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arXiv:cond-mat/9712078 · Physical Review Letters

Phonon Squeezed States Generated by Second-Order Raman Scattering

Xuedong Hu, Franco Nori

Published Dec 8, 1997• 96 citations
arXivHTMLPDF

Abstract

We study squeezed states of phonons, which allow a reduction in the quantum fluctuations of the atomic displacements to below the zero-point quantum noise level of coherent phonon states. We investigate the generation of squeezed phonon states using a second-order Raman scattering process. We calculate the expectation values and fluctuations of both the atomic displacement and the lattice amplitude operators, as well as the effects of the phonon squeezed states on macroscopically measurable quantities, such as changes in the dielectric constant. These results are compared with recent experiments.

DOI
10.1103/physrevlett.79.4605

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We study squeezed states of phonons, which allow a reduction in the quantum fluctuations of the atomic displacements to below the zero-point quantum noise level of coherent phonon states. We investigate the generation of squeezed phonon states using a second-order Raman scattering process. We calculate the expectation values and fluctuations of both the atomic displacement and the lattice amplitude operators, as well as the effects of the phonon squeezed states on macroscopically measurable quantities, such as changes in the dielectric constant. These results are compared with recent experiments.
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.
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.
Summary form only given. The investigation of coherent phonons has been a field of extensive efforts since the first observation of coherent phonons in 1990. Several excitation mechanisms for coherent phonons in solids have been identified among which the most prominent is impulsive stimulated first order Raman scattering. Coherent states exhibit an oscillating expectation value of the phonon amplitude of a given mode while the statistic properties like amplitude variances and covariances remain static. However, dynamics of these statistic variables can be driven by second-order Raman-scattering (SOR), e.g., oscillating amplitude variances (phonon squeezed states) as first reported by Garret et al. Here we report-to our knowledge for the first time-on correlated states of phonon-mode-pairs consisting of different phonons driven by ultrashort light pulses. KTaO/sub 3/, is the ideal material for this study since first order Raman processes are not allowed.
Many non-classical states have been found in the field of quantum mechanics, among which is the squeezing state. In general, according to the requirements of the uncertainty principle, a squeezed state may have lower quantum fluctuation in one quadrature than that in a coherent state, while another quadrature is greater than that of a coherent state. The idea of the squeezing states can be used to reduce quantum noise in measuring high precise signal. In this paper, the authors discussed the effect of temperature on the quantum fluctuations in the second-order Raman scattering. The domain of temperature is obtained, which satisfies the conditions of generating squeezed states.
A theoretical analysis of the fluctuation properties of optical phonons generated by the optical excitation of a quantum dot is presented. In particular we study whether squeezed states may be generated where either the fluctuations of the displacement or of the momentum fall below the vacuum level. The calculations are based on a generating functions formalism which provides analytical results for the case of excitation by ultrashort optical pulses. While after a single pulse excitation no squeezing occurs we find that after an excitation with two phase-locked pulses phonon states can be created where the uncertainties of displacement or momentum temporarily fall below their vacuum values.