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arXiv:2012.00836 · Optical and Quantum Sensing and Precision Metrology

Broadband sensitivity improvement via coherent quantum feedback with PT-symmetry

Xiang Li, Maxim Goryachev, Yiqiu Ma, Michael Edmund Tobar, Chunnong Zhao, R. X. Adhikari, Yanbei Chen

Published Mar 4, 2021• 9 citations
arXivHTMLPDF

Abstract

A conventional resonant detector is often subject to a trade-off between bandwidth and peak sensitivity. Anomalous dispersion has been shown to improve the bandwidth-sensitivity limit by signal amplification, but its unstable issue in operation needs additional feedback control. Here we propose a stable quantum amplifier enabled by two-mode non-degenerate parametric amplification. As the amplifier operates at threshold, one mode of the amplifier forms a parity-time(PT)-symmetric system with the mode of the original detector, while the other mode of the amplifier collects signal and gets extracted by a readout. Viewed more broadly in the context of coherent quantum control theory, we are attaching a controller that consists of a time reversal of the plant, which, by canceling the inertia of the plant, helps drive up the closed-loop signal gain. Examples of microwave cavity axion detectors and laser-interferometric gravitational-wave detectors will be discussed for this technique.

DOI
10.1117/12.2586469

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A conventional resonant detector is often subject to a trade-off between bandwidth and peak sensitivity. Anomalous dispersion has been shown to improve the bandwidth-sensitivity limit by signal amplification, but its unstable issue in operation needs additional feedback control. Here we propose a stable quantum amplifier enabled by two-mode non-degenerate parametric amplification. As the amplifier operates at threshold, one mode of the amplifier forms a parity-time(PT)-symmetric system with the mode of the original detector, while the other mode of the amplifier collects signal and gets extracted by a readout. Viewed more broadly in the context of coherent quantum control theory, we are attaching a controller that consists of a time reversal of the plant, which, by canceling the inertia of the plant, helps drive up the closed-loop signal gain. Examples of microwave cavity axion detectors and laser-interferometric gravitational-wave detectors will be discussed for this technique.
Feedback control in classical systems is an indispensable, ubiquitous tool. The theoretical basis for achieving optimal classical control is well understood, and crucially relies on a very classical assumption: that measurements of the state of a system under control need not perturb that state. In a quantum context this assumption is fundamentally invalid. Although many aspects of the theory of quantum feedback control are relatively well developed, the technological basis for feedback control of a single quantum system has only very recently matured. We demonstrate the experimental realization of a quantum feedback control protocol, perpetually stabilizing the coherent Rabi oscillations of a superconducting qubit. This is the first utilization of quantum feedback control for stabilizing a dynamical process, and the first application of quantum feedback in a solid-state system of any kind. This demonstration comprises the first half of this thesis. The feedback protocol is predicated on the ability to make high-fidelity quantum measurements, which are enabled by quantum-limited Josephson parametric amplifiers (JPAs). The design and realization of the novel Josephson traveling-wave parametric amplifier (JTWPA) comprises the second half of this thesis. The JTWPA achieves order-of-magnitude improvements over state of the art JPAs in bandwidth and signal power handling while providing quantum-limited noise performance, potentially enabling the simultaneous readout of dozens of superconducting qubits and the generation of broadband multi-mode squeezing in the microwave domain.
Feedback control in classical systems is an indispensable, ubiquitous tool. The theoretical basis for achieving optimal classical control is well understood, and crucially relies on a very classical assumption: that measurements of the state of a system under control need not perturb that state. In a quantum context this assumption is fundamentally invalid. Although many aspects of the theory of quantum feedback control are relatively well developed, the technological basis for feedback control of a single quantum system has only very recently matured. We demonstrate the experimental realization of a quantum feedback control protocol, perpetually stabilizing the coherent Rabi oscillations of a superconducting qubit. This is the first utilization of quantum feedback control for stabilizing a dynamical process, and the first application of quantum feedback in a solid-state system of any kind. This demonstration comprises the first half of this thesis. The feedback protocol is predicated on the ability to make high-fidelity quantum measurements, which are enabled by quantum-limited Josephson parametric amplifiers (JPAs). The design and realization of the novel Josephson traveling-wave parametric amplifier (JTWPA) comprises the second half of this thesis. The JTWPA achieves order-of-magnitude improvements over state of the art JPAs in bandwidth and signal power handling while providing quantum-limited noise performance, potentially enabling the simultaneous readout of dozens of superconducting qubits and the generation of broadband multi-mode squeezing in the microwave domain.
