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Creating stable superposed states of matter is one of the most intriguing aspects of quantum physics, leading to a variety of counter-intuitive scenarios along with a possibility of restructuring the way we understand, process and communicate information. Accordingly, there has been a major research thrust in understanding and quantifying such coherent superposed states. Here we propose and experimentally explore a quantifier that captures effective coherent superposition of states in an atomic ensemble at room-temperature. The quantifier provides a direct measure of ground state coherence for electromagnetically induced transparency (EIT) along with distinct signature of transition from EIT to Autler-Townes splitting (ATS) regime in the ensemble. Using the quantifier as an indicator, we further demonstrate a mechanism to coherently control and freeze coherence by introducing an active decay compensation channel. In the growing pursuit of quantum systems at room-temperature, our results provide a unique way to phenomenologically quantify and coherently control coherence in atom-like systems.Ability to generate, probe and control superposed states of physical systems provide distinct technological advantages in quantum protocols, when compared to their corresponding classical counterparts [1][2][3][4][5][6]. Even entanglement [7-10], a critically important resource in quantum information, relies on superposed states of distinctly measurable channels. Over last few decades, there has therefore been a tremendous thrust in research, to better quantify such states theoretically [11][12][13], and to generate and control them experimentally [14][15][16][17][18][19][20][21]. A widely used technique to generate superposed states in atomlike systems [22,23] is based on the phenomenon of electromagnetically induced transparency(EIT) [14][15][16][17], where a strong control field is used to drive an effective three level atomic system into a particular coherent superposition of ground-state sub-levels (|1 and |2 , Fig. 1a), known as dark state, in presence of a weak probe field. Such superposed dark states remain mostly decoupled from the lossy excited state (|3 ) [14-17] leading to dramatic effects such as slow [24], stopped [25] and stored [25][26][27] light, generation of entangled photons [7-10] and enhanced optical non-linearities at the level of single photons [28][29][30]. With such broad applicability [22,23], harnessing superposed states to their complete potential requires a concrete means of quantifying the corresponding coherence.Traditionally, superposition in EIT is characterized spectroscopically, through its signature transparency window in probe absorption profile ( Fig. 1b). However, it is also well acknowledged that such a transparency is not necessarily a unique signature of superposed states, but can also appear due to the strong control field either optically pumping atoms out of the Λ system [31] or hybridizing the ground state with the excited state, leading to Autler-Townes splitting (ATS) in the abs...

In a thermal ensemble of atoms driven by coherent fields, how does evolution of quantum superposition compete with classical dynamics of optical pumping and atomic diffusion? Is it optical pumping that first prepares a thermal ensemble, with coherent superposition developing subsequently or is it the other way round: coherently superposed atoms driven to steady state via optical pumping? Using a stroboscopic probing technique, here we experimentally explore these questions. A 100 ns pulse is used to probe an experimentally simulated, closed three-level, Λ-like configuration in rubidium atoms, driven by strong coherent (control) and incoherent fields. Temporal evolution of probe transmission shows an initial overshoot with turn-on of control, resulting in a scenario akin to lasing without inversion. The corresponding rise time is dictated by coherent dynamics, with a distinct experimental signature of half-cycle Rabi flop in a thermal ensemble of atoms. Our results indicate that, in fact, optical pumping drives the atoms to a steady state in a significantly longer time-scale that sustains superposed dark states. Eventual control turn-off leads to a sudden fall in transmission with an ubiquitous signature for identifying closed and open systems. Numerical simulations and toy-model predictions confirm our claims. These studies reveal new insights into a rich and complex dynamics associated with atoms in thermal ensemble, which are otherwise absent in state-prepared, cold atomic ensembles.

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