We present a medium-dependent quantum optics approach to describe the influence of electron-acoustic phonon coupling on the emission spectra of a strongly coupled quantum-dot cavity system. Using a canonical Hamiltonian for light quantization and a photon Green function formalism, phonons are included to all orders through the dot polarizability function obtained within the independent Boson model. We derive simple user-friendly analytical expressions for the linear quantum light spectrum, including the influence from both exciton and cavity-emission decay channels. In the regime of semiconductor cavity-QED, we study cavity emission for various exciton-cavity detunings and demonstrate rich spectral asymmetries as well as cavity-mode suppression and enhancement effects. Our technique is nonperturbative, and non-Markovian, and can be applied to study photon emission from a wide range of semiconductor quantum dot structures, including waveguides and coupled cavity arrays. We compare our theory directly to recent and apparently puzzling experimental data for a single site-controlled quantum dot in a photonic crystal cavity and show good agreement as a function of cavity-dot detuning and as a function of temperature.
The generation of photons in a microcavity coupled to a laser-driven quantum dot interacting with longitudinal acoustic (LA) phonons is studied in the regime of simultaneously strong driving and strong dot-cavity coupling. The stationary cavity photon number is found to depend in a non-trivial way on the detuning between the laser and the exciton transition in the dot. In particular, the maximal efficiency of the cavity feeding is obtained for detunings corresponding to transition energies between cavity-dressed states with excitation numbers larger than one. Phonons significantly enhance the …
For a semiconductor quantum dot strongly coupled to a microcavity, we theoretically investigate phonon-assisted transitions from the exciton to a cavity photon, where the energy mismatch is compensated by phonon emission or absorption. By means of a Schrieffer-Wolff transformation we derive an effective Hamiltonian, which describes the combined effect of exciton-cavity and exciton-phonon coupling, and compute the scattering rates within a Fermi golden rule approach. The results of this approach are compared with those of a recently reported description scheme based on the independent Boson mod…
Recent experiments have demonstrated that for a quantum dot in an optical resonator off-resonant cavity mode emission can occur even for detunings of the order of 10 meV. We show that Coulomb mediated Auger processes based on additional carriers in delocalized states can facilitate this far off-resonant emission. Using a novel theoretical approach for a non-perturbative treatment of the Auger-assisted quantum-dot carrier recombination, we present numerical calculations of the far off-resonant cavity feeding rate and cavity mean photon number confirming efficient coupling at higher densities of…
We experimentally probe the non-resonant feeding of photons into the optical mode of a two dimensional photonic crystal nanocavity from the discrete emission from a quantum dot. For a strongly coupled system of a single exciton and the cavity mode, we track the detuning-dependent photoluminescence intensity of the polariton peaks at different lattice temperatures. At low temperatures we observe a clear asymmetry in the emission intensity depending on whether the exciton is at higher or lower energy than the cavity mode. At high temperatures this asymmetry vanishes when the probabilities to emi…
Surface acoustic waves (SAWs) in the GHz frequency range can inject spin currents dynamically into adjacent nonmagnetic layers via spin pumping effect associated with ferromagnetic resonance. Here, we demonstrate an enhancement of acoustic ferromagnetic resonance and spin current generation by a pair of SAW reflector gratings, which form an acoustic analogue of the distributed Bragg reflector cavity. In the experiment, we confirmed 2.04 $\pm$ 0.02 times larger SAW power absorption in a device with cavity than in case of no acoustic cavity. We confirmed up to 2.96 $\pm$ 0.02 times larger spin c…