The precise control, entanglement, and measurement of quantum systems are central challenges in realizing scalable quantum information processing. This dissertation investigates how parametric modulation and engineered nonlinearity can be harnessed to both manipulate and measure superconducting qubits with high fidelity. In one part, controlled parametric drives are used to generate entanglement between qubit pairs and employ their joint states as probes of environmental dynamics. This approach enables the exploration of the non-Markovian nature of quantum environments, revealing how memory effects influence qubit coherence and energy relaxation. In a separate but conceptually related study, the same principle of parametric driving is utilized to design and analyze quantum-limited amplifiers based on three-wave mixing in weakly nonlinear Josephson circuits. An amplifier with a higher coupling quality factor than conventional JPAs is employed, allowing the two modes of a parity-time (PT) symmetric dimer to be mapped onto the in-phase (I) and quadrature (Q) components of the Josephson parametric amplifier. This mapping enables controlled exploration of non-Hermitian dynamics and mode coalescence within the amplifier’s quadrature space, offering new insights into PT-symmetric behavior and quantum-limited detection. Collectively, these investigations unify the themes of parametric control, entanglement, and amplification, advancing the broader understanding of quantum measurement and open-system dynamics.
Josephson traveling wave parametric amplifiers have enabled ultra-sensitive detection of microwave photons in radio astronomy and real-time readout of superconducting quantum bits. To achieve a large gain, the interaction time with the non-linearity of the amplifier needs to be maximized. Traveling wave parametric amplifiers exhibit long interaction times by providing long propagation paths, enabling a greater gain and higher bandwidths than other microwave parametric amplifiers. In the case of the degenerate Josephson parametric amplifier (DJPA) below threshold of parametric oscillation, a squeezed vacuum state can be generated, and above threshold a second bifurcation point exists, where the device generates amplitude squeezed radiation.
The sensitivity of laser interferometers is fundamentally limited by the quantum nature of light. Recent theoretical studies have opened a new avenue to enhance their quantum-limited sensitivity by using active parity-time-symmetric and phase-insensitive quantum amplification. These systems can enhance the signal response without introducing excess noise in the ideal case. However, such active systems must be causal, stable, and carefully tuned to be practical and applicable to precision measurements. In this paper, we show that phase-insensitive amplification in laser interferometers can be implemented in a tabletop experiment. The layout consists of two coupled cavities and an active medium comprised of a silicon nitride membrane and an auxiliary pump field. Our design relies on existing membrane and cryogenic technology and can demonstrate three distinct features: (i) the self-stabilized dynamics of the optical system, (ii) quantum enhancement of its sensitivity in the presence of the amplifier, and (iii) optical control of the amplifier gain. These features are needed to enhance the sensitivity of future interferometric gravitational-wave and axion detectors.
Feedback amplification is a key technique for synthesizing various functionalities, especially in electronic circuits involving op amps. This paper presents a quantum version of this methodology, where the general phase-preserving quantum amplifier and coherent (i.e., measurement-free) feedback are employed to construct various types of systems having useful functionalities: quantum versions of differentiator, integrator, self-oscillator, and active filters. The class of active filters includes the Butterworth filter, which can be used to enhance the capacity of an optical quantum communication channel, and the nonreciprocal amplifier, which enables measurement of a superconducting qubits system as well as protection of it by separating input from output fields. A particularly detailed investigation is performed on the active phase-canceling filter for realizing a broadband gravitational-wave detector; that is, the feedback-amplification method is used to construct an active filter that compensates the phase delay of the signal and eventually recovers the sensitivity in the high-frequency regime.