While a propagating state of light can be generated with arbitrary squeezing by pumping a parametric resonator, the intra-resonator state is limited to 3 dB of squeezing. Here, we implementa reservoir engineering method to surpass this limit using superconducting circuits. Two-tone pumping of a three-wave-mixing element implements an effective coupling to a squeezed bath which stabilizes a squeezed state inside the resonator. Using an ancillary superconducting qubit as a probe allows us to perform a direct Wigner tomography of the intra-resonator state. The raw measurement provides a lower bound on the squeezing at about 6.7±0.2 dB below the zero-point level. Further, we show how to correct for resonator evolution during the Wigner tomography and obtain a squeezing as high as 8.2±0.8 dB. Moreover, this level of squeezing is achieved with a purity of −0.4±0.4 dB.
A crucial limit to measurement efficiencies of superconducting circuits comes from losses involved when coupling to an external quantum amplifier. Here, we realize a device circumventingthis problem by directly embedding a two-level artificial atom, comprised of a transmon qubit, within a flux-pumped Josephson parametric amplifier. Surprisingly, this configuration is able to enhance dispersive measurement without exposing the qubit to appreciable excess backaction. This is accomplished by engineering the circuit to permit high-power operation that reduces information loss to unmonitored channels associated with the amplification and squeezing of quantum noise. By mitigating the effects of off-chip losses downstream, the on-chip gain of this device produces end-to-end measurement efficiencies of up to 80 percent. Our theoretical model accurately describes the observed interplay of gain and measurement backaction, and delineates the parameter space for future improvement. The device is compatible with standard fabrication and measurement techniques, and thus provides a route for definitive investigations of fundamental quantum effects and quantum control protocols.
We analyze a modified Bose-Hubbard model, where two cavities having on-site Kerr interactions are subject to two-photon driving and correlated dissipation. We derive an exact solutionfor the steady state of this interacting driven-dissipative system, and use it show that the system permits the preparation and stabilization of pure entangled non-Gaussian states, so-called entangled cat states. Unlike previous proposals for dissipative stabilization of such states, our approach requires only a linear coupling to a single engineered reservoir (as opposed to nonlinear couplings to two or more reservoirs). Our scheme is within the reach of state-of-the-art experiments in circuit QED.
An entangled quantum state of two or more particles or objects exhibits some of the most peculiar features of quantum mechanics. Entangled systems cannot be described independentlyof each other even though they may have an arbitrarily large spatial separation. Reconciling this property with the inherent uncertainty in quantum states is at the heart of some of the most famous debates in the development of quantum theory. Nonetheless, entanglement nowadays has a solid theoretical and experimental foundation, and it is the crucial resource behind many emerging quantum technologies. Entanglement has been demonstrated for microscopic systems, such as with photons, ions, and electron spins, and more recently in microwave and electromechanical devices. For macroscopic objects, however, entanglement becomes exceedingly fragile towards environmental disturbances. A major outstanding goal has been to create and verify the entanglement between the motional states of slowly-moving massive objects. Here, we carry out such an experimental demonstration, with the moving bodies realized as two micromechanical oscillators coupled to a microwave-frequency electromagnetic cavity that is used to create and stabilise the entanglement of the centre-of-mass motion of the oscillators. We infer the existence of entanglement in the steady state by combining measurement of correlated mechanical fluctuations with an analysis of the microwaves emitted from the cavity. Our work qualitatively extends the range of entangled physical systems, with implications in quantum information processing, precision measurement, and tests of the limits of quantum mechanics.
The standard quantum limit constrains the precision of an oscillator position measurement. It arises from a balance between the imprecision and the quantum back-action of the measurement.However, a measurement of only a single quadrature of the oscillator can evade the back-action and be made with arbitrary precision. Here we demonstrate quantum back-action evading measurements of a collective quadrature of two mechanical oscillators, both coupled to a common microwave cavity. The work allows for quantum state tomography of two mechanical oscillators, and provides a foundation for macroscopic mechanical entanglement and force sensing beyond conventional quantum limits.
We use a reservoir engineering technique based on two-tone driving to generate and stabilize a quantum squeezed state of a micron-scale mechanical oscillator in a microwave optomechanicalsystem. Using an independent backaction evading measurement to directly quantify the squeezing, we observe 4.7±0.9 dB of squeezing below the zero-point level, surpassing the 3 dB limit of standard parametric squeezing techniques. Our measurements also reveal evidence for an additional mechanical parametric effect. The interplay between this effect and the optomechanical interaction enhances the amount of squeezing obtained in the experiment.
In this article we propose a protocol to autonomously stabilize a Fock state within a circuit QED architecture that doesn’t recourse to any ac-drive nor pulse. This protocol isrealized with a microwave cavity driven by a Josephson junction and coupled to quantum engineered reservoir. It relies on two important ingredients. First, a high-impedance resonator to enable photon-dependent driving used as the cavity. Such device has recently been implemented in circuit QED platforms and removes the need for periodic driving. Second, on an auxiliary, low-quality factor cavity used as a engineered environment. Its damping rate must be scaled with respect to the Josephson energy and the main cavity quality factor in order to stabilize a quantum state. A second protocol, based on the same platform, is used to produce a flying qubit.
We present an impedance engineered Josephson parametric amplifier capable of providing bandwidth beyond the traditional gain-bandwidth product. We achieve this by introducing a positivelinear slope in the imaginary component of the input impedance seen by the Josephson oscillator using a λ/2 transformer. Our theoretical model predicts an extremely flat gain profile with a bandwidth enhancement proportional to the square root of amplitude gain. We experimentally demonstrate a nearly flat 20 dB gain over a 640 MHz band, along with a mean 1-dB compression point of -110 dBm and near quantum-limited noise. The results are in good agreement with our theoretical model.
We discuss a general method for constructing nonreciprocal, cavity-based photonic devices, based on matching a given coherent interaction with its corresponding dissipative counterpart;our method generalizes the basic structure used in the theory of cascaded quantum systems. In contrast to standard interference-based schemes, our approach allows directional behavior over a wide bandwidth. We show how it can be used to devise isolators and directional, quantum-limited amplifiers. We discuss in detail how this general method allows the construction of a directional, noise-free phase-sensitive amplifier which is not limited by any fundamental gain-bandwidth constraint. Our approach is particularly well-suited to implementations using superconducting microwave circuits and optomechanical systems.
We describe a new kind of phase-preserving quantum amplifier which utilizes dissipative interactions in a parametrically-coupled three-mode bosonic system. The use of dissipative interactionsprovides a fundamental advantage over standard cavity-based parametric amplifiers: large photon number gains are possible with quantum-limited added noise, with no limitation on the gain-bandwidth product. We show that the scheme is simple enough to be implemented both in optomechanical systems and in superconducting microwave circuits.