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arXiv:1506.07972 · Physical Review B

Theory of intersubband resonance fluorescence

Nathan Shammah, Simone De Liberato

Published Nov 9, 2015• 4 citations
arXivHTMLPDF

Abstract

The fluorescence spectrum of a strongly pumped two-level system is characterized by the Mollow triplet that has been observed in a variety of systems, ranging from atoms to quantum dots and superconducting qubits. We theoretically studied the fluorescence of a strongly pumped intersubband transition in a quantum well. Our results show that the many-electron nature of such a system leads to a modification of the usual Mollow theory. In particular, the intensity of the central peak in the fluorescence spectrum becomes a function of the electron coherence, allowing access to the coherence time of a two-dimensional electron gas through a fluorescence intensity measurement.

DOI
10.1103/physrevb.92.201402

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The fluorescence spectrum of a strongly pumped two-level system is characterized by the Mollow triplet that has been observed in a variety of systems, ranging from atoms to quantum dots and superconducting qubits. We theoretically studied the fluorescence of a strongly pumped intersubband transition in a quantum well. Our results show that the many-electron nature of such a system leads to a modification of the usual Mollow theory. In particular, the intensity of the central peak in the fluorescence spectrum becomes a function of the electron coherence, allowing access to the coherence time of a two-dimensional electron gas through a fluorescence intensity measurement.
Intersubband transitions are unbound electronic transitions of doped quantum wells, semiconductors heterostructures with a planar symmetry. I theoretically studied the fluorescence of a strongly pumped intersubband transition, finding that the many electron nature of such a system leads to a modification of the usual Mollow triplet. In particular, the intensity of the central peak in the fluorescence spectrum becomes a function of the electron coherence, allowing access to the coherence time of a quasi two-dimensional electron gas through a fluorescence intensity measurement. Moreover, while transitions between the two states of the ac Stark-split doublet are forbidden in centrosymmetric systems, and thus almost impossible to observe in experiments performed with atoms they become allowed in asymmetric quantum wells, in which the wave function symmetry can be broken. I developed a many-body theory describing also this intradoublet emission, showing that by using doped asymmetry, the emission can be orders of magnitude higher than in previously studied systems. This opens the way to the realization of monolithic and tunable terahertz emitters since the Rabi frequency at which this emission occurs lies in the terahertz range and can be tuned by the pump power. Finally, I have investigated if superfluorescence can occur in intersubband transitions. In order to do so I used a general quantum master equation that includes dephasing and nonradiative emission to model the many-body system in solid state. Performing a second-order approximation allowed to obtain a closed system of equations that were studied analytically and numerically, verifying that in the regimes characteristic of intersubband transitions cooperative effects leading to powerful bursts of light could be observed experimentally.
We show that the resonance fluorescence spectrum of a quantum dot excited by a strong optical pulse contains multiple peaks beyond those of the Mollow triplet. We show that as the area of the optical pulse is increased, new side peaks split off the central peak and shift in frequency. A simple analytical theory has been derived, which quantitatively accounts for the appearance and position of the peaks. This theory explains the physics responsible for the multiple peaks. By considering the time-dependent spectrum we demonstrate a time ordering of the side peaks, which is further evidence for the suggested physical explanation.
We experimentally demonstrate the resonance fluorescence of a two-level artificial atom strongly coupled to a single-mode cavity field. The effect was theoretically predicted thirty years ago by Savage [Phys. Rev. Lett. 63, 1376 (1989)]. The system consists of a superconducting qubit circuit and a one-dimensional transmission line resonator. In addition, a one-dimensional transmission line strongly coupled to the atom serves as an open space. The effect takes place, when a microwave field is applied to the cavity, which in turn is resonantly coupled to the atom. The fluorescence spectrum is measured via the emission into the transmission line. We find that the central peak is determined by the atom spontaneous emission to the open space and the widths of side peaks are largely determined by the coherent interaction between the atom and the cavity, that is, the fluorescence spectrum here is very different from that of the Mollow triplet. We also derive analytical form for the spectrum. Our experimental results agree well with theoretical calculations.
Summary form only given. The problem of an atom driven by a strong laser was first investigated theoretically in 1969 by B.R. Mollow. He discovered that the resonance fluorescence spectrum has a three-peaked structure with the central peak being more pronounced than the two side peaks. The common Mollow triplet fluorescence pattern can be altered in many ways, by making adjustments to the system. The system can be placed in a squeezed vacuum, the atom can be placed in a cavity, or a bichromatic field can be used instead of a monochromatic laser. These alterations all have an effect on the resulting resonance fluorescence and probe absorption spectra. Other interesting modifications occur when the atom interacts with a stochastic field as well as a laser. The previous approaches were numerical. Here we also obtain analytic solutions (in certain limits) which provide additional insight.
Fluorescence from a coherently driven two-level atom that is damped by a squeezed vacuum is studied. We show that the mean atomic polarization depends on the relative phases of the squeezed vacuum and the coherent driving field. The fluorescent spectrum is calculated and shows several modifications over the spectrum for normal resonance fluorescence. In particular, the central peak of the Mollow triplet has a linewidth that depends on the phase of the driving field. For strong squeezing this peak can either be much narrower or much broader than the natural linewidth of the atom.
A counterpart of the Mollow triplet (luminescence line shape of a two-level system under coherent excitation) is obtained for the case of incoherent excitation in a cavity. The system acquires coherence through the strong-coupling between the cavity and the emitter. Analytical expressions, in excellent agreement with numerical results, pinpoint analogies and differences between the conventional resonance fluorescence spectrum and its cavity QED analogue under incoherent excitation. Most notably, the satellites broaden and split sublinearly with increasing incoherent pumping.