We experimentally investigate the non-resonant feeding of photons into the optical mode of a zero dimensional nanocavity by quantum dot multiexciton transitions. Power dependent photoluminescence measurements reveal a super-linear power dependence of the mode emission, indicating that the emission stems from multiexcitons. By monitoring the temporal evolution of the photoluminescence spectrum, we observe a clear anticorrelation of the mode and single exciton emission; the mode emission quenches as the population in the system reduces towards the single exciton level whilst the intensity of the…
Two series of [Ru10/Cox)]12 and [Ru6/Cr3/Cox)]12 x=16-60 easy-plane anisotropy multilayers (all thicknesses in Å), prepared by sputter deposition, are studied by cavity FMR. The acoustic modes are excited by setting the RF field perpendicular to the saturating in-plane field. Their resonance fields are in good agreement with the values predicted for acoustic modes by macrospin models, using the interlayer RKKY exchange and anisotropy fields derived by the magnetic measurements. The resonance fields of the modes excited by setting the RF field parallel to the saturating field, are lower than th…
We consider an optomechanical system comprising a single cavity mode and a dense spectrum of acoustic modes and solve for the quantum dynamics of initial cavity mode Fock (i.e., photon number) superposition states and thermal acoustic states. The optomechanical interaction results in dephasing without damping and bears some analogy to gravitational decoherence. For a cavity mode locally coupled to a one-dimensional (1D) elastic string-like environment or two-dimensional (2D) elastic membrane-like environment, we find that the dephasing dynamics depends respectively on the string length and mem…
We present measurements at millikelvin temperatures of the microwave-frequency acoustic properties of a crystalline silicon nanobeam cavity incorporating a phononic bandgap clamping structure for acoustic confinement. Utilizing pulsed laser light to excite a co-localized optical mode of the nanobeam cavity, we measure the dynamics of cavity acoustic modes with single-phonon sensitivity. Energy ringdown measurements for the fundamental $5$~GHz acoustic mode of the cavity shows an exponential increase in phonon lifetime versus number of periods in the phononic bandgap shield, increasing up to $τ…
Magnons, namely spin waves, are collective spin excitations in ferromagnets, and their control through coupling with other excitations is a key technology for future hybrid spintronic devices. Although strong coupling has been demonstrated with microwave photonic structures, an alternative approach permitting high density integration and minimized electromagnetic crosstalk is required. Here we report a planar cavity magnomechanical system, where the cavity of surface acoustic waves enhances the spatial and spectral power density to thus implement magnon-phonon coupling at room temperature. Exc…
We investigate an acoustical analog of circuit quantum electrodynamics that facilitates compact high-Q (${>}20,000$) microwave-frequency cavities with dense spectra. We fabricate and characterize a device that comprises a flux tunable transmon coupled to a $300\,\mathrm{μm}$ long surface acoustic wave resonator. For some modes, the qubit-cavity coupling reaches $6.5\,\mathrm{MHz}$, exceeding the cavity loss rate ($200\,\mathrm{kHz}$), qubit linewidth ($1.1\,\mathrm{MHz}$), and the cavity free spectral range ($4.8\,\mathrm{MHz}$), placing the device in both the strong coupling and strong multim…
Surface acoustic waves (SAWs) are a versatile tool for coherently interfacing with a variety of solid-state quantum systems spanning microwave to optical frequencies, including superconducting qubits, spins, and quantum emitters. Here, we demonstrate SAW cavity optomechanics with quantum emitters in 2D materials, specifically monolayer WSe$_2$, on a planar lithium niobate SAW resonator driven by superconducting electronics. Using steady-state photoluminescence spectroscopy and time-resolved single-photon counting, we map the temporal dynamics of modulated 2D emitters under coupling to differen…
A hybrid device comprising a (Al)GaAs quantum dot heterostructure and a LiNbO$_3$ surface acoustic wave resonator is fabricated by heterointegration. High acoustic quality factors $Q>4000$ are demonstrated for an operation frequency $f\approx 300$ MHz. The measured large quality factor-frequency products $Q\times f>10^{12}$ ensures the suppression of decoherence due to thermal noise for temperatures exceeding $T>50\,\mathrm{K}$. Frequency and position dependent optomechanical coupling of single quantum dots and the resonator modes is observed.
