Electromagnetically induced transparency

Electromagnetically induced transparency (EIT) is a coherent optical nonlinearity which renders a medium transparent within a narrow spectral range around an absorption line. Extreme dispersion is also created within this transparency 'window' which leads to 'slow light', described below. It is in essence a quantum interference effect that permits the propagation of light through an otherwise opaque atomic medium. Electromagnetically induced transparency (EIT) is a coherent optical nonlinearity which renders a medium transparent within a narrow spectral range around an absorption line. Extreme dispersion is also created within this transparency 'window' which leads to 'slow light', described below. It is in essence a quantum interference effect that permits the propagation of light through an otherwise opaque atomic medium. Observation of EIT involves two optical fields (highly coherent light sources, such as lasers) which are tuned to interact with three quantum states of a material. The 'probe' field is tuned near resonance between two of the states and measures the absorption spectrum of the transition. A much stronger 'coupling' field is tuned near resonance at a different transition. If the states are selected properly, the presence of the coupling field will create a spectral 'window' of transparency which will be detected by the probe. The coupling laser is sometimes referred to as the 'control' or 'pump', the latter in analogy to incoherent optical nonlinearities such as spectral hole burning or saturation. EIT is based on the destructive interference of the transition probability amplitude between atomic states. Closely related to EIT are coherent population trapping (CPT) phenomena. The quantum interference in EIT can be exploited to laser cool atomic particles, even down to the quantum mechanical ground state of motion. This was used in 2015 to directly image individual atoms trapped in an optical lattice. There are specific restrictions on the configuration of the three states. Two of the three possible transitions between the states must be 'dipole allowed', i.e. the transitions can be induced by an oscillating electric field. The third transition must be 'dipole forbidden.' One of the three states is connected to the other two by the two optical fields. The three types of EIT schemes are differentiated by the energy differences between this state and the other two. The schemes are the ladder, vee, and lambda. Any real material system may contain many triplets of states which could theoretically support EIT, but there are several practical limitations on which levels can actually be used. Also important are the dephasing rates of the individual states. In any real system at non-zero temperature there are processes which cause a scrambling of the phase of the quantum states. In the gas phase, this means usually collisions. In solids, dephasing is due to interaction of the electronic states with the host lattice. The dephasing of state | 3 ⟩ {displaystyle |3 angle } is especially important; ideally | 3 ⟩ {displaystyle |3 angle } should be a robust, metastable state. Current EIT research uses atomic systems in dilute gases, solid solutions, or more exotic states such as Bose–Einstein condensate. EIT has been demonstrated in electromechanical and optomechanical systems, where it is known as optomechanically induced transparency. Work is also being done in semiconductor nanostructures such as quantum wells, quantum wires and quantum dots. EIT was first proposed theoretically by professor Jakob Khanin and graduate student Olga Kocharovskaya at Gorky State University (renamed to Nizhny Novgorod in 1990), Russia; there are now several different approaches to a theoretical treatment of EIT. One approach is to extend the density matrix treatment used to derive Rabi oscillation of a two-state, single field system. In this picture the probability amplitude for the system to transfer between states can interfere destructively, preventing absorption. In this context, 'interference' refers to interference between quantum events (transitions) and not optical interference of any kind. As a specific example, consider the lambda scheme shown above. Absorption of the probe is defined by transition from | 1 ⟩ {displaystyle |1 angle } to | 2 ⟩ {displaystyle |2 angle } . The fields can drive population from | 1 ⟩ {displaystyle |1 angle } - | 2 ⟩ {displaystyle |2 angle } directly or from | 1 ⟩ {displaystyle |1 angle } - | 2 ⟩ {displaystyle |2 angle } - | 3 ⟩ {displaystyle |3 angle } - | 2 ⟩ {displaystyle |2 angle } . The probability amplitudes for the different paths interfere destructively. If | 3 ⟩ {displaystyle |3 angle } has a comparatively long lifetime, then the result will be a transparent window completely inside of the | 1 ⟩ {displaystyle |1 angle } - | 2 ⟩ {displaystyle |2 angle } absorption line. Another approach is the 'dressed state' picture, wherein the system + coupling field Hamiltonian is diagonalized and the effect on the probe is calculated in the new basis. In this picture EIT resembles a combination of Autler-Townes splitting and Fano interference between the dressed states. Between the doublet peaks, in the center of the transparency window, the quantum probability amplitudes for the probe to cause a transition to either state cancel.