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arXiv:1611.03716 · Europhysics Letters (EPL)

Non-Ergodicity in open quantum systems through quantum feedback

Lewis A. Clark, Fiona Torzewska, Ben Maybee, Almut Beige

Published Jun 30, 2020• 4 citations
arXivHTMLPDF

Abstract

It is well known that quantum feedback can alter the dynamics of open quantum systems dramatically. In this paper, we show that non-ergodicity may be induced through quantum feedback and resultantly create system dynamics that have lasting dependence on initial conditions. To demonstrate this, we consider an optical cavity inside an instantaneous quantum feedback loop, which can be implemented relatively easily in the laboratory. Non-ergodic quantum systems are of interest for applications in quantum information processing, quantum metrology and quantum sensing and could potentially aid the design of thermal machines whose efficiency is not limited by the laws of classical thermodynamics.

DOI
10.1209/0295-5075/130/54002

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It is well known that quantum feedback can alter the dynamics of open quantum systems dramatically. In this paper, we show that non-ergodicity may be induced through quantum feedback and resultantly create system dynamics that have lasting dependence on initial conditions. To demonstrate this, we consider an optical cavity inside an instantaneous quantum feedback loop, which can be implemented relatively easily in the laboratory. Non-ergodic quantum systems are of interest for applications in quantum information processing, quantum metrology and quantum sensing and could potentially aid the design of thermal machines whose efficiency is not limited by the laws of classical thermodynamics.
© CopyrightEPLA, 2020.It is well known that quantum feedback can alter the dynamics of open quantum systems dramatically. In this paper, we show that non-Ergodicity may be induced through quantum feedback and resultantly create system dynamics that have lasting dependence on initial conditions. To demonstrate this, we consider an optical cavity inside an instantaneous quantum feedback loop, which can be implemented relatively easily in the laboratory. Non-Ergodic quantum systems are of interest for applications in quantum information processing, quantum metrology and quantum sensing and could potentially aid the design of thermal machines whose efficiency is not limited by the laws of classical thermodynamics.
Open quantum systems usually reach a unique stationary state with ergodic dynamics. In other words, the ensemble averages and the time averages of the expectation values of open quantum systems are usually the same for all quantum trajectories. Although open quantum systems are in general ergodic, many classical stochastic processes are not. Hence if classical physics emerges from microscopic quantum models, there have to be mechanisms which induce non-ergodicity in open quantum systems. In this paper, we identify such a mechanism by showing that quantum feedback dramatically alters the dynamics of open quantum systems, thereby possibly inducing non-ergodicity and a persistent dependence of ensemble averages on initial conditions. As a concrete example, we study an optical cavity inside an instantaneous quantum feedback loop.
There are a number of different strategies to measure the phase shift between two pathways of light more efficiently than suggested by the standard quantum limit. One way is to use highly entangled photons. Another way is to expose photons to a non-linear or interacting Hamiltonian. This paper emphasises that the conditional dynamics of open quantum systems provides an interesting additional tool for quantum-enhanced metrology. As a concrete example, we review a recent scheme which exploits the conditional dynamics of a laser-driven optical cavity with spontaneous photon emission inside a quantum feedback loop. Deducing information from second-order photon correlation measurements requires neither optical non-linearities nor entangled photons and should therefore be of immediate practical interest.
It is widely believed that quantum physics is a fundamental theory describing the Universe. As such, one would expect to be able to see how classical physics that is observed in the macroscopic world emerges from quantum theory. This has so far largely eluded physicists, due to the inherent linear nature of quantum physics and the non-linear behaviour of classical physics. One of the principle differences between classical and quantum physics is the statistical, probabilistic nature of quantum theory. It is from this property that non-classical states can arise, such as entangled states. These states possess maximal correlations. However, they are not the only way in which correlations are created in quantum systems. This thesis aims to show how open quantum systems naturally contain correlations from their quantum nature. Moreover, even seemingly simple open quantum systems can behave far more complexly than expected upon the introduction of quantum feedback. Using this effect, the dynamics may become non-linear and as such behave non-trivially. Furthermore, it is shown how these effects may be exploited for a variety of tasks, including a computational application in hidden quantum Markov models and a quantum metrology scheme that does not require the use of exotic quantum states. This results in the design of systems that benefit from the use of quantum mechanics, but are not constrained by the use of experimentally difficulties such as entanglement.
In the conventional picture of quantum feedback control, sensors make measurements on a quantum system, a classical controller processes the results of the measurements, and semi-classical actuators act back on the system to alter its behavior. Quantum measurements are well known to yield probabilistic results and to introduce unavoidable disturbances in the system measured. Accordingly, quantum feedback is traditionally considered to be both probabilistic and destructive. This paper proposes and provides an experimental demonstration of an alternative method for quantum feedback control, in which sensors, controller, and actuators are themselves quantum systems that interact coherently with the system to be controlled. The resulting feedback loop preserves quantum coherence. Such coherent quantum feedback control is deterministic, non-destructive, and can be used to perform actions such as transferring quantum entanglement that are not possible using conventional feedback control of quantum systems. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Open quantum systems continually lose information to their surroundings. In some cases this information can be readily retrieved from the environment and put to good use by engineering a feedback loop to control the system dynamics. Two cases are distinguished: one where the feedback mechanism involves a measurement of the environment, and the other where no measurement is made. It is shown that the latter case can always replicate the former, but not vice versa. This emphasizes the quantum nature of the information being fed back. Two approaches are used to describe the feedback: quantum trajectories (which apply only for feedback based on measurement) and quantum Langevin equations (which can be used in either case), and the results are shown to be equivalent. The obvious applications for the theory are in quantum optics, where the information is lost by radiation damping and can be retrieved by photodetection. A few examples are discussed, one of which is particularly interesting as it has no classical counterpart.