Session V51: Nonreciprocal Devices with Circuits and Optomechanics

Experimental demonstrations of nonreciprocal microwave amplification

Many superconducting quantum circuits rely on microwave photons to measure or couple quantum systems, such as superconducting qubits or micro-mechanical resonators. The ability to process microwave fields with minimal degradation is crucial to the observation of truly quantum behavior. It finds applications in quantum computing, quantum feedback or position measurements. However, to date, there is no system that is able to achieve an ideal measurement of such microwave fields. Indeed, parametric amplifiers, while intrinsically quantum-limited, reflect the amplified signal and back-act onto the system under test, requiring a circulator to break reciprocity and separate incoming and outgoing fields. Unfortunately, conventional ferrite circulators are ultimately incompatible with microwave quantum circuits due to size, loss and magnetic field. In this talk I will describe the development of a new generation of quantum-limited, nonreciprocal microwave amplifiers [1,2]. Using microwave drives, the experimentalist turns on a set of parametric interactions between the modes of a microwave resonant circuit, allowing one to choose in-situ between different modes of operation: frequency conversion, circulation or any combination of reciprocal/nonreciprocal and phase sensitive/preserving amplification. With low insertion loss (\textless 0.5dB), high return loss (\textless -15dB), high directivity (\textless -15dB) and high gain (\textgreater 18dB), these devices are a new tool for quantum measurements. [1] L. Ranzani and J. Aumentado, New J. Phys. 17, 023024 (2015) [2] F. Lecocq., et al, `Nonreciprocal microwave signal processing with a Field-Programmable Josephson Amplifier', Arxiv (2016)   

Design of multimode parametric devices for quantum-limited directional amplification

Parametric interactions provide near quantum-limited amplification of weak microwave signals, which results in enhanced measurement fidelity of quantum information circuits. While conventional Josephson parametric amplifiers consist of a resonator driven by a single strong microwave pump, it was recently realized that multiple parametric interactions can be combined to provide novel functionalities, such as nonreciprocal propagation and directional amplification. Such operations can be implemented in a single device by simultaneously turning on a set of parametric processes between multiple resonant modes. In this talk we are going to discuss the design of multi-mode parametric devices and their signal and noise properties. We will begin with the basic building modules consisting of either two of three mutually coupled modes and connect them in a modular fashion to build more complex coupling topologies. The resulting devices provide programmable routing and quantum-limited amplification of microwave signals with low backaction on the device under test.   

Minimal models of nonreciprocity with biharmonic pumps

Nonreciprocal transmission and amplification has emerged as a new and important outlook in the field of quantum-limited detection. There have recently been multiple proposals aimed at realizing on-chip nonreciprocity at acoustic, microwave and optical frequencies. In this talk, we present a general scheme for nonreciprocal photon dynamics that emphasizes minimality of both the amplification mode space and parametric pumping -- a feature especially desirable for hardware-efficient and scalable implementations of nonreciprocal detection protocols. We focus on a three-mode parametrically coupled system pumped with a time-asymmetric biharmonic pump and show how this system can be readily configured to realize gainless photon circulation, and phase-preserving or phase-sensitive directional amplification. Explicit frequency-dependent calculations within this minimal paradigm highlight the separation of amplification and directionality bandwidths, generic to such schemes.   

Non-reciprocal quantum interactions and devices via autonomous feed-forward

In a recent work [A. Metelmann and A. A. Clerk, Phys.~Rev.~X {\bf 5}, 021025 (2015)], a general reservoir-engineering approach for generating non-reciprocal quantum interactions and devices was described. We present how in many cases this general recipe can be viewed as an example of autonomous feed-forward: the full dissipative evolution is identical to the unconditional evolution in a setup where an observer performs an ideal quantum measurement of one system, and then uses the results to drive a second system. We also extend the application of this approach to non-reciprocal quantum amplifiers, showing the added functionality possible when using two engineered reservoirs. In particular, we demonstrate how to construct an ideal phase-preserving cavity-based amplifier which is full non-reciprocal, quantum-limited and free of any fundamental gain-bandwidth constraint.   

Using topology and parametric driving to design robust, non-reciprocal quantum amplifiers

Among the many motivations for the study of topological photonic systems is the possibility to realize new kinds of robust non-reciprocal devices.~ Here, we discuss a fundamentally new kind of topologically protected device, an amplifier based on exploiting the unstable edge states that arise when one combines a synthetic gauge field with parametric driving in a coupled cavity array.~ By coupling to input/output waveguides, we obtain a quantum-limited, non-reciprocal amplifier that shows robustness both against backscattering \textit{and} against internal losses.~ We also discuss the generation of squeezed light in such a system, as well as quantum heating effects and the emergence of an effective temperature.~ Our system could be realized in a variety of settings, including arrays of coupled superconducting microwave cavities where time-reversal symmetry is broken (e.g. Ref. [1]). [1] Brandon M.Anderson, Ruichao Ma, Clai Owens, David I.Schuster, Jonathan Simon. arXiv.1605.03177   

Nonreciprocal Signal Routing in an Active Quantum Network

As superconductor quantum technologies are moving towards large-scale integrated circuits, a robust and flexible approach to routing photons at the quantum level becomes a critical problem. Active circuits, which contain driven linear or non-linear elements judiciously embedded in the circuit offer a viable solution. We present a general strategy for routing non-reciprocally quantum signals between two sites of a given lattice of resonators, implementable with existing superconducting circuit components. Our approach makes use of a dual lattice of superconducting non-linear elements on the links connecting the nodes of the main lattice. Solutions for spatially selective driving of the link-elements can be found, which optimally balance coherent and dissipative hopping of microwave photons to non-reciprocally route signals between two given nodes. In certain lattices these optimal solutions are obtained at the exceptional point of the scattering matrix of the network. The presented strategy provides a design space that is governed by a dynamically tunable non-Hermitian generator that can be used to minimize the added quantum noise as well.   

