Squeezing in harmonic oscillators with time-dependent frequencies

Ma, Xin; Rhodes, William C.

doi:10.1103/physreva.39.1941

Cited by 68 publications

(42 citation statements)

References 13 publications

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“…where p q and u q are the corresponding normal mode momentum and displacement and g q specifies the strength of the anharmonic coupling between the zone-center phonon and phonons at ±q. Note that a coherent zone-center phonon has U 0 ∼ cos(Ωt) such that it parametrically modulates the frequency of the other phonons, driving squeezing oscillations in their mean square displacements [15,20]…”

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confidence: 99%

Direct Measurement of Anharmonic Decay Channels of a Coherent Phonon

et al. 2018

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We observe anharmonic decay of the photoexcited coherent A1g phonon in bismuth to points in the Brillouin zone where conservation of momentum and energy are satisfied for three-phonon scattering. The decay of a coherent phonon can be understood as a parametric resonance process whereby the atomic displacement periodically modulates the frequency of a broad continuum of modes. This results in energy transfer through resonant squeezing of the target modes. Using ultrafast diffuse x-ray scattering, we observe build up of coherent oscillations in the target modes driven by this parametric resonance over a wide range of the Brillouin zone. We compare the extracted anharmonic coupling constant to first principles calculations for a representative decay channel.Lattice anharmonicity governs a broad range of phenomena in condensed matter physics, from structural phase transitions [1] to heat transport and thermoelectricity [2,3]. Recent advances in first-principles calculations have allowed for precise calculations of thermal properties including effects due to phonon-phonon scattering [4][5][6]. However, experimental validation is indirect, mostly limited to bulk properties like the thermal conductivity, and experimental probes of the microscopic details of anharmonicity remain elusive. While scattering techniques like inelastic neutron scattering [7][8][9] and inelastic x-ray scattering [10][11][12][13] can measure quasiharmonic properties of phonons such as frequencies and linewidths across the Brillouin zone, these techniques lack the ability to resolve the individual decay channels of a given mode. Such a measurement would provide a unique view of the processes occurring during thermal equilibration, including a quantitative measurement of anharmonic force constants.Here, we report direct measurements of the anharmonic coupling of the zone center Raman active A 1g optic phonon in bismuth to longitudinal acoustic phonons at high wavevector, and extract an anharmonic coupling constant for a subset of these modes that is within an order of magnitude of that obtained by first-principles calculations. These measurements utilize femtosecond xray diffuse scattering to probe the temporal evolution of the phonon mean square displacements following optical excitation [14]. It was proposed in [15] that a parametric resonance of the zone-center mode with the acous-tic branch would be observable in femtosecond scattering measurements using an x-ray free electron laser (FEL).Bismuth is a group V semimetal that exhibits particularly strong electron-phonon coupling due to its Peierls distored structure, making it an ideal testbed for the study of large-amplitude phonon motion. Upon photoexcitation, the sudden change in the lattice potential causes the atoms to move coherently along the A 1g mode coordinate, resulting in a macroscopic modulation of both the optical reflectivity [16] and the Bragg peaks that are sensitive to the A 1g structure factor modulation [17][18][19].We use the theoretical framework developed in reference [15]...

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confidence: 99%

Direct Measurement of Anharmonic Decay Channels of a Coherent Phonon

et al. 2018

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“…The squeezing mechanisms were carefully examined in an ample sequence of papers, the most complete ones by Dodonov et al [31,51,52,53,54,57,66,73,96,101,105,112,118,119]; so our approach cannot dissent too much, though it can contribute with some more observations:…”

Section: Dark Areas: the Squeezingmentioning

confidence: 99%

Magnetic operations: a little fuzzy mechanics?

Mielnik¹,

Ramirez²

2011

Phys. Scr.

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Abstract. We examine the behaviour of charged particles in homogeneous, constant and/or oscillating magnetic fields in the non-relativistic approximation. A special role of the geometric center of the particle trajectory is elucidated. In quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an element of non-commutative geometry which enters into the traditional control problems. We show that its application extends beyond the usually considered time independent magnetic fields of the quantum Hall effect. Some simple cases of magnetic control by oscillating fields lead to the stability maps differing from the traditional Strutt diagram.

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“…Note that the focusing, in general, is not the scale transformation [12], (as the matrix (3.3) is triangular), though it is an example of squeezing [13,14,15]. The scale transformation (η = 0) is an exceptional effect which can happen only for some φ's (see [18]), whereas the focusing is a typical phenomenon which must occur for any positive φ(x), on an infinite ladder of λ's.…”

Section: -The Helmholtz Spectrummentioning

confidence: 99%