Theory of intersubband resonance fluorescence

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.The fluorescence spectrum of a resonantly pumped two level system (TLS) is characterised by the three peak profile named after Mollow [1]. Under strong pumping, the levels of the TLS are split by the ac Stark effect into doublets, |± , whose splitting, Ω, is directly proportional to the pump amplitude. Of the four possible spontaneous emission channels between two doublets, two are resonant with the bare frequency of the TLS, ω 12 , and the other two are at frequency ω 12 ± Ω [see Fig. 1 for a scheme of the emission channels and frequencies]. From this simple picture it can be inferred that the emission from the central peak and from the satellites are in ratio 1:2:1, a result that still holds for more refined theoretical approaches [2][3][4]. To date the Mollow triplet has been observed in a wealth of different systems well modelled by a TLS: atoms [5,6], quantum dots [7][8][9][10][11][12], single molecules [13], superconducting qubits [14][15][16], and semiconductor quantum well (QW) excitons [17,18].Intersubband transitions (ISBTs) occur between two QW conduction subbands, with the lower one containing a two dimensional electron gas (2DEG) created through doping [19], temperature [20], or by optically exciting electrons from the valence band [21,22]. Unbound excitations, ISBTs have a narrow absorption line thanks to the fact that conduction subbands are quasi-parallel [23,24] (see Fig. 2 (a) for a graphical representation). Although in ISBTs the Mollow triplet has not yet been directly measured, the ac Stark effect, which can be interpreted as indirect evidence, has been clearly observed [25]. While ISBTs are usually theoretically described as collections of independent TLSs [25-28], it has recently been shown [29] that such an approximation breaks down in the nonlinear regime, when a macroscopic fraction of the total number of electrons is in the excited subband. As explained in Ref. [29], the origin of such a difference can be intuitively traced to the different dimensionality of the Hilbert space: 2 N for a collection of N TLSs and 2N N for an ISBT involving N electrons and neglecting border effects, which tends tofor large N . In a setup adapted to measure the resonance fluorescence of the system, almost all the electrons in the first subband are excited at the same time [25]. We can thus expect that the TLS approximation, used to derive the...

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