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Quantum Binary Decision for Driven Harmonic Oscillator

Matteo G. A. Paris

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement schemes. Detection probability has been evaluated for different initial state preparations of oscillator. The corresponding lower bounds on minimum detectable perturbation intensity has been evaluated and a general bound for random phase perturbation has been also induced. 1

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Quantum Binary Decision for Driven Harmonic Oscillator

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We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement scheme according to the Neyman–Pearson criterion. Detection probability has been evaluated for different initial state preparations of oscillator. The corresponding lower bounds on minimum detectable perturbation intensity has been evaluated and a general bound for random phase perturbation has been also induced.

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American Journal of Physics•Feb 1, 1995•5 citations
We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement schemes. Detection probability has been evaluated for different initial state preparations of oscillator. The corresponding lower bounds on minimum detectable perturbation intensity has been evaluated and a general bound for random phase perturbation has been also induced. 1
We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement scheme according to the Neyman–Pearson criterion. Detection probability has been evaluated for different initial state preparations of oscillator. The corresponding lower bounds on minimum detectable perturbation intensity has been evaluated and a general bound for random phase perturbation has been also induced.
The von Neumann interaction between a particle and an apparatus, both of arbitrary mass, has been considered in the measurement of the position of a simple harmonic oscillator acted on by an external force. When the measurement has finite duration, both the motion of the pointer and the oscillator influence the result of the measurement. Provided that the oscillator is in an eigenstate of its position at the start of the measurement, the pointer will indicate the arithmetic average between the initial and final position of the particle with an added term which depends on the duration of the measurement and the frequency of the oscillator. This additional term is determined by the external force which also causes the appearance of a phase factor in the wave function at the end of the measurement. This phase factor depends on the average of the initial and final positions of the particle. Furthermore, the probability that the pointer will indicate a given average value is equal to the transition probability for the undisturbed free oscillator to experience the change in position. If the initial state of the pointer is a narrow wavepacket, then for any initial state of the oscillator, the measurement yields, approximately, the undisturbed probability distribution for the position of the free oscillator at the end of the measurement. The transition probability for the pointer to experience a change in its position has also been evaluated.
Transition amplitudes and probabilities for the harmonic oscillator with a forcing function proportional to cos(ωt) beginning at time zero are calculated to lowest nonvanishing order using time-dependent perturbation theory. The results are compared with the exact amplitudes and probabilities. When the exact amplitude is expanded in a Taylor series in powers of the coupling constant, the individual terms turn out to be the perturbation amplitudes, showing that the complete series of perturbation amplitudes converges to the exact amplitude.