Quantum theory of cavity-assisted sideband cooling of mechanical motion

We present a quantum-mechanical theory of the cooling of a cantilever coupled via radiation pressure to an illuminated optical cavity. Applying the quantum noise approach to the fluctuations of the radiation pressure force, we derive the optomechanical cooling rate and the minimum achievable phonon number. We find that reaching the quantum limit of arbitrarily small phonon numbers requires going into the good-cavity (resolved phonon sideband) regime where the cavity linewidth is much smaller than the mechanical frequency and the corresponding cavity detuning. This is in contrast to the common assumption that the mechanical frequency and the cavity detuning should be comparable to the cavity damping.     

Optomechanical cavity cooling of an atomic ensemble

We demonstrate cavity sideband cooling of a single collective motional mode of an atomic ensemble down to a mean phonon occupation number ?n?(min?)=2.0(-0.3)(+0.9). Both ?n?(min) and the observed cooling rate are in good agreement with an optomechanical model. The cooling rate constant is proportional to the total photon scattering rate by the ensemble, demonstrating the cooperative character of the light-emission-induced cooling process. We deduce fundamental limits to cavity cooling either the collective mode or, sympathetically, the single-atom degrees of freedom.     

Anomalous phonon-mediated damping of a driven quantum dot embedded in a high-Q semiconductor microcavity

We describe and employ a recently developed polaron master equation model to study the fluorescence spectra of a coherently driven quantum dot (QD) placed within a high-Q semiconductor microcavity (with Q the quality factor). We investigate phonon-induced damping in a regime where many cavity photons are required, and we also compare the resonance fluorescence spectra obtained using an effective phonon master equation in Lindblad form where simple analytical expressions are identified for various phonon-induced scattering rates. We consider two separate continuous-wave pumping scenarios, where either the system is driven through exciton pumping or the system is driven via the cavity. The cavity-QED (quantum electrodynamics) system is pumped sufficiently strongly such that the low-energy sideband of the Mollow triplet is tuned across the cavity mode resonance which is negatively detuned from the QD. For comparison, we also consider the case where the QD-cavity detuning is large enough such that the Mollow triplets do not spectrally overlap with the cavity mode. We find that the full width at half maximum (FWHM) of the high-energy Mollow sideband shows a pronounced nonlinear dependence on the pump intensity when the low-energy component of the triplet overlaps with the cavity mode (or vice versa), and can even be reduced with increased pumping. However, the FWHM depends linearly on the pump intensity when the Mollow triplets are far from the cavity resonance. We observe similar fluorescence spectra for both the exciton-driven system and the cavity-driven system.     

Single-electron-phonon interaction in a suspended quantum dot phonon cavity

An electron-phonon cavity consisting of a quantum dot embedded in a freestanding GaAs/AlGaAs membrane is characterized using Coulomb blockade measurements at low temperatures. We find a complete suppression of single electron tunneling around zero bias leading to the formation of an energy gap in the transport spectrum. The observed effect is induced by the excitation of a localized phonon mode confined in the cavity. This phonon blockade of transport is lifted at discrete magnetic fields where higher electronic states with nonzero angular momentum are brought into resonance with the phonon energy.     

Microscopic theory of Raman spectra of heavy fermion systems in the normal state

In this communication, we develop the microscopic theory of Raman spectra of the heavy fermion (HF) system in its normal state at low temperatures. The system is described by the Periodic Anderson Model along with the coupling of the phonon to the bare f-electrons as well as to the hybridization between the conduction band and the f-electrons. The phonon Green's function and the phonon self-energy are evaluated by the equations of motion method of Zubarev. The phonon spectral density function (SDF) is evaluated at low temperatures in the long wavelength limit. The calculation depicts three Raman active modes one of which corresponds to the strongly renormalized phonon at the value of the reduced frequency ) around 0.57 denoted as (P₀), and the other two at low reduced frequencies of and in the SDF. The effect of electron–phonon (EP) coupling on Raman excitation peaks is investigated to probe the nature of the electronic states of the system.     

