23. Coherence III

The paragraph introduces the topic of coherence in three-level systems, highlighting the unique processes that arise with the presence of three energy levels. The professor emphasizes the role of interference in these systems, which can lead to both constructive and destructive effects. A key concept discussed is the 'dark state,' a superposition state that does not absorb light due to destructive interference. This phenomenon is central to the discussion of lasing without inversion, a process that challenges the traditional understanding of lasing requiring a population inversion.

This section delves deeper into the concept of dark states, explaining how they can be achieved through the interaction with two laser beams. The professor discusses how dark states can lead to lasing without inversion, a process that seems counterintuitive because it does not require the traditional population inversion between energy levels. The paragraph also touches on the narrow frequency interval in which dark states exist and how this can affect the group velocity of light, leading to electromagnetically induced transparency.

The professor provides a detailed explanation of how dark states can be observed and manipulated in a laboratory setting. The discussion includes the use of Hamiltonian mechanics to describe the system and the role of Rabi frequencies in the interaction between atoms and laser light. The concept of coherent population trapping is introduced, which is a process where atoms are pumped into a dark state, ceasing to scatter light and thus becoming 'trapped' in this state.

This paragraph addresses the challenges that dark states present in laser cooling experiments, particularly with molecules. The professor explains that the presence of dark states can interrupt the cycling transition necessary for laser cooling. To overcome this, additional techniques such as applying a transverse magnetic field or using magneto-optical traps are discussed, which can help atoms exit the dark state and continue to scatter light.

The discussion shifts to the transition between dark and bright states, which are orthogonal states in a two-dimensional Hilbert space. The professor explains how the bright state is strongly coupled to the excited state by the laser field, leading to photon scattering. The paragraph also explores the concept of optical pumping in the context of these states and the subtleties that arise when the Raman resonance is not perfectly met.

The professor introduces STIRAP, a technique for adiabatic population transfer between quantum states. The process is explained as being robust against various experimental imperfections and does not require precise control of pulse areas, unlike traditional pi pulses. The paragraph discusses the concept of changing laser parameters to transition between dark and bright states and the importance of maintaining the dark state during the transfer process.

This section explores the counter-intuitive sequence used in STIRAP, where the laser beams are applied in a non-obvious order to achieve population transfer. The professor discusses the rationale behind this approach and contrasts it with the intuitive sequence, which would involve stimulating the system in a way that may not be as robust against experimental variations.

The professor demystifies the concept of dark state transfer in STIRAP, explaining that while it may seem like the system can transition between states without populating the excited state, this is not entirely accurate. The discussion includes a quantitative analysis of the population in the excited state during the transfer process and the factors that influence it.

This paragraph compares STIRAP with incoherent transfer methods, such as pi pulse transfers, in terms of their efficiency and the probability of spontaneous emission. The professor highlights the advantages of STIRAP, particularly its robustness and the reduced likelihood of populating the excited state, which can lead to heating and other undesired effects.

The professor introduces two-photon Raman transitions as an alternative method for population transfer that can achieve similar results to STIRAP. The discussion includes a comparison of the integrated population in the excited state and the conditions under which both methods perform optimally.

The final paragraph introduces the concept of lasing without inversion, which challenges the traditional belief that a population inversion is necessary for lasing. The professor explains how destructive interference can suppress absorption, allowing for lasing even when the ground state population is larger than that of the excited state. The potential realization of this phenomenon in hydrogen atoms using a DC electric field is also discussed.

The professor concludes the lecture with a reminder of the next class and encourages students to prepare for the continuation of the topic. The summary acknowledges the progress made in understanding complex quantum systems and looks forward to further exploration in the upcoming sessions.