Rabi cycle

In physics, the Rabi cycle (or Rabi flop) is the cyclic behaviour of a two-level quantum system in the presence of an oscillatory driving field. A great variety of physical processes belonging to the areas of quantum computing, condensed matter, atomic and molecular physics, and nuclear and particle physics can be conveniently studied in terms of two-level quantum mechanical systems, and exhibit Rabi flopping when coupled to an oscillatory driving field. The effect is important in quantum optics, magnetic resonance and quantum computing, and is named after Isidor Isaac Rabi.This oscillation of the electron between the two states corresponds to an oscillation of themean value of the electric dipole moment of the molecule. Thus when the molecule is not in a stationary state, an oscillating electric dipole moment can appear.Such an oscillating dipolemoment can exchange energy with an electromagnetic wave of same frequency. Consequently, this frequency must appear in the absorption and emission spectrum of Ionized hydrogen molecule. In physics, the Rabi cycle (or Rabi flop) is the cyclic behaviour of a two-level quantum system in the presence of an oscillatory driving field. A great variety of physical processes belonging to the areas of quantum computing, condensed matter, atomic and molecular physics, and nuclear and particle physics can be conveniently studied in terms of two-level quantum mechanical systems, and exhibit Rabi flopping when coupled to an oscillatory driving field. The effect is important in quantum optics, magnetic resonance and quantum computing, and is named after Isidor Isaac Rabi. A two-level system has two possible levels, and if they are not degenerate (i.e. not equal energy), the system can become 'excited' when it absorbs a quantum of energy. When an atom (or some other two-level system) is illuminated by a coherent beam of photons, it will cyclically absorb photons and re-emit them by stimulated emission. One such cycle is called a Rabi cycle and the inverse of its duration the Rabi frequency of the photon beam. The effect can be modeled using the Jaynes–Cummings model and the Bloch vector formalism. A detailed mathematical description of the effect can be found on the page for the Rabi problem. For example, for a two-state atom (an atom in which an electron can either be in the excited or ground state) in an electromagnetic field with frequency tuned to the excitation energy, the probability of finding the atom in the excited state is found from the Bloch equations to be: where ω {displaystyle omega } is the Rabi frequency. More generally, one can consider a system where the two levels under consideration are not energy eigenstates. Therefore, if the system is initialized in one of these levels, time evolution will make the population of each of the levels oscillate with some characteristic frequency, whose angular frequency is also known as the Rabi frequency. The state of a two-state quantum system can be represented as vectors of a two-dimensional complex Hilbert space, which means every state vector | ψ ⟩ {displaystyle vert psi angle } is represented by good complex coordinates. If the vectors are normalized, c 1 {displaystyle c_{1}} and c 2 {displaystyle c_{2}} are related by | c 1 | 2 + | c 2 | 2 = 1 {displaystyle {|c_{1}|}^{2}+{|c_{2}|}^{2}=1} . The basis vectors will be represented as | 0 ⟩ = ( 1 0 ) {displaystyle |0 angle ={egin{pmatrix}1\0end{pmatrix}}} and | 1 ⟩ = ( 0 1 ) {displaystyle |1 angle ={egin{pmatrix}0\1end{pmatrix}}} All observable physical quantities associated with this systems are 2 × {displaystyle imes } 2 Hermitian matrices, which means the Hamiltonian of the system is also a similar matrix. One can construct an oscillation experiment consisting of following steps: (1) Prepare the system in a fixed state say | 1 ⟩ {displaystyle |1 angle }