We report a development of an electro-optomechanical system based on a surface acoustic wave (SAW), where a piezoelectric material with a large optoelastic susceptibility is used for the coupling of both a radio wave and optical light to the SAW. In the optical domain, we exploit a tensorial nature of the optoelastic effect to show a polarization dependence of the photon-SAW interaction. We discuss the construction of two-dimensional SAW focusing circuits for the coupling enhancement and the optical cavity enhanced photon-phonon scattering. We estimate an optomechanical coupling rate $g_0$ of …
We demonstrate feedback cooling of a millimeter-scale, 40 kHz SiN membrane from room temperature to 5 mK (3000 phonons) using a Michelson interferometer, and discuss the challenges to ground state cooling without an optical cavity. This advance appears within reach of current membrane technology, positioning it as a compelling alternative to levitated systems for quantum sensing and fundamental weak force measurements.
In the same way that micro-mechanical resonators resemble guitar strings and drums, Surface Acoustic Waves (SAW) resemble the sound these instruments produce, but moving over a solid surface rather than through air. In contrast with oscillations in suspended resonators, such propagating mechanical waves have not before been studied near the quantum mechanical limits. Here, we demonstrate local probing of SAW with a displacement sensitivity of 30amRMS/sqrt(Hz) and detection sensitivity on the single-phonon level after averaging, at a frequency of 932MHz. Our probe is a piezoelectrically coupled…
The time-reversal mirror (TRM) prescribes the reverse playback of a signal to focalize an acoustic excitation as a Loschmidt echo. In the quantum domain, the perfect inverse filter (PIF) processes this signal to ensure an exact reversion provided that the excitation originated outside the cavity delimited by the transducers. We show that PIF takes a simple form when the initial excitation is created inside this cavity. This also applies to the acoustical case, where it corrects the TRM and improves the design of an acoustic bazooka. We solve an open chaotic cavity modeling a quantum bazooka an…
We resolve phonon number states in the spectrum of a superconducting qubit coupled to a multimode acoustic cavity. Crucial to this resolution is the sharp frequency dependence in the qubit-phonon interaction engineered by coupling the qubit to surface acoustic waves in two locations separated by $\sim40$ acoustic wavelengths. In analogy to double-slit diffraction, the resulting self-interference generates high-contrast frequency structure in the qubit-phonon interaction. We observe this frequency structure both in the coupling rate to multiple cavity modes and in the qubit spontaneous emission…
Electron-phonon coupling in semiconductor quantum dots plays a significant role in determining the optical properties of excited excitons, especially the spectral nature of emitted photons. This paper presents a comprehensive theory and analysis of emission spectra from artificial atoms or quantum dots coupled to structured photon reservoirs and acoustic phonons, when excited with incoherent pump fields. As specific examples of structured reservoirs, we chose a Lorentzian cavity and a coupled cavity waveguide, which are of current experimental interest. For the case of optical cavities, we dir…
We demonstrate that in quantum-dot cavity systems, the interplay between acoustic phonons and photon losses introduces novel features and characteristic dependencies in the system dynamics. In particular, the combined action of both loss mechanisms strongly affects the transition from the weak to the strong coupling regime as well as the shape of Mollow-type spectra in untypical ways. For weak coupling, where the spectra degenerate to a single line, we predict that their widths decrease with rising temperature.
