Session E28: Experiment and Theory of Quantum Input-output Networks

Experimental approaches to quantum input-output networks

Since the development of input-output and cascaded quantum optic theory in the 1980s and 90s, much progress has been made in expanding this approach to far more complex networks. In particular, it is now possible to model many modular components simultaneously connected in series, parallel, and feeding back on each other via far-field quantum and/or classical signals. In this talk, I will review some of the experimental work in free-space optics, integrated photonics, and superconducting microwave systems that have leveraged these techniques to model networks beyond simple cascaded interconnections. Looking to the future, I believe that these modeling techniques will have an even greater experimental impact as they evolve and hybridize with other approaches in quantum and classical electronics, for example.   

How to model almost any quantum experiement: a tutorial on the SLH formalism

Large scale communication and computing technologies are integral to modern life. The ubiquity of these technologies is due to the emergence of large scale integrated electronic circuits, which in turn are enabled by mature and powerful tools for circuit design automation and analysis (e.g., SPICE, gEDA). For quantum technologies there is no agreed upon counterpart to these tools. An important next step, to realizing large scale quantum technologies, will require the development of sophisticated modeling and analysis tools for quantum hardware that parralell classical simulation and design tools – e.g., these tools should incorporate useful abstractions, such as modularity, networks and hierarchy, and enable coordination between high-level software and algorithmic needs and low-level hardware design.

In this tutorial style talk I will summarize progress in developing such a modeling framework, known as the SLH framework. Importantly, it incorporates many of the useful abstractions listed above, and thus has the potential to form the foundation for developing tools that enable design and analysis of large scale assemblies of quantum coherent systems.

This talk is based on the reivew https://arxiv.org/abs/1611.00375 or Advances in Physics: X, Vol. 2, 784 (2017).   

Single-qubit Probe of a 1D Transmission Line Modified by Two Qubit Mirrors

A qubit that is strongly coupled to a 1D transmission line is known to reflect single-photon excitations, acting as a highly-reflecting qubit mirror. The presence of a qubit mirror modifies the mode environment in the 1D transmission line because the line’s right and left propagating modes are no longer independent. We experimentally probe the modified mode environment due to two such qubit mirrors arranged in a cavity-like configuration by exciting a third qubit—a probe qubit—that is also coupled to the transmission line. The relaxation of the probe qubit is enhanced / suppressed by the modified environment of the transmission line. We will discuss the connection of these results to the fluctuation-dissipation theorem.   

Dissipation-driven Entangled State Preparation of Two Qubits Coupled to a Transmission Line

Pairwise entanglement of superconducting qubits is conventionally achieved through either direct capacitive or inductive coupling, or mediated by a cavity photon mode. Here, we instead study multiple transmon qubits coupled to a continuum of field modes along a transmission line. We experimentally explore the use of correlated decay to mediate dissipation-driven entanglement of a pair of qubits.   

Coherent quantum effects in networks of degenerate optical parametric oscillators

Recent experiments have shown that networks of degenerate optical parametric oscillators (OPOs) can encode and approximately solve combinatorial optimization problems. While these experiments presently operate in a regime well described by semiclassical models, it is interesting to ask whether coherent quantum effects such as entanglement or non-Gaussianity due to strong nonlinearities could qualitatively or quantitatively change the mechanism of the “solution” process. Using the SLH formalism for quantum input-output theory, we describe a general quantum network model for multiple degenerate OPOs connected via arbitrary beamsplitter couplings [1]. For a small number of oscillators, we numerically compare the solution process of this model in the mean-field limit against the extremely quantum regime where two-photon loss dominates linear loss in the individual OPOs.
[1] T. Onodera, E. Ng, and H. Mabuchi, doi: 10.1364/QIM.2017.QW3B.2 (2017).   

Photon Capture into a Bound State in the Continuum of a Waveguide-Qubit System

We show that it is possible to excite an exact bound state in the continuum (BIC) of a waveguide-qubit system by using a two photon pulse. The existence of such BIC states in the single photon sector is well-known but populating these states with an injected pulse is problematic. We study photon capture-- two photons are injected but only one comes out because the other is trapped in the BIC-- in two geometries, a single qubit in a semi-infinite waveguide or two qubits in an infinite waveguide. Photon capture proceeds by inelastic scattering due to the nonlinearity of the qubit and is suppressed for small qubit-qubit or qubit-mirror separation. Thereby, the system should in fact be in the non-Markovian regime due to non-negligible photon delay times. We investigate this effect in both a continuum model with linear dispersion and a coupled cavity array. In the case of two qubits, one outcome is heralded generation of very long-lived entanglement.   

