Rabi cycle
Encyclopedia
In physics
, the Rabi cycle is the cyclic behaviour of a two-state quantum system in the presence of an oscillatory driving field. A two-state system has two possible states, and if they are not degenerate energy level
s the system can become "excited" when it absorbs a quantum
of energy.
The effect is important in quantum optics
, nuclear magnetic resonance
and quantum computing. The term is named in honor of Isidor Isaac Rabi
.
When an atom
(or some other two-level system
) is illuminated by a coherent beam of photon
s, 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.
This mechanism is fundamental to quantum optics. It can be modeled using the Jaynes-Cummings model
and the Bloch vector formalism.
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
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
.
A Java applet that visualizes Rabi Cycles of two-state systems (laser driven).
extended version of the applet. Includes electron phonon interaction.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, the Rabi cycle is the cyclic behaviour of a two-state quantum system in the presence of an oscillatory driving field. A two-state system has two possible states, and if they are not degenerate energy level
Degenerate energy level
In physics, two or more different quantum states are said to be degenerate if they are all at the same energy level. Statistically this means that they are all equally probable of being filled, and in Quantum Mechanics it is represented mathematically by the Hamiltonian for the system having more...
s the system can become "excited" when it absorbs a quantum
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...
of energy.
The effect is important in quantum optics
Quantum optics
Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter.- History of quantum optics :...
, nuclear magnetic resonance
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
and quantum computing. The term is named in honor of Isidor Isaac Rabi
Isidor Isaac Rabi
Isidor Isaac Rabi was a Galician-born American physicist and Nobel laureate recognized in 1944 for his discovery of nuclear magnetic resonance.-Early years:...
.
When an atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
(or some other two-level system
Two-level system
In quantum mechanics, a two-state system is a system which has two possible states. More formally, the Hilbert space of a two-state system has two degrees of freedom, so a complete basis spanning the space must consist of two independent states...
) is illuminated by a coherent beam of photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s, it will cyclically absorb
Absorption (electromagnetic radiation)
In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...
photons and re-emit them by stimulated emission
Stimulated emission
In optics, stimulated emission is the process by which an atomic electron interacting with an electromagnetic wave of a certain frequency may drop to a lower energy level, transferring its energy to that field. A photon created in this manner has the same phase, frequency, polarization, and...
. One such cycle is called a Rabi cycle and the inverse of its duration the Rabi frequency
Rabi frequency
The Rabi frequency is the frequency of population oscillation for a given atomic transition in a given light field. It is associated with the strength of the coupling between the light and the transition. Rabi flopping between the levels of a 2-level system illuminated with resonant light, will...
of the photon beam.
This mechanism is fundamental to quantum optics. It can be modeled using the Jaynes-Cummings model
Jaynes-Cummings model
The Jaynes–Cummings model is a theoretical model in quantum optics. It describes the system of a two-level atom interacting with a quantized mode of an optical cavity, with or without the presence of light...
and the Bloch vector formalism.
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
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
Angular frequency
In physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity...
is also known as the Rabi frequency
Rabi frequency
The Rabi frequency is the frequency of population oscillation for a given atomic transition in a given light field. It is associated with the strength of the coupling between the light and the transition. Rabi flopping between the levels of a 2-level system illuminated with resonant light, will...
.
See also
- Atomic coherenceAtomic coherenceIn physics, atomic coherence is the induced coherence between levels of a multi-level atomic system sometimes observed when it interacts with a coherent electromagnetic field....
- Bloch sphereBloch sphereIn quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system , named after the physicist Felix Bloch....
- Laser pumpingLaser pumpingLaser pumping is the act of energy transfer from an external source into the gain medium of a laser. The energy is absorbed in the medium, producing excited states in its atoms. When the number of particles in one excited state exceeds the number of particles in the ground state or a less-excited...
- Optical pumpingOptical pumpingOptical pumping is a process in which light is used to raise electrons from a lower energy level in an atom or molecule to a higher one. It is commonly used in laser construction, to pump the active laser medium so as to achieve population inversion...
- Rabi frequencyRabi frequencyThe Rabi frequency is the frequency of population oscillation for a given atomic transition in a given light field. It is associated with the strength of the coupling between the light and the transition. Rabi flopping between the levels of a 2-level system illuminated with resonant light, will...
- Rabi problemRabi problemThe Rabi problem concerns the response of an atom to an applied harmonic electric field, with an applied frequency very close to the atom's natural frequency...
- Vacuum Rabi oscillationVacuum Rabi oscillationA vacuum Rabi oscillation is a damped oscillation of an initially excited atom coupled to an electromagnetic resonator or cavity in which the atom alternately emits photon into a single-mode electromagnetic cavity and reabsorbs them. The atom interacts with a single-mode field confined to a limited...
External links
- http://www.itp.tu-berlin.de/menue/lehre/owl/quantenmechanik/zweiniveau/parameter/en/
A Java applet that visualizes Rabi Cycles of two-state systems (laser driven).
- http://www.itp.tu-berlin.de/menue/lehre/owl/quantenmechanik/elektron-phonon-wechselwirkung/parameter/en/
extended version of the applet. Includes electron phonon interaction.