We present a comprehensive theoretical study of the resonance fluorescence spectra of an exciton-driven quantum dot (QD) placed inside a high-$Q$ semiconductor cavity and interacting with an acoustic phonon bath. We derive a quantum master equation (ME) in the polaron frame which includes exciton-phonon and exciton-cavity coupling to all orders. This work details and extends the theory used in a recent issue of {\em Physical Review Letters} (C. Roy and S. Hughes 2011: Phys. Rev. Lett. {\bf 106} 247403) to describe the QD Mollow triplet in the regime of semiconductor cavity-QED. Here we introdu…
We develop a theoretical frame to investigate the single-photon emission spectral efficiency of a solid-state nano-emitter embedded in a high quality factor micro-cavity. This study encompasses the case of localized excitons embedded in a one, two or three-dimensional matrix. The populations evolutions are calculated based on a spin-boson model, using the non-interacting blip approximation (NIBA). We find that the single-photon spectral efficiency of the cavity-coupled emitter can be expressed by a simple formula, taking as inputs the free-space emission and absorption spectra of the emitter a…
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 obtained in the polaron frame. We demonstrate pronounced spectral broadening of the Mollow sidebands through cavity-emission which, for small cavity-coupling rates, increases quadratically with the Rabi frequency. However, for larger cavity coupling rates, this broadening dependence is found to be more complex. This field-dependent Mollow triplet broadening is prima…
We show that, under an appropriate out-of-plane static magnetic field, nuclear spins in a thin specimen on a surface acoustic wave (SAW) cavity can be resonantly excited and detected through spin-rotation coupling. Since such a SAW cavity can have the quality factor as high as $10^{4}$ and the mode volume as small as $10^{-2}$ mm$^{3}$ the signal-to-noise ratio in detecting the resonance is estimated to be quite high. We argue that detecting nuclear spin resonance of a single flake of an atomically-thin layer of two-dimensional semiconductor, which has so far been beyond hope with the conventi…
Open Nanoacoustic Resonators Based on SrTiO$_3$/YBa$_2$Cu$_3$O$_{7-x}$ Superlattices
Université Paris-Saclay（巴黎萨克雷大学）；Centre de Nanosciences et de Nanotechnologies (C2N)（纳米科学和纳米技术中心）；Laboratoire Albert Fert（阿尔贝·费尔实验室）；Thales（泰雷兹集团）；Instituto de Nanociencia y Nanotecnología, CNEA-CONICET（国家原子能委员会-国家科学研究委员会纳米科学与技术研究所）
We present here precise measurement of the resonance frequency, lifetime and shape of confined acoustic modes in the tens of GHz regime in GaAs/AlAs superlattice planar and micropillar cavities at low temperature ($\sim 20\,\textrm{K}$). The subharmonic resonant pump-probe technique, where the repetition rate of the pump laser is tuned to a subharmonic of the cavity resonance to maximize the amplitude of the acoustic resonance, in combination with a Sagnac interferometer technique for high sensitivity ($\sim 10 \,\textrm{fm}$) to the surface displacement, has been used. The cavity fundamental …
We present an experimental and theoretical study on the gain mechanism in a photonic-crystal-cavity nanolaser with embedded quantum dots. From time-resolved measurements at low excitation power we find that four excitons are coupled to the cavity. At high excitation power we observe a smooth low-threshold transition from spontaneous emission to lasing. Before lasing emission sets in, however, the excitons are observed to saturate, and the gain required for lasing originates rather from multi-electronic transitions, which give rise to a broad emission background. We compare the experiment to a …
The interaction of optical and mechanical modes in nanoscale optomechanical systems has been widely studied for applications ranging from sensing to quantum information science. Here, we develop a platform for cavity optomechanical circuits in which localized and interacting 1550 nm photons and 2.4 GHz phonons are combined with photonic and phononic waveguides. Working in GaAs facilitates manipulation of the localized mechanical mode either with a radio frequency field through the piezo-electric effect, or optically through the strong photoelastic effect. We use this to demonstrate a novel aco…
We experimentally demonstrate that the Mollow triplet sidebands of a quantum dot strongly coupled to a cavity exhibit anomalous power induced broadening and enhanced emission when one sideband is tuned over the cavity frequency. We observe a nonlinear increase of the sideband linewidth with excitation power when the Rabi frequency exceeds the detuning between the quantum dot and the cavity, consistent with a recent theoretical model that accounts for acoustic phonon-induced processes between the exciton and the cavity. In addition, the sideband tuned to the cavity shows strong resonant emissio…