A method to calculate the thermal conductivity of HMX under high pressure

A method based on Debye theory is developed to calculate the thermal conductivity of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX). The phonon–phonon interaction model is built up for solid HMX. The phonon lifetime formula is derived by the phonon–phonon scattering mechanism, and the thermal conductivity tensor is derived by the phonon dispersion model. The thermal conductivities of α/β/δ-HMX are calculated in the temperature range 0–700?K and pressure range of 0–10?GPa. The phonon softening process of HMX is investigated. We have proven that the Debye frequency and thermal conductivity tend to 0 at the phonon softening point. A physical picture of the phonon–phonon interaction, phonon lifetime and phonon softening is built up.     

Dynamics of polaritons resonantly created at the upper polariton branch

We have studied the polariton relaxation dynamics in a CdTe microcavity at low temperatures after resonant excitation into the upper polariton branch (UPB). Initially, we have set a negative exciton–cavity detuning, such that the energy difference between the two polariton branches coincides with that of an LO phonon. Our experimental results reveal a sublinear dependence of the integrated emission from the lower polariton branch (LPB) with excitation power. This evidences not only an inefficient LO phonon mediated relaxation from the UPB to the LPB but also a substantial inhibition of polariton relaxation along the LPB. After that, we have progressively reduced the negative detuning, approaching the exciton–cavity resonance. Under these conditions it is possible to observe a nonlinear emission arising from K0 LPB-states similar to that observed after nonresonant excitation. Marked oscillations are present in the time evolution traces, with a period that does not depend on excitation power or detuning.     

Superradiance-Driven Phonon Laser

We propose to enhance the generation of a phonon laser by exploiting optical superradiance. In our scheme, the optomechanical cavity contains a movable membrane, which supports a mechanical mode, and the superradiance cavity can generate the coherent collective light emissions by applying a transverse pump to an ultracold intracavity atomic gas. The superradiant emission turns out to be capable of enhancing the phonon laser performance.This indicates a new way to operate a phonon laser with the assistance of coherent atomic gases trapped in a cavity or lattice potentials.     

Excitation and detection of narrow,movable hypersound beams in the GHz-range

Narrow, movable coherent phonon beams are excited and detected piezoelectrically in the GHz-range by using a modified re-entrant type of coaxial resonator. Longitudinal as well as transverse phonon pulses are generated simultaneously. The diameter of the phonon beams are measured and show a diameter less than 1 mm. The phonon beams can be displaced easily in lateral direction through a large crystal by a relative motion of crystal and reentrant cavity.Supported by Deutsche Forschungsgemeinschaft     

A method to calculate thermal conductivity of a nonperiodic system,bamboo Si<Subscript>1−x</Subscript>Ge<Subscript>x</Subscript> nanowire with axially degraded components

For a nonperiodic system, a bamboo Si_1?x Ge _x nanowire with axially degraded components, it is impossible to obtain its phonon dispersion relations through lattice dynamic or the first principle calculation. Therefore, we present a simple and available method to solve this problem. At first, the Si_1?x Ge _x nanowire with axially degraded component is divided into several sections according to its component distribution like bamboos’ sections formed in the growth process. For each section with a given x value, we constructed a pseudo-cell to calculate its phonon dispersion relations. Thermal conductances of junctions and of each section are then calculated by the phonon mismatch model and the phonon transmission probability with diffusive and ballistic portions. The dependences of thermal conductivity on the length of each section and the gradient of degraded component between sections are presented. We studied thermal conductivity dependence on temperature, length and diameter of the Si_1?x Ge _x nanowire with axially degraded component. And we found κ ~ l ^0.8, in which the exponent 0.8 is ascribed to the competition between phonons ballistic and diffusive transport. Furthermore, thermal conductivities along axial (100), (110), and (111) directions are discussed in detail. The method provides a simple and available tool to study thermal conductivity of a non-period system, such as a quasiperiodic superlattice or a nanowire with axially degraded component.     

