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arXiv:2106.12599

Non-invasive measurement of currents in analog quantum simulators

Kevin T. Geier, Janika Reichstetter, Philipp Hauke

Published Jun 23, 2021• 3 citations
arXivHTMLPDF

Abstract

Despite the pristine abilities of analog quantum simulators to study quantum dynamics, possibilities to detect currents are sparse. Here, we propose a flexible non-invasive technique to measure currents in quantum many-body systems by weakly coupling the system to an ancilla, followed by a measurement of the ancilla population. We numerically benchmark the scheme at the example of interacting bosons in a Harper-Hofstadter optical-lattice ladder, and discuss potential experimental error sources. The highly flexible protocol can be used with both hard-core and soft-core bosons as well as fermions, is easily extendable to more general observables like current-current correlations, and applies to other setups beyond cold atoms as we exemplify for the trapped-ion platform.

DOI
10.48550/arxiv.2106.12599

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Despite the pristine abilities of analog quantum simulators to study quantum dynamics, possibilities to detect currents are sparse. Here, we propose a flexible non-invasive technique to measure currents in quantum many-body systems by weakly coupling the system to an ancilla, followed by a measurement of the ancilla population. We numerically benchmark the scheme at the example of interacting bosons in a Harper-Hofstadter optical-lattice ladder, and discuss potential experimental error sources. The highly flexible protocol can be used with both hard-core and soft-core bosons as well as fermions, is easily extendable to more general observables like current-current correlations, and applies to other setups beyond cold atoms as we exemplify for the trapped-ion platform.
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Recent advances in superconducting circuit technology have made the fabrication of large, customizable circuits routine. This has led to applications beyond quantum information, including quantum simulation. A key challenge in this effort is the identification of the quantum states realized. Here, we propose a probe circuit capable of measuring many-body correlations in an analog quantum simulator superconducting circuit. This probe, which is specially designed for many-photon states, exploits the nonlinearity of the Josephson junction to measure two-point correlation functions of the superconducting phase operator. We demonstrate the capabilities of this design in the context of an LC-ladder with a quantum impurity. The proposed probe allows for the measurement of inherently quantum correlations, such as two-mode squeezing, and it has the potential to significantly expand the scope of analog quantum simulations using superconducting circuits.
Measurement-induced phase transitions are the subject of intense current research, both from an experimental and a theoretical perspective. We explore the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom (implemented using two additional sites), on which projective measurements are performed. We analyze the effect of repeated (``stroboscopic'') measurements on the dynamical correlations of interacting hard-core bosons in a one-dimensional chain. An important distinctive ingredient of the protocol is the fact that the detector ancillae are not reinitialized after each measurement step. The detector thus maintains memory of the accumulated influence by the measured correlated system. Initially, we consider a model in which the ancilla is coupled to a single lattice site. This setup allows obtaining information about the system through Rabi oscillations in the ancillary degrees of freedom, modulated by the ancilla-system interaction. The statistics of quantum trajectories exhibits a ``quantum-Zeno-valve effect'' that occurs when the measurement becomes strong, with sharp branching between low and high entanglement. We proceed by extending numerical simulations to the case of two ancillae and, then, to measurements on all sites. With this realistic measurement apparatus, we find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models. The dynamics features a broad distribution of the entanglement entropy.