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Laser Physics

Absorption of a weak probe in singly charged n-doped quantum dots in the Voigt geometry

F. Carreño, M. A. Antón

Published Jan 4, 2019• 1 citation
Publisher

Abstract

Abstract We analyze the absorption of a weak probe field in singly charged n -doped quantum dots in the presence of an external magnetic field in the Voigt geometry. The dots are modeled as double lambda systems. A laser field pumps two of the four active transitions while a probe field is applied along the two undriven transitions. It is shown that for both on resonance and out of resonance driving gain (without inversion) is obtained at two sidebands of the dressed QDs. We found that the peak value of gain can be maximized by a proper selection of both the external magnetic field and the Rabi frequency of the pump field for out of resonance driving. We also show that the coherent driving in combination with above-band excitation allows one to turn the absorption peaks into gain (with inversion) in the whole spectral range.

DOI
10.1088/1555-6611/aaf639

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Abstract We analyze the absorption of a weak probe field in singly charged n -doped quantum dots in the presence of an external magnetic field in the Voigt geometry. The dots are modeled as double lambda systems. A laser field pumps two of the four active transitions while a probe field is applied along the two undriven transitions. It is shown that for both on resonance and out of resonance driving gain (without inversion) is obtained at two sidebands of the dressed QDs. We found that the peak value of gain can be maximized by a proper selection of both the external magnetic field and the Rabi frequency of the pump field for out of resonance driving. We also show that the coherent driving in combination with above-band excitation allows one to turn the absorption peaks into gain (with inversion) in the whole spectral range.
We report on the resonance fluorescence and phase-dependent spectra in singly charged nnn-doped quantum dots in the presence of a strong external magnetic field in the Voigt geometry. The use of a nonresonant laser field driving two of the four active transitions results in the obtention of fluorescent photons along the four channels. The fluorescent photons coming from the two undriven transitions exhibit sidebands whose spectral location can be tuned through the Rabi frequency of the driving field and, most interestingly, their linewidths remain subnatural even for large values of the Rabi frequency of the laser field. It is shown that those sidebands present quantum fluctuations below the fundamental limit set by vacuum fluctuations. The numerical findings are fully explained by considering how the dressed states evolve in terms of the external physical magnitudes: the detuning, the Rabi frequency, and the dephasing rates.
Density-matrix equations for electrons in laser-coupled quantum wells are derived in second quantization, including an off-diagonal radiative-decay coupling between a pair of electron transitions. Calculations of spontaneous photoluminescence and time-resolved optical absorption for the probe field are formulated. The zero absorption of the pump-laser field within an overlapping region between two absorption peaks is found in a resonant asymmetric double-quantum-well system and explained as the quantum interference between two nearly degenerate electron transitions. Quantum interference is clearly demonstrated through phase cancellation between the two statistically averaged transition dipole moments. The laser frequency for zero absorption can be tuned within a tunneling gap by applying a small dc bias field. The ${k}_{\ensuremath{\Vert}}$-dependent energy-level separation is found to be a crucial factor for destroying quantum interference. The optical gain of the probe field is seen as a hole in the weak absorption peak for the resonant asymmetric double quantum wells selectively coupled by a laser field and shown to be a result of the partial inversion of the electron occupation probabilities in momentum space after laser excitation. The probe-field gain increases with the strength of the pump laser. The effects of transition blocking, induced quantum coherence, and off-diagonal radiative-decay coupling are quantitatively analyzed for this gain.
Although individual spins in quantum dots have been studied extensively as qubits, their investigation under strong resonant driving in the scope of accessing Mollow physics is still an open question. Here, we have grown high quality positively charged quantum dots embedded in a planar microcavity that enable enhanced light-matter interactions. Under a strong magnetic field in the Voigt configuration, individual positively charged quantum dots provide a double lambda level structure. Using a combination of above-band and resonant excitation, we observe the formation of Mollow triplets on all optical transitions. We find that when the strong resonant drive power is used to tune the Mollow-triplet lines through each other, we observe anticrossings. We also demonstrate that the interaction that gives rise to the anticrossings can be controlled in strength by tuning the polarization of the resonant laser drive. Quantum-optical modeling of our system fully captures the experimentally observed spectra and provides insight on the complicated level structure that results from the strong driving of the double lambda system.
The obtention of spontaneous Raman photons is analyzed in singly charged ppp-doped quantum dots in the absence of an external magnetic field. The use of a far detuned single driving laser allows one to obtain a Raman photon line which exhibits a subnatural linewidth, and whose center can be tuned by changing the detuning and/or the Rabi frequency of the driving field. The Raman photons are produced along the undriven transition and they arise from a weak interaction of the trion states with the nuclear spins. The operating point for the gate voltage of the heterostructure can also be used to modify the linewidth and the peak value of the fluorescent signal.
The Rabi splitting of the negatively charged exciton in a single InGaAs quantum dot is observed in resonance transmission spectroscopy. We use a pump laser excitation to drive strongly the unpolarized trion transition in a quantum dot and detect its modified absorption spectrum with a second weak probe laser. By tuning the pump laser near resonance, we observe an ac-Stark effect dispersion, with a power dependent Rabi splitting on resonance, both signatures of a strongly coupled two level system. Although the pump and probe laser fields are resonant with the same transition, we do not observe all features in the Mollow spectrum. We combine the results of pump probe with saturation spectroscopy data to deduce the individual contributions to the low power linewidth.
We calculate the absorption spectrum of a weak probe interacting with a \ensuremath{\Lambda}-shaped three-level system driven by a single pump. We find that there are four types of terms that contribute to the probe absorption: population-difference and two-photon coherence terms which derive solely from interaction with the pump (dc terms) and population-difference and two-photon coherence terms that pulsate at the pump-probe frequency offset. We find that the main features of the probe spectrum derive from the pulsating terms whereas the dc terms either interfere destructively with each other or with the pulsating terms. This is a clear extension to the three-level system of the concept of light amplification by coherence. We calculate the spectrum for three cases: (i) a degenerate population-trapped system, (ii) a degenerate system in which both transitions are population inverted, and (iii) a nondegenerate population-trapped system. The results of case (i) are similar to those for the two-level system but the population-trapped system has the advantage of avoiding pump absorption. We show that the Rabi frequency of the nonabsorbed pump can be found by determining the probe frequencies at which probe nonabsorption occurs. In (ii), the results are compared with the case where two pumps interact resonantly with a nondegenerate system. In (iii), we find that the populations in the lower states behave dispersively as a function of the pump detuning. For Rabi frequencies that are small compared to the separation between the lower levels, the lower level nearer to resonance is less populated than the other level. However, at higher Rabi frequencies, the situation is reversed. The probe spectrum contains two absorption peaks when the pump Rabi frequency is small and two emission peaks when it is large.