Raman scattering as a probe of the tensile strain distribution in GaAs grown on Si(111) by molecular beam epitaxy

Epitaxial layers of GaAs grown on Si substrates, where the layer thickness greatly exceeds any critical thickness based on mismatch in lattice constant alone, have been shown to be under tensile strain for temperature at or below 300 K. This "thermal" strain arises from the difference in thermal expansion coefficients between GaAs and Si. We have performed Raman experiments on GaAs layers grown on both Si (001) and Si (111) substrates. We have observed a shift in the optical modes towards lower frequencies which is indicative of tensile strain in the GaAs layers, this is greater in the (111) growth direction than in the (001) one. In order to investigate the strain distribution as a function of distance from the GaAs/Si interface we have measured Raman spectra after successive removing of the epitaxial layer by chemical etching. We have found out that the strain decreases with increasing distance from the interface. We have developed the theory of Cerdeira et al. (1) to determine quantitatively the strain present in the heteroepitaxial layers. We have used, for the first time, polarization selection rules to separate the various components of the optical phonon modes. According to the theory we have observed that the doubly degenerate TO phonon line exhibits both a splitting and shift with strain, while only a shift is observed for the LO phonon line. In conformity with Cerdeira we have remarked that the strain dependence of the LO phonon is equal to that of the TO phonon mode observed in crossed polarization configuration.     

Instantaneous measurement of field quadrature moments and entanglement

We present a method of measuring expectation values of quadrature moments of a multimode field through two-level probe “homodyning”. Our approach is based on an integral transform formalism of measurable probe observables, where analytically derived kernels unravel efficiently the required field information at zero interaction time, minimizing decoherence effects. The proposed scheme is suitable for fields that, while inaccessible to a direct measurement, enjoy one and two-photon Jaynes-Cummings interactions with a two-level probe, like spin, phonon, or cavity fields. Available data from previous experiments are used to confirm our predictions.     

Force-insensitive optical cavity

We describe a rigidly mounted optical cavity that is insensitive to inertial forces acting in any direction and to the compressive force used to constrain it. The design is based on a cubic geometry with four supports placed symmetrically about the optical axis in a tetrahedral configuration. To measure the inertial force sensitivity, a laser is locked to the cavity while it is inverted about three orthogonal axes. The maximum acceleration sensitivity is 2.5×10?11/g (where g=9.81 ms?2), the lowest passive sensitivity to be reported for an optical cavity.     

Microwave cooling of Josephson plasma oscillations

An extended Josephson junction can be described as a microwave cavity coupled to a Josephson oscillator. This is formally equivalent to a Fabry-Perot cavity with a freely vibrating mirror, where it has been shown that radiation pressure from photons in the cavity can reduce (increase) the vibrations of the mirror, effectively cooling (heating) it. We demonstrate that, similarly, the superconducting phase difference across a Josephson junction-the Josephson phase-can be "cooled" or "heated" by microwave excitation of the junction and that both these effects increase with microwave power.     

Longitudinal-phonon relaxation mechanisms in cubic crystals of germanium,silicon, and diamond

The relaxation rates of thermal and high-frequency longitudinal phonons are calculated using an anisotropic-continuum model. Three-phonon scattering mechanisms (L ? L + L, L ? T + L) for the phonon relaxation are considered. Anisotropic anharmonic phonon scattering in cubic crystals is described in terms of the second-and third-order elastic moduli. The parameters determining the longitudinal-phonon relaxation rates are found for germanium, silicon, and diamond crystals. The long-wavelength limit and the transition to the isotropic-medium model are considered, and the dependences of the relaxation rates of thermal and high-frequency phonons on temperature and phonon wave vector are analyzed for these crystals.     

Phonon‐polariton entrapment in homogenous surface phonon cavities

Surface phonon cavities that are homogenous in both mechanical and dielectric properties are reported. The cavities are formed by the placement of a defect of a single domain within periodic domain inversion of single crystal piezoelectric lithium niobate that exhibits surface phononic bandgap through the phonon‐polariton coupling. Surface cavity resonances are observed within the bandgap, which manifest in entrapment of phonon‐polariton within the defect. In addition to demonstrating that the observed resonances are non‐radiative and decoupled to bulk radiation, which is critical for high Q cavities, it is also shown the possibility to tune the surface cavity resonance spectra simply by varying the defect width. Such an ability to excite surface cavity resonance that is non‐radiative with simultaneous localization of the electric field together with the advantage of a cavity that is physically formed from a completely monolithic and uniform material offers unique opportunities for widespread applications for example in actuation, detection, and phonon lasing that can be fully integrated with other physical systems such as quantum acoustics, photonics, and microfluidics.

