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arXiv:1307.7400 · Physical Review A

Mollow triplet for cavity-mediated laser cooling

Oleg Kim, Almut Beige

Published Nov 15, 2013• 6 citations
arXivHTMLPDF

Abstract

Here we analyze cavity-mediated laser cooling for an experimental setup with an external trap which strongly confines the motion of a particle in the direction of the cavity axis. It is shown that the stationary-state phonon number exhibits three sharp minima as a function of the atom-cavity detuning due to a direct atom-phonon-photon coupling term in the system Hamiltonian. These resonances have the same origin as the Mollow triplet in the resonance fluorescence of a laser-driven atomic system. It is shown that a laser-Rabi-frequency-dependent atom-cavity detuning yields the lowest stationary-state phonon number for a wide range of experimental parameters.

DOI
10.1103/physreva.88.053417

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Here we analyze cavity-mediated laser cooling for an experimental setup with an external trap which strongly confines the motion of a particle in the direction of the cavity axis. It is shown that the stationary-state phonon number exhibits three sharp minima as a function of the atom-cavity detuning due to a direct atom-phonon-photon coupling term in the system Hamiltonian. These resonances have the same origin as the Mollow triplet in the resonance fluorescence of a laser-driven atomic system. It is shown that a laser-Rabi-frequency-dependent atom-cavity detuning yields the lowest stationary-state phonon number for a wide range of experimental parameters.
Cavity-mediated cooling has the potential to become one of the most efficient techniques to cool molecular species down to very low temperatures. This thesis studies the use of rate equations to analyse the cooling process in such systems. In particular the master equation is used to find rate equations that can determine the rate of change of phonons in the system. The general idea behind cavity cooling is the continuous conversion of phonons into cavity photons. While there is no spontaneous emission and decay rate associated with the concept of phonons, photons are created after a change in the phonon number has occurred and can then leak out through the cavity mirrors easily. Hence the conversion of phonons into photons can result in the constant removal of phonon energy from the system. In this thesis we compare cavity mediated cooling with single particle laser cooling. It is shown that cavity cooling is essentially the same as ordinary laser cooling. This is done by calculating the stationary state phonon number mss and the cooling rate y as a function of the system parameters. For example, when the trap phonon frequency υ is either much larger or much smaller than the cavity decay rate k , the minimum stationary state phonon number scales as k²/16v² (strong confinement regime) and as k/4 (weak confinement regime), respectively. Replacing k with Ѓ yields the steady states associated with ordinary laser cooling.
We present both experimental and theoretical investigations of a laser-driven quantum dot (QD) in the dressed-state regime of resonance fluorescence. We explore the role of phonon scattering and pure dephasing on the detuning-dependence of the Mollow triplet and show that the triplet sidebands may spectrally broaden or narrow with increasing detuning. Based on a polaron master equation approach, which includes electron-phonon interaction nonperturbatively, we derive a fully analytical expression for the spectrum. With respect to detuning dependence, we identify a crossover between the regimes of spectral sideband narrowing or broadening. We also predict regimes of phonon-induced squeezing and anti-squeezing of the spectral resonances. A comparison of the theoretical predictions to detailed experimental studies on the laser detuning-dependence of Mollow triplet resonance emission from single In(Ga)As QDs reveals excellent agreement.
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.
This paper analyzes the cooling of a single particle in a harmonic trap with red-detuned laser light with fewer approximations than previously done in the literature. We avoid the adiabatic elimination of the excited atomic state but are still interested in Lamb-Dicke parameters $\ensuremath{\eta}\ensuremath{\ll}1$. Our results show that the Rabi frequency of the cooling laser can be chosen higher than previously assumed, thereby increasing the effective cooling rate but not affecting the final outcome of the cooling process. Since laser cooling is already a well-established experimental technique, the main aim of this paper is to present a model which can be extended to more complex scenarios, like cavity-mediated laser cooling.
We present a comprehensive theoretical study of the resonance fluorescence spectra of an coherently-driven quantum dot (QD) placed inside a high-QQQ 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 paper [C. Roy and S. Hughes, Phys. Rev. Lett. 106, 247403 (2011)] to describe the QD Mollow triplet in the regime of semiconductor cavity QED. Here, we introduce two ME forms, Nakajima-Zwanzig and time convolutionless (TC), both to second order in the system--phonon-reservoir perturbation. In the polaron frame, these two ME forms are shown to yield equivalent population dynamics and fluorescence spectra for a continuous wave (cw) driving field. We also demonstrate that a Markov approximation is valid for computing the incoherent scattering processes, and we subsequently exploit the TC ME to explore the resonance fluorescence spectra of an exciton-driven QD. Both cavity-emitted and exciton-emitted spectra are studied, and these are found to have qualitatively different spectral features. Using a coherent driving field, the well-known characteristics of the atomic Mollow triplet are shown to be considerably modified with electron--acoustic-phonon scattering, and we highlight the key effects arising from both cavity coupling and electron-phonon coupling. Regimes of pronounced cavity feeding and anharmonic cavity QED are exemplified, and we find that the cavity coupling depends sensitively on the exciton-cavity detuning and the temperature of the phonon bath. We show how the full width at half maximum (linewidth) of the Mollow-triplet sidebands varies as a function of the square of the Rabi frequency of the cw pump. Phonon-mediated cavity coupling also contributes to the spectral broadening of the Mollow triplet, depending upon the exciton-cavity detuning and the strength of the exciton-cavity coupling rate. Finally, we calculate the fluorescence spectra for off-resonance cw driving and investigate the resulting Mollow-triplet linewidths.
Cavity-mediated cooling of the center--of--mass motion of a transversally, coherently pumped atom along the axis of a high--Q cavity is studied. The internal dynamics of the atomic dipole strongly coupled to the cavity field is treated by a non-perturbative quantum mechanical model, while the effect of the cavity on the external motion is described classically in terms of the analytically obtained linear friction and diffusion coefficients. Efficient cavity-induced damping is found which leads to steady-state temperatures well-below the Doppler limit. We reveal a mathematical symmetry between the results here and for a similar system where, instead of the atom, the cavity field is pumped. The cooling process is strongly enhanced in a degenerate multimode cavity. Both the temperature and the number of scattered photons during the characteristic cooling time exhibits a significant reduction with increasing number of modes involved in the dynamics. The residual number of spontaneous emissions in a cooling time for large mode degeneracy can reach and even drop below the limit of a single photon.