We present detuning-dependent spectral and decay-rate measurements to study the difference between spectral and dynamical properties of single quantum dots embedded in micropillar and photonic-crystal cavities. For the micropillar cavity, the dynamics is well described by the dissipative Jaynes-Cummings model, while systematic deviations are observed for the emission spectra. The discrepancy for the spectra is attributed to coupling of other exciton lines to the cavity and interference of different propagation paths towards the detector of the fields emitted by the quantum dot. In contrast, qu…
Single-Wall Carbon Nanotubes (SWNTs) are among the very few candidates for single-photon sources operating in the telecom bands since they exhibit large photon antibunching up to room temperature. However, coupling a nanotube to a photonic structure is highly challenging because of the random location and emission wavelength in the growth process. Here, we demonstrate the realization of a widely tunable single-photon source by using a carbon nanotube inserted in an original repositionable fiber micro-cavity : we fully characterize the emitter in the free-space and subsequently form the cavity …
Quantum acoustodynamics (QAD) is a rapidly developing field of research, offering possibilities to realize and study macroscopic quantum-mechanical systems in a new range of frequencies, and implement transducers and new types of memories for hybrid quantum devices. Here we propose a novel design for a versatile diamond QAD cavity operating at GHz frequencies, exhibiting effective mode volumes of about $10^{-4}λ^3$. Our phononic crystal waveguide cavity implements a non-resonant analogue of the optical lightning-rod effect to localize the energy of an acoustic mode into a deeply-subwavelength …
This work presents some peculiarities of the near quantum ground state behaviour of curved (phonon trapping) Bulk Acoustic Wave (BAW) cavities when compared to a conventional mechanical resonator. The curved cavity system resolves the quandary of the conventional mechanical system where the Bose-Einstein distribution requires higher frequencies for lower quantum occupation factors contrary to the constraint of an inverse frequency dependence of the quantum fluctuations of displacement. We demonstrate how the non-trivial cavity geometry can lead to better phonon trapping, enhancing the variance…
We demonstrate the simultaneous dressing of both vacuum-to-exciton and exciton-to-biexciton transitions of a single semiconductor quantum dot in a high-Q micropillar cavity, using photoluminescence spectroscopy. Resonant two-photon excitation of the biexciton is achieved by spectrally tuning the quantum dot emission with respect to the cavity mode. The cavity couples to both transitions and amplifies the Rabi-frequency of the likewise resonant cw laser, driving the transitions. We observe strong-field splitting of the emission lines, which depend on the driving Rabi field amplitude and the cav…
We describe a chip-based, solid-state analogue of cavity-QED utilizing acoustic phonons instead of photons. We show how long-lived and tunable acceptor impurity states in silicon nanomechanical cavities can play the role of a matter non-linearity for coherent phonons just as, e.g., the Josephson qubit plays in circuit-QED. Both strong coupling (number of Rabi oscillations ~ 100) and strong dispersive coupling (0.1-2 MHz) regimes can be reached in cavities in the 1-20 GHz range, enabling the control of single phonons, phonon-phonon interactions, dispersive phonon readout of the acceptor qubit, …
We propose to pump semiconductor quantum dots with surface acoustic waves which deliver an alternating periodic sequence of electrons and holes. In combination with a good optical cavity such regular pumping could entail anti-bunching and sub-Poissonian photon statistics. In the bad-cavity limit a train of equally spaced photons would arise.
We employ detuning-dependent decay-rate measurements of a quantum dot in a photonic-crystal cavity to study the influence of phonon dephasing in a solid-state quantum-electrodynamics experiment. The experimental data agree with a microscopic non-Markovian model accounting for dephasing from longitudinal acoustic phonons, and identifies the reason for the hitherto unexplained difference between non-resonant cavity feeding in different nanocavities. From the comparison between experiment and theory we extract the effective phonon density of states experienced by the quantum dot. This quantity de…