     

Phonon-dressed Mollow triplet in the regime of cavity quantum electrodynamics: excitation-induced dephasing and nonperturbative cavity feeding effects

We study the resonance fluorescence spectra of a driven quantum dot placed inside a high-Q semiconductor cavity and interacting with an acoustic phonon bath. The dynamics is calculated using a time-convolutionless master equation in the polaron frame. We predict pronounced spectral broadening of the Mollow sidebands through off-resonant cavity emission which, for small cavity-coupling rates, increases quadratically with the Rabi frequency in direct agreement with recent experiments using semiconductor micropillars [S.?M. Ulrich et al., preceding Letter, Phys. Rev. Lett. 106, 247402 (2011)]. We also demonstrate that, surprisingly, phonon coupling actually helps resolve signatures of the elusive second rungs of the Jaynes-Cummings ladder states via off-resonant cavity feeding. Both multiphonon and multiphoton effects are shown to play a qualitatively important role on the fluorescence spectra.     

Dispersive anisotropic ballistic phonon propagation in [100] GaAs

We report experimental observations of the phonon focusing pattern in [100] GaAs using low temperature electron beam scanning for phonon generation. The typical dispersive effects for high-frequency phonons expected from the calculations by Tamura have clearly been observed using PbIn tunnel junctions for phonon detection. The quantitative comparison of our experimental results with the frequency dependent calculations by Tamura allowed to determine the dominant phonon frequencies contributing to the detector signal in our different experiments. Above the temperature of the -point the dominant phonon frequencies appear to be shifted considerably to lower values, which could be explained by a heating effect in the liquid-He layer adjacent to the tunnel junction detector. By comparing the observed magnitude of the detector signal with different theoretical treatments of the detector response, we have found satisfactory agreement for a model where the perturbation due to the high-frequency phonons is restricted to the base electrode of the detector reached first by the phonons following their passage through the crystal.     

Theory of non-Markovian dynamics in resonance fluorescence spectrum

We present a detailed theoretical study of non-Markovian dynamics in the fluorescence spectrum of a driven semiconductor quantum dot (QD), embedded in a cavity and coupled to a three-dimensional (3D) acoustic phonon reservoir. In particular, we investigate the effect of pure dephasing on one of the side-peaks of the Mollow-triplet spectrum, expressed in terms of the off-diagonal element of the reduced system operator. The QD is modeled as a two-level system with an excited state representing a single exciton, and ground state represents the absence of an exciton. Coupling to the radiative modes of the cavity is treated within usual Born–Markov approximation, whereas dot-phonon coupling is discussed within non-Markovian regime beyond Born approximation. Using an equation-of-motion technique, the dot-phonon coupling is solved exactly and found that the exact result coincides with that of obtained within Born approximation. Furthermore, a Markov approximation is carried out with respect to the phonon interaction and compared with the non-Markovian lineshape for different values of the phonon bath temperature. We have found that coupling to the phonons vanishes for a resonant pump laser. For a non-resonant pump, we have characterized the effect of dot-laser detuning and temperature of the phonon bath on the lineshape. The sideband undergoes a distinct narrowing and acquires an asymmetric shape with increasing phonon bath temperature. We have explained this behavior using a dressed-state picture of the QD levels.     

Ortho-para conversion rate in solid hydrogen under pressure

We report new measurements of the ortho-para conversion rate in solid H₂ at 4.2 K for densities ?₀ ? ? ? 1.7?₀, where ?₀ is the density at zero pressure. The conversion rate shows evidence of two maxima, at ～ 1.3?₀ and at ～ 1.5?₀ respectively. A qualitative discussion of this behavior is presented in terms of the theory of phonon creation during the conversion, and this discussion shows the consistency between the observed maxima and the shape of the phonon spectrum.