Absence of phase-dependent noise in time-domain reflectivity studies of impulsively excited phonons

Abstract

There have been several reports of phase-dependent noise in time-domain reflectivity studies of optical phonons excited by femtosecond laser pulses in semiconductors, semimetals, and superconductors. It was suggested that such behavior is associated with the creation of squeezed phonon states although there is no theoretical model that directly supports such a proposal. We have experimentally re-examined the studies of phonons in bismuth and gallium arsenide, and find no evidence of any phase-dependent noise signature associated with the phonons. We place an upper limit on any such noise at least 40-50 dB lower than previously reported. DOI: 10.1103/PhysRevB.81.224304 PACS number͑s͒: 78.47.jg, 63.20.Ϫe, 42.50.Lc Coherent phonons in semiconductors, superconductors, metals, and insulators have been widely studied in the time domain since the first report of their excitation by femtosecond laser pulses in about 1990.1,2 The most general excitation mechanism is impulsive stimulated Raman scattering ͑ISRS͒.3 A special case of ISRS in opaque materials is sometimes referred to as the displacive mechanism 1 and is associated with electronic excitation from bonding to antibonding orbitals. Longitudinal optical phonons in semiconductors can also be driven by the transient polarization associated with the screening of surface space-charge fields following interband excitation. 2The amplitude of a phonon mode may be decomposed into two quadrature components with the time dependences cos t and sin t. In a coherent state, the closest quantum counterpart to a classical field, the fluctuations in the two quadratures have the same variance and are randomly distributed in phase. The product of the variances in each quadrature is the minimum allowed by the Heisenberg uncertainty principle. Minimum uncertainty states in which the fluctuations in one quadrature have a variance that falls below the zero-point quantum noise level are called squeezed states. 4 Squeezed electromagnetic fields were experimentally studied for the first time in the mid-1980s ͑Ref. 5͒ and nonclassical light is now an established area of research.6 A phasedependent nonlinear process is necessary to generate a squeezed state. For example, squeezed optical fields can be produced by parametric amplification or four-wave mixing. Recently, there has been interest in extending the study of nonclassical fields to lattice vibrations in condensed matter but except for a few studies of squeezing, 7-12 and amplitude collapse and revival, 13 there has been relatively little work on phonon fields. Squeezing of phonons generated by secondorder Raman scattering was predicted 7 and later reported 9,11 in low temperature, femtosecond pump-probe transmission measurements on KTaO 3 . In this case the mechanism is a three-phonon parametric process analogous to that used to produce coherent two-photon states. This type of experiment has been extended to the creation of coexcited coherent and squeezed vibrations 10 and to squeezed spin waves 14 in MnF 2 but in no case has the...

Generation and detection of squeezed phonons in lattice dynamics by ultrafast optical excitations

“…Thermal environment. In the case of a thermal reservoir, the master equation takes the form (20). In this case, it is useful to express the phonon density matrix ρ in phase space using the displacement operator D, 7 Notice that ifâ,ˆ † a were substituted by α, * a in the expression of the operator implementing the probing process (see (10)), there would be no reading of the phonon properties by the probe photons, since in this caseˆˆˆ † † †   = a a a a a a.…”

“…Assuming a perfect correspondence between the features of the detected scattered photon state and those of the excited phonons in the material, the presence of oscillations in the fluctuations with twice the frequency of the excited phonon mode was seen as a sign of phonon squeezing. Still, a shadow of doubt was cast also on these results, since the observed oscillations in the fluctuation data could be attributed to an intrinsically imprecise phase determination in the used apparatus, giving rise to the so-called jittering effects [20]. More recent experiments have been performed using ultrafast x-ray diffraction, granting a reduced pulse duration, hence reduced jittering errors [23]; despite this experimental advantage, the results concerning the presence of squeezed phonons seem to need further analysis.…”

Generation and dynamics of phononic cat states after optical excitation of a quantum dot

“…In particular, the search for squeezed phonon states has been the focus of various experimental and theoretical investigations. [1][2][3][4][5][6][7][8] Phonons are in many aspects similar to photons, where squeezing has been extensively studied in the past. 9 However, for phonons, a direct measurement of the fluctuation properties seems rather complicated and, thus, only more or less indirect hints for squeezed phonons were found.…”

“…[1][2][3][4][5] However, such an oscillation turned out not to be an unambiguous proof for squeezing. 8,10 Squeezing can be achieved in different ways. One way is to deform ("squeeze") the vacuum or a coherent state in phasespace representation.…”

Controlling phonon squeezing and correlation via one- and two-phonon interference

“…To date the coherent phonons have been observed in a great variety of solids [1][2][3][4][5] with increasing attention being turned towards not only observation but also understanding of physics which occurs at this short time scale. In analogy with photon states in quantum optics [6][7][8] the generation and manipulation of specific phonon states has become a major issue in condensed matter physics [9][10][11][12][13][14][15][16][17][18][19][20]. Yet, notwithstanding the recent experimental and theoretical advances, a clear relation between quantum mechanical coherent phonon state and the experimentally observed coherent phonons, typically described in classical terms, is still missing.…”