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Physical Review A

Proposed test for realist theories using Rydberg atoms coupled to a high- Q resonator

Susana F. Huelga, Trevor W. Marshall, Emilio Santos

Published Oct 1, 1995• 58 citations
Publisher

Abstract

From the hypotheses of realism and stationarity, the latter related to the Leggett-Garg assumption of non-invasive measurability, we derive inequalities, involving three autocorrelation functions, to be fulfilled by any two-state stochastic process. We seek to test a broad class of realist theories against quantum mechanics for a system consisting of a Rydberg atom interacting with a single quantized mode in a superconducting resonant cavity. Departures from quantum predictions are enhanced when the temperature is decreased to about 0.5 K and the state of the cavity approximates a Fock state.

DOI
10.1103/physreva.52.r2497

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From the hypotheses of realism and stationarity, the latter related to the Leggett-Garg assumption of non-invasive measurability, we derive inequalities, involving three autocorrelation functions, to be fulfilled by any two-state stochastic process. We seek to test a broad class of realist theories against quantum mechanics for a system consisting of a Rydberg atom interacting with a single quantized mode in a superconducting resonant cavity. Departures from quantum predictions are enhanced when the temperature is decreased to about 0.5 K and the state of the cavity approximates a Fock state.
Macroscopic realism is the thesis that macroscopically observable properties must always have definite values. The idea was introduced by Leggett and Garg (1985), who wished to show a conflict with the predictions of quantum theory, by using it to derive an inequality that quantum theory violates. However, Leggett and Garg's analysis required not just the assumption of macroscopic realism per se, but also that the observable properties could be measured non-invasively. In recent years there has been increasing interest in experimental tests of the violation of the Leggett-Garg inequality, but it has remained a matter of controversy whether this second assumption is a reasonable requirement for a macroscopic realist view of quantum theory. In a recent critical assessment Maroney and Timpson (2014) identified three different categories of macroscopic realism, and argued that only the simplest category could be ruled out by Leggett-Garg inequality violations. Allen, Maroney, and Gogioso (2016) then showed that the second of these approaches was also incompatible with quantum theory in Hilbert spaces of dimension 4 or higher. However, we show that the distinction introduced by Maroney and Timpson between the second and third approaches is not noise tolerant, so unfortunately Allen's result, as given, is not directly empirically testable. In this paper we replace Maroney and Timpson's three categories with a parameterization of macroscopic realist models, which can be related to experimental observations in a noise tolerant way, and recover the original definitions in the noise-free limit. We show how this parameterization can be used to experimentally rule out classes of macroscopic realism in Hilbert spaces of dimension 3 or higher, without any use of the non-invasive measurability assumption. Even for relatively low precision experiments, this will rule out the original category of macroscopic realism, that is tested by the Leggett-Garg inequality, while as the precision of the experiments increases, all cases of the second category and many cases of the third category, will become experimentally ruled out.
This thesis presents a series of circuit QED (cQED) experiments, in which artificial atoms consisting of superconducting circuits are strongly coupled to the electromagnetic field stored in a microwave resonator. This resonator can be used as a measurement apparatus for the atom, allowing both to address fundamental issues in quantum mechanics, and to develop building blocks for a quantum processor. In a first experiment we continuously monitored the evolution of a quantum system while varying the measurement strength. We observed the crossover from weak to strong measurement regimes, and, ultimately, the freezing of the dynamics by the Quantum Zeno Effect. In the weak measurement regime, we probed if the artificial atom complies with the macroscopic realism hypotheses, from which Leggett and Garg have derived a Bell's inequality in time. The violation of this inequality confirms that although macroscopic, the artificial atom is a truly quantum object. On the quantum information side, we have enriched the proposed cQED quantum processor architecture by demonstrating a high fidelity single-shot qubit readout, a crucial element for quantum processors. This new circuit relies on a dynamical transition of a non-linear resonator. The coupled system formed by the qubit and the non-linear resonator allows in addition to investigate the interplay between strong coupling and non-linear effects --parametric amplification, squeezing...-- opening the new field of non-linear cQED. Finally we have operated a circuit which would potentially be able to mediate operations between two arbitrary qubits: a superconducting resonator which is tunable in frequency.
Quantitative predictions for the quantum electrodynamics of a few atoms interacting with quantized modes of the radiation field are becoming accessible to experimental test—particularly for Rydberg atoms in microwave cavities.1 For these one needs essentially exact predictions in realistic cavities, and these show losses. At microwave frequencies1 the very few thermal photons present even at very low temperatures1 can be significant. We show in this paper that if a single two-level atom is contained in a cavity of high enough Q, interaction with a quantized cavity mode can induce new spectral features.
We construct quantifiable generalizations of Leggett-Garg tests for macro- and mesoscopic realism and noninvasive measurability that apply when not all outcomes of measurement can be identified as arising from one of two macroscopically distinguishable states. We show how quantum mechanics predicts a negation of the Leggett-Garg premises for strategies involving ideal negative-result, weak, and minimally invasive (``nonclumsy'') projective measurements on dynamical entangled systems, as might be realized with Bose-Einstein condensates in a double-well potential, path-entangled NOON states, and atom interferometers. Potential loopholes associated with each strategy are discussed.