Optomechanical nonreciprocity: Minimal conditions for ideal isolation and circulation

Artificial systems that allow a specifically tailored flow of electromagnetic radiation are important for the design of nonreciprocal components such as isolators and circulators as well as multimode systems exhibiting nontrivial topological transport of photons. A possible route to breaking reciprocity without a magnetic field relies on a spatiotemporal modulation of the refractive index, which is straightforwardly achieved in optomechanical systems. We derive the minimal requirements to create nonreciprocity in a wide class of optomechanical systems that involve a pair of optical modes parametrically coupled to a mechanical mode, and can be implemented for both microwave and optical photons. These conditions highlight the importance of an appropriately tailored phase difference between the intracavity bias photons of the two optical modes. Suitable modal symmetry with respect to coupling channels allows near-ideal isolation and circulation over tunable bandwidths. We illustrate these general principles in an optomechanical ring resonator, demonstrating up to 10 dB optical isolation at telecom wavelengths. In line with our theoretical model, nonreciprocal transmission is preserved in the case of non-degenerate modes and also yields unidirectional parametric amplification.   

Demonstration of nonreciprocity in a microwave cavity optomechanical circuit

The ability to engineer nonreciprocal interactions is essential for many applications including quantum signal processing and quantum transduction. While attributes such as high efficiency and low added noise are always beneficial, for quantum applications these metrics are crucial. Here we present recent experimental results on a parametric, nonreciprocal microwave circuit based on the optomechanical interaction between a superconducting microwave resonator and a mechanically compliant vacuum gap capacitor. Unlike standard Faraday-based circulators, this parametric interaction does not require magnetic fields, and the direction of circulation can be controlled dynamically in situ. Looking forward, such devices could enable programmable, high-efficiency connections between disparate nodes of a quantum network.   

Nonreciprocal frequency conversion in a multimode microwave optomechanical circuit

Nonreciprocal devices such as isolators, circulators, and directional amplifiers are pivotal to quantum signal processing with superconducting circuits. In the microwave domain, commercially available nonreciprocal devices are based on ferrite materials. They are barely compatible with superconducting quantum circuits, lossy, and cannot be integrated on chip. Significant potential exists for implementing non-magnetic chip-scale nonreciprocal devices using microwave optomechanical circuits. Here we demonstrate a possibility of nonreciprocal frequency conversion in a multimode microwave optomechanical circuit using solely optomechanical interaction between modes. The conversion scheme and the results reflecting the actual progress on the experimental implementation of the scheme will be presented.   

Enhanced qubit readout via engineering of subpoissonian qubit relaxation

Qubit readout is often performed by mapping the microscopic qubit state to a macroscopic signal using available experimental tools. In many cases, however, the physical dynamics of the readout apparatus may be engineered to further optimize the measurement procedure [1,2]. In recent years, several works have shown that qubit readout fidelity can be enhanced by forcing the qubit to relax through auxiliary intermediate states. The usual rationale for the use of these intermediate states is that 1) they couple more strongly to the readout device and/or that 2) they are longer-lived than the original qubit excited state. Here we theoretically show that the use of intermediate states can enhance readout even when neither of these effects is present. More precisely, we show that the addition of intermediate states leads to subpoissonian relaxation statistics which strongly reduce the randomness of the relaxation process and thereby significantly increase readout fidelity. Our work highlights a previously unappreciated aspect of qubit readout engineering and paves the way for further optimization of existing qubit readout schemes. REFERENCES: [1] D'Anjou \& Coish, Phys. Rev. A 89 012313 (2014); [2] D'Anjou, Kuret, Childress \& Coish, Phys. Rev. X 6 011017 (2016).   

A photonic quantum diode using superconducting qubits

Strong coupling between quantum emitters and photons in a one-dimensional waveguide is a key element for waveguide quantum electrodynamics (QED), a regime of great interest for universal quantum computing and communication. The basic ingredient of waveguide QED, a single two-level system (TLS) in a waveguide, can behave as a mirror whose transparency depends on the frequency and power of the incoming radiation. In this work we present our experimental results on the system consisting of two superconducting transmon-like qubits embedded in a copper waveguide realizing an analogue of a Fabry-P\'erot interferometer. Two external coils provide control over the flux threading the transmons, thus allowing us to individually tune their transition frequencies and to change the effective distance between the mirrors {\it in situ}. By exploiting the quantum properties of the mirrors we achieve new functionalities of the interferometer. Most notably, when the TLSs are asymmetrically detuned with respect to the frequency of the incident radiation, the system exhibits previously unobserved non-reciprocal behavior and operate as a microscopic light diode.