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Journal of Optics B Quantum and Semiclassical Optics

What does an observed atom reveal to its observer?

P. E. Toschek, Chr. Balzer

Published Aug 1, 2002• 6 citations
Publisher

Abstract

Reiterated measurement blocks the quantum evolution of the measured object. An attempt at experimental demonstration of this postulate was reported a decade ago; it applied series of light pulses during the microwave-induced evolution of an ensemble of trapped ions, followed by a measurement of the ensemble’s state. The results agreed with quantum mechanical predictions. However, the blockade of the quantum evolution by acts of measurement cannot, in principle , be verified on an ensemble, since such a measurement yields, as the result, an expectation value, not an eigenvalue, and the micro-state of the system remains unknown. Moreover, each radiative intervention requires subsequent detection of the emerging state in order to qualify as a measurement. A recent experiment has used a single quantum entity (an ion) and has included repeated probing of the ion’s state alternating with the laser-driven evolution. Here, each measurement signals the eigen state of the system. The statistics of correlated results contains complete information on the evolution of the ion, in particular on the blocking effect of reiterated measurements. Recently, an extended relaxationless version has included coherently driving such an ion on the ground-state hyperfine transition by a microwave.

DOI
10.1088/1464-4266/4/4/338

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Reiterated measurement blocks the quantum evolution of the measured object. An attempt at experimental demonstration of this postulate was reported a decade ago; it applied series of light pulses during the microwave-induced evolution of an ensemble of trapped ions, followed by a measurement of the ensemble’s state. The results agreed with quantum mechanical predictions. However, the blockade of the quantum evolution by acts of measurement cannot, in principle , be verified on an ensemble, since such a measurement yields, as the result, an expectation value, not an eigenvalue, and the micro-state of the system remains unknown. Moreover, each radiative intervention requires subsequent detection of the emerging state in order to qualify as a measurement. A recent experiment has used a single quantum entity (an ion) and has included repeated probing of the ion’s state alternating with the laser-driven evolution. Here, each measurement signals the eigen state of the system. The statistics of correlated results contains complete information on the evolution of the ion, in particular on the blocking effect of reiterated measurements. Recently, an extended relaxationless version has included coherently driving such an ion on the ground-state hyperfine transition by a microwave.
The evolution of mechanics has followed the critical analysis of gedanken experiments. Many of these concrete speculations can become implemented today in the laboratory – thanks to now available techniques. A key experiment is concerned with the time evolution of a system under repeated or continuing observation. Here, three problems overlap: 1. The microphysical measurement by a macroscopic device, 2. the system's temporal evolution, and 3. the emergence of macroscopic reality out of the microcosmos. A well-known calculation shows the evolution of a system being slowed down, or even obstructed, when the system is merely observed.An experiment designed to demonstrate this quantum Zeno and performed in the late eighties on an ensemble of identical atomic ions confirmed its description, but turned out inconclusive with respect to the very origin of the impediment of evolution. During the past years, experiments on individualelectrodynamically stored and laser-cooled ions have been performed that unequivocally demonstrate the observed system's evolution being impeded. Strategy and results exclude any physical reaction on the measured object, but reveal the effect of the gain of information as put forward by the particular correlation of the ion state with the detected signal. They shed light on the process of measurement as well as on the evolution and allow an epistemological interpretation.
Reiterated or continuous measurement on a quantum system impedes the quantum object's evolution. This "quantum Zeno" effect (QZE), contemplated for decades, has been conventionally attributed to the reaction of the measuring device on the quantum object being measured, in the sense of the Heisenberg microscope. However, even reactionless "quantum non-demolition" measurements seem to qualify for that inhibition to take place and may constitute a "quantum Zeno paradox" (QZP). An experimental proof of QZE had been attempted in the past on clouds of ions confined in a Paul trap. In the meantime it has been shown, however, that the anticipated impediment of the quantum evolution by a sheer gain of information, i.e. by reactionless measurement cannot be, in principle, proven with an ensemble. Recently, experiments have been performed with the use of a single quantum system: an 172Yb+ ion, laser-driven on its E2 line S1/2 - D5/2, or an 171Yb+ ion, microwave-driven on its ground-state hyperfine resonance. The results of these experiments demonstrate that mere gain of information on the quantum system, while lacking dynamic action, modifies the system's evolution as it is predicted by quantum mechanics, based on the system's preparation. This seems plausible if we attribute reality to the results of the measurements. If, in contrast, reality is claimed for the prediction, two-fold discontinuity must be admitted: loss of coherence with potential measurements, and renormalization from the results of actual measurements.
The evolution of a quantum system is supposed to be impeded by measurement of an involved observable. This effect has been proven indistinguishable from the effect of dephasing the system's wave function, except in an individual quantum system. The coherent dynamics, on an optical E2 line, of a single trapped ion driven by light of negligible phase drift has been alternated with interrogations of the internal ion state. Retardation of the ion's nutation, equivalent to the quantum Zeno effect, is demonstrated in the statistics of sequences of probe-light scattering ''on'' and ''off'' detections, the latter representing back-action-free measurement.
The evolution of a quantum system is impeded by the system’s state being observed. A test on an ensemble neither proves the causal nexus nor discloses the nature of the inhibition. Two recent experiments that make use of sequential optical or microwave-optical double resonance on an individual trapped ion disprove a dynamical effect of back action by meter or environment. They rather indicate the ionic states involved in the evolution being entangled with the potentially recorded bivalued scattered-light signal.
In this thesis I describe how we achieve control over the quantum state of a single H2+ hydrogen molecular ion. Scientific progress is based on the comparison of theories with experimental measurements. For the simplest molecular quantum systems, such as the hydrogen molecular ions H2+ or HD+, the theoretical predictions of quantum electrodynamics are very accurate. In order to test the theory or to extract fundamental constants from the combination of theory and experiments, the experiments must also achieve high precision. In the recent past, hydrogen molecular ions were mainly measured in ensembles. For example, measurements exist both on molecular beams and with dissociative detection in ion traps. However, the spectroscopy of single ions is one of the most precise measurement methods in physics, which was demonstrated by the spectroscopy of a single ytterbium ion in an ion trap. To perform spectroscopy of a single ion in this way, it must have a suitable energy structure for laser cooling, state preparation and fluorescence detection. This is not the case for many ions, including H2+. Quantum logic spectroscopy (QLS) is a technique that makes it possible to perform measurements on an ion without such an energy structure. The ion to be measured (spectroscopy ion) is trapped in an ion trap with a second ion (helper ion), which has the properties described in the previous paragraph. The shared modes of motion between the two ions allow cooling, preparation and detection of the spectroscopy ion via the helper ion. This was demonstrated with an aluminum spectroscopy ion co-trapped with a magnesium helper ion. QLS can also be used for molecules. This has been shown with MgH+, CaH+ and N2+. We implement QLS to enable spectroscopy of a single H2+ ion. For this we trap H2+ together with a 9Be+ ion. We cool the joint motion of the ions to their ground state. We combine buffer gas cooling with a laser and microwave pulse based state preparation sequence to prepare the H2+ molecule in a pure quantum state. This allows us to perform high contrast QLS on a single H2+ ion. Furthermore, we can change and control the quantum state in the hyperfine structure using microwave pulses. We demonstrate the power of our technique by performing microwave spectroscopy on a magnetic field insensitive hyperfine transition. We use QLS to read out the result of the measurement. Within half an hour, we can achieve a statistical uncertainty of 2 Hz. This paves the way for future high-precision measurements on H2+. The techniques described here could potentially be applied to other light molecular ions.