Routing of propagating microwave phonons at the quantum level

It has recently been shown that surface acoustic waves (SAWs) can interact with artificial atoms at the quantum level. This has opened up new possibilities for utilizing SAWs (phonons) instead of electromagnetic waves (photons). Here we explore routing of propagating phonons using SAW scattering from an artificial atom, an analogy to previous experiments performed using photons in quantum optics. The SAW phonons have a five orders of magnitude slower speed than photons in vacuum, which results in ample time for inflight manipulations of the propagating phonons. The artificial atom can be tuned on or off resonance with the incident SAW field using an external magnetic field or the Autler-Townes splitting, and thus the reflection and transmission of the SAW field can be controlled. On resonance, we observe a 96 % extinction in the transmission of the low power continuous signal. The possibilities to also route short (100 ns) pulses further enables experiments where an acoustic pulse is captured between two artificial atoms and released in a controlled way.   

Quantum Op-amp and Functionalities

Quantum amplifier is an essential component in quantum information technology. In [Phys. Rev. Applied, 5, 044012, 2016], I presented the control scheme for improving the sensitivity of a general phase-insensitive amplifier via coherent (i.e., measurement-free) feedback. In this presentation I show that this feedback amplification scheme can be further extended and applied to construct systems that produce several useful functionalities; this is exactly a quantum version of op-amp in electrical circuits. For example in quantum optics, by feedback-connecting a high-gain non-degenerate parametric amplifier with an optical cavity, one can devise an integrator for itinerant fields, which can be used to improve the detection efficiency of those fields. Also I show that a similar feedback amplification scheme yields a quantum version of active filters such as a Butterworth filter; thanks to the steep roll-off characteristic in frequency, such an active filter enhances the capacity of a quantum communication channel. Another example is that a feedback connection of some high-gain amplifiers produces a robust nonreciprocal amplifier, which enables measurement of the state of a superconducting system while protecting it from the back-action noise of the amplifier.   

Quantum Fisher Information of non-Hermitian sensing near exceptional points

Exceptional points are points in the parameter space of a non-hermitian system when two eigenvectors of the hamiltonian coalesce. Eigenvalue change of the non-hermitian system near exceptional points can have abnormal dependence on external perturbation, which is recently proposed and demonstrated as a way to enhance the sensitivity of resonant frequency shifts to small external signal. However, physical realization of non-hermitian system unavoidably introduces noises accompanying loss and gain to a hermitian system, which may potentially decrease the signal-to-noise ratio. To understand the combined effect of exceptional points on both sensitivity and signal-to-noise ratio, we computed the quantum fisher information of typical non-hermitian sensing processes, whose inverse give us a lower bound of the estimation error. Our work provides not only a fundamental bound for the sensing limit using exceptional points, but also a design tool to achieve the same scaling as the fundamental sensing limit.   

Multiphoton Scattering Tomography with Coherent States

We have proposed an experimental procedure to reconstruct the scattering matrix of an unknown quantum system interacting with propagating photons. Our method requires coherent state laser or microwave inputs and homodyne detection at the scatterer's output, and provides simultaneous information about multiple ---elastic and inelastic--- segments of the scattering matrix. The method is resilient to detector noise and its errors can be made arbitrarily small by combining experiments at various laser powers. Finally, we show that the tomography of scattering has to be performed using pulsed lasers to efficiently gather information about the nonlinear processes in the scatterer. The techniques in this work are general, allowing a full characterization of how a small quantum system interacts with the environment, and it is particularly well suited for working with superconducting circuits. This work has been published in Tomás Ramos, Juan José García-Ripoll, Phys. Rev. Lett. 119, 153601 (2017).   

Input-output theory for chiral Majorana fermions

The Bosonic version of Input-output theory describes multiple one dimensional fields coupled to spatially local systems such as atoms, beam splitters, and cavities. The generalization to cascaded systems makes it a powerful tool for modeling quantum optics experiments. We extend the earlier work on Fermionic input-output formalism to include propagating Majorana Fermions and Majorana bound states. We also derive network composition rules similar to the Bosonic case. Finally we describe how to integrate Bosonic, Fermionic, and Majorana input-ouput theory. We hope that this will aid analysis an design of experiments in a systematic way.