Here, we present the first protocol for the entanglement concentration on microwave photons, resorting to the cross-Kerr effect in circuit quantum electrodynamics (QED). Two superconducting transmission line resonators (TLRs) coupled to superconducting molecule with the N-type level structure induce the effective cross-Kerr effect for realizing the quantum nondemolition (Q…
Quantum Kerr-nonlinear oscillator is a paradigmatic model in cavity and circuit quantum electrodynamics, and quantum optomechanics. We theoretically study the echo phenomenon in a single impulsively excited ("kicked") Kerr-nonlinear oscillator. We reveal two types of echoes, "quantum" and "classical" ones, emerging on the long and short time-scales, respectively. The mechanisms of the echoes are discussed, and their sensitivity to dissipation is considered. These echoes may be useful for studying decoherence processes in a number of systems related to quantum information processing.
Quantum states can be stabilized in the presence of intrinsic and environmental losses by either applying active feedback conditioned on an ancillary system or through reservoir engineering. Reservoir engineering maintains a desired quantum state through a combination of drives and designed entropy evacuation. We propose and implement a quantum reservoir engineering protocol that stabilizes Fock states in a microwave cavity. This protocol is realized with a circuit quantum electrodynamics platform where a Josephson junction provides direct, nonlinear coupling between two superconducting wavegu…
Single-mode Josephson junction-based parametric amplifiers are often modeled as perfect amplifiers and squeezers. We show that, in practice, the gain, quantum efficiency, and output field squeezing of these devices are limited by usually neglected higher-order corrections to the idealized model. To arrive at this result, we derive the leading corrections to the lumped-element Josephson parametric amplifier of three common pumping schemes: monochromatic current pump, bichromatic current pump, and monochromatic flux pump. We show that the leading correction for the last two schemes is a single K…
We review recent advances in the research on quantum parametric phenomena in superconducting circuits with Josephson junctions. We discuss physical processes in parametrically driven tunable cavity and outline theoretical foundations for their description. Amplification and frequency conversion are discussed in detail for degenerate and non-degenerate parametric resonance, including quantum noise squeezing and photon entanglement. Experimental advances in this area played decisive role in successful development of quantum limited parametric amplifiers for superconducting quantum information te…
We report a first-principles study of the driven dissipative dynamics for Kerr oscillators in the mesoscopic regime. This regime is characterized by large Kerr nonlinearity, realized here using the nonlinear kinetic inductance of a large array of Josephson junctions. The experimentally measured nonlinear resonance lineshapes of the junction array modes show significant deviations from steady-state numerical predictions, and necessitate time-dependent numerical simulations indicative of strong measurement-induced dephasing in the system arising from the large cross-Kerr effect between array mod…
Quantum-limited Josephson parametric amplifiers are crucial components in circuit QED readout chains. The dynamic range of state-of-the-art parametric amplifiers is limited by signal-induced Stark shifts that detune the amplifier from its operating point. Using a Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) as an active component, we show the ability to in situ tune the device flux and pump to a dressed Kerr-free operating point, which provides a 10-fold increase in the number of photons that can be processed by our amplifier, compared to the nominal working point. Our propos…
Thin films of disordered superconductors such as titanium nitride (TiN) exhibit large kinetic inductance (KI), high critical temperature, and large quality factors at the single-photon level. KI nonlinearity can be exploited as an alternative to Josephson junctions for creating novel nonlinear quantum devices with the potential to operate at higher frequencies and at elevated temperatures. We study a means of magnifying KI nonlinearity by confining the current density of resonant electromagnetic modes in nanowires with a small volume $V \simeq 10^{-4}\text{um}^3$. Using this concept, we realiz…
We review recent developments concerning non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. We start with quantum impurity models summarizing the effect of dissipation and of driving the system. We mention theoretical and experimental efforts to characterize these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect is characterized by a renormalized light-frequency and a peak in the Rayleigh elastic transmission of a …
Nonlinear Josephson circuits play a crucial role in the growing landscape of quantum information and technologies. The typical circuits studied in this field consist of qubits, whose anharmonicity is much larger than their linewidth, and also of parametric amplifiers, which are engineered with linewidths of tens of MHz or more. The regime of small anharmonicity but also narrow linewidth, corresponding to the dynamics of a high-$Q$ Duffing oscillator, has not been extensively explored using Josephson cavities. Here, we use two-tone spectroscopy to study the susceptibility of a strongly driven h…
