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Journal of Nonlinear Optical Physics & Materials

Detecting Phonon Vacuum Squeezing

M. Artoni

Published Jun 1, 1998• 2 citations
Publisher

Abstract

We examine quantum states of the atomic displacement which allow for the possibility of modulating its quantum fluctuations below the zero-point motion level. We address the issue of measuring such a squeezing of the phonon field and the framework for a suitable detection method is presented.
DOI
10.1142/s021886359800020x

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We study squeezed quantum states of phonons, which allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of coherent phonon states. We calculate the corresponding expectation values and fluctuations of both the atomic displacement and lattice amplitude operators, and also investigate the possibility of generating squeezed phonon states using a three-phonon parametric amplification process based on phonon-phonon interactions. Furthermore, we also propose a detection scheme based on reflectivity measurements.
We investigate coherent and squeezed quantum states of phonons. The latter allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of coherent states. The expectation values and quantum fluctuations of both the atomic displacement and the lattice amplitude operators are calculated in these states---in some cases analytically. We also study the possibility of squeezing quantum noise in the atomic displacement using a polariton-based approach. \textcopyright{} 1996 The American Physical Society.
Detection of the weakest forces in nature is aided by increasingly sensitive measurements of the motion of mechanical oscillators. However, the attainable knowledge of an oscillator's motion is limited by quantum fluctuations that exist even if the oscillator is in its lowest possible energy state. We demonstrate a technique for amplifying coherent displacements of a mechanical oscillator with initial magnitudes well below these zero-point fluctuations. When applying two orthogonal squeezing interactions, one before and one after a small displacement, the displacement is amplified, ideally with no added quantum noise. We implemented this protocol with a trapped-ion mechanical oscillator and determined an increase by a factor of up to 7.3 (±0.3) in sensitivity to small displacements.
Quantum fluctuations are an important feature of isolated systems at low temperatures. This quantum noise is unavoidable due to Heisenberg's uncertainty principle. However, squeezed states can lower the quantum noise in one of a pair of variables at the expense of increasing it in the other variable. This ability to reduce quantum fluctuations makes squeezed states very promising in high-precision measurements. This thesis studies the quantum fluctuation properties of two condensed matter systems: phonons and Josephson junctions. In particular, we theoretically investigate several approaches for the generation and detection of squeezed states in these systems. We study for the first time coherent and squeezed quantum states of phonons, in analogy to the coherent and squeezed states of photons. We introduce and study a lattice amplitude operator, which is the phonon analog of the electric field. Our work provides a clear link between quantum mechanical phonon coherent states and the experimentally observed coherent phonons--typically described in classical terms. We then study phonon squeezed states, which can modulate the quantum fluctuations of atomic displacements below the zero-point quantum noise level. We explore the possibility of generating squeezed phonon states with a variety of different approaches, such as a phonon parametric down-conversion process and a polariton-based mechanism. Furthermore, we propose a possible detection scheme based on reflectivity measurements. We also study quantum fluctuation properties of superconducting Josephson junctions, which have the nonlinear interactions necessary for modulating quantum noise. We obtain approximate ground and excited states, and calculate the variances of the charge and phase in various circuit configurations. This thesis provides a first systematic study of quantum noise and its suppression in condensed matter systems. It also proposes different directions for future studies in the control of quantum noise in solids.
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