Optomechanical wave mixing by a single quantum dot

Abstract

Wave mixing is an archetypical phenomenon in bosonic systems. In optomechanics, the bidirectional conversion between electromagnetic waves or photons at optical frequencies and elastic waves or phonons at radio frequencies is building on precisely this fundamental principle. Surface acoustic waves (SAWs) provide a versatile interconnect on a chip and thus enable the optomechanical control of remote systems. Here we report on the coherent nonlinear three-wave mixing between the coherent fields of two radio frequency SAWs and optical laser photons via the dipole transition of a single quantum dot exciton. In the resolved sideband regime, we demonstrate fundamental acoustic analogues of sum and difference frequency generation between the two SAWs and employ phase matching to deterministically enhance or suppress individual sidebands. This transfer between the acoustic and optical domains is described by theory that fully takes into account direct and virtual multiphonon processes. Finally, we show that the precision of the wave mixing is limited by the frequency accuracy of modern radio frequency electronics.

Photon scattering from a quantum acoustically modulated two-level system

“…Recent studies have focused on light scattering experiments from a single semiconductor QD in the presence of SAW fields. 8,9 There, it was shown that the treatment of the SAW in the semiclassical limit by simply considering a timedependent transition energy of the QD's leads to excellent agreements with the experiments. As first benchmark for our quantum acoustic model we consider the semiclassical limit of a coherent phonon state with a large amplitude.…”

“…Our approach to approximate this situation is to expand the equations in powers of the light field to retrieve the optical signal in the second order of E which is sufficient to simulate the optical scattering spectrum. 8 Therefore, we express the generating functions into a series Y = Y (0) +Y (1) +Y (2) +. .…”

“…The procedure to derive the correlation function follows the same strategy as used in Ref. [8] (see Supporting Material therein). Starting from the ground state G(t 0 ) = G (0) (t 0 ) and Y (t 0 ) = C(t 0 ) = 0 we first follow the red path, with a lightinduced transition into the polarization Y (1) * (t) (Eq.…”

“…It has been demonstrated that surface acoustic waves (SAWs) can be interfaced with single semiconductor QDs in order to coherently control the single photon emission properties of the QD. 7 We have recently demonstrated that nonlinear wave mixing can be used to precisely tailor the optical scattering spectrum 8 and that the photon emission time depends on the SAWs' properties. 9 While these recent results were obtained in the semiclassical limit of the phonon coupling, where the phonon field enters purely classically, in the present work we go a crucial step further and model the phonon im-pact on the quantum level.…”

Coherent dynamics of a single Mn-doped quantum dot revealed by four-wave mixing spectroscopy

“…16 Conversely, optical or electrical control of single quantum states confined to a QD is challenging, nonetheless intensely pursued in fundamental research. [17][18][19][20] Over the last decade, a major progress has been achieved in measuring [21][22][23] and controlling [24][25][26] the coherence of optical transitions attributed to the bound electron-hole pair, forming a QD exciton. This was achieved by performing coherent ultrafast nonlinear spectroscopy, 27 in particular four-wave mixing (FWM) on photonic devices hosting InGaAs QDs.…”