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Rabi Problem
The 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. It provides a simple and generally solvable example of light–atom interactions and is named after Isidor Isaac Rabi. Classical Rabi problem In the classical approach, the Rabi problem can be represented by the solution to the driven damped harmonic oscillator with the electric part of the Lorentz force as the driving term: : \ddot_a + \frac \dot_a + \omega_a^2 x_a = \frac E(t, \mathbf_a), where it has been assumed that the atom can be treated as a charged particle (of charge ''e'') oscillating about its equilibrium position around a neutral atom. Here ''xa'' is its instantaneous magnitude of oscillation, \omega_a its natural oscillation frequency, and \tau_0 its natural lifetime: : \frac = \frac, which has been calculated based on the dipole oscillator's energy loss from electromagnetic radiation. To apply this to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atom
Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. Atoms with the same number of protons but a different number of neutrons are called isotopes of the same element. Atoms are extremely small, typically around 100 picometers across. A human hair is about a million carbon atoms wide. Atoms are smaller than the shortest wavelength of visible light, which means humans cannot see atoms with conventional microscopes. They are so small that accurately predicting their behavior using classical physics is not possible due to quantum mechanics, quantum effects. More than 99.94% of an atom's mass is in the nucleus. Protons hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-state Quantum System
In quantum mechanics, a two-state system (also known as a two-level system) is a quantum system that can exist in any quantum superposition of two independent (physically distinguishable) quantum states. The Hilbert space describing such a system is two-dimensional. Therefore, a complete basis spanning the space will consist of two independent states. Any two-state system can also be seen as a qubit. Two-state systems are the simplest quantum systems that are of interest, since the dynamics of a one-state system is trivial (as there are no other states in which the system can exist). The mathematical framework required for the analysis of two-state systems is that of linear differential equations and linear algebra of two-dimensional spaces. As a result, the dynamics of a two-state system can be solved analytically without any approximation. The generic behavior of the system is that the wavefunction's amplitude oscillates between the two states. A well known example of a two-s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacuum Rabi Oscillation
A 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(s) into a single-mode electromagnetic cavity and reabsorbs them. The atom interacts with a single-mode field confined to a limited volume ''V'' in an optical cavity. Spontaneous emission is a consequence of coupling between the atom and the vacuum fluctuations of the cavity field. Mathematical treatment A mathematical description of vacuum Rabi oscillation begins with the Jaynes–Cummings model, which describes the interaction between a single mode of a quantized field and a two level system inside an optical cavity. The Hamiltonian for this model in the rotating wave approximation is :\hat_ = \hbar \omega \hat^\hat +\hbar \omega_0 \frac +\hbar g \left(\hat\hat_+ +\hat^\hat_-\right) where \hat is the Pauli z spin operator for the two eigenstates , e \rangle and , g\rangle of the isolated two level s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rabi Frequency
The Rabi frequency is the frequency at which the Probability amplitude, probability amplitudes of two atomic electron transition, atomic energy levels fluctuate in an oscillating electromagnetic field. It is proportional to the transition dipole moment of the two levels and to the amplitude (''not'' Irradiance, intensity) of the electromagnetic field. Population transfer between the levels of such a 2-level system illuminated with light exactly resonant with the difference in energy between the two levels will occur at the Rabi frequency; when the incident light is detuned from this energy difference (detuned from resonance) then the population transfer occurs at the #Generalized Rabi frequency, generalized Rabi frequency. The Rabi frequency is a semiclassical concept since it treats the atom as an object with quantized Energy level, energy levels and the electromagnetic field as a continuous wave. In the context of a nuclear magnetic resonance experiment, the Rabi frequency is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 optical 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 is one that has two possible energy levels. One level is a ground state with lower energy, and the other is an excited state with higher energy. If the energy levels are not degenerate (i.e. don't have equal energies), the system can absorb or emit a quantum of energy and transition from the ground state to the excited state or vice versa. When an atom (or some other two-level system) is illu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jaynes–Cummings Model
In quantum optics, the Jaynes–Cummings model (sometimes abbreviated JCM) is a theoretical model that describes the system of a Two-level system, two-level atom interacting with a quantized mode of an optical cavity (or a bosonic field), with or without the presence of light (in the form of a bath of electromagnetic radiation that can cause spontaneous emission and absorption). It was originally developed to study the interaction of atoms with the quantized electromagnetic field in order to investigate the phenomena of spontaneous emission and absorption of photons in a cavity quantum electrodynamics, cavity. It is named after Edwin Thompson Jaynes and Fred Cummings in the 1960s and was confirmed experimentally in 1987. The Jaynes–Cummings model is of great interest to atomic physics, quantum optics, solid-state physics and Superconducting quantum computing, quantum information circuits, both experimentally and theoretically. Journal special issues have commemorated the 50th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word ''laser'' originated as an acronym for light amplification by stimulated emission of radiation. The first laser was built in 1960 by Theodore Maiman at Hughes Research Laboratories, based on theoretical work by Charles H. Townes and Arthur Leonard Schawlow and the optical amplifier patented by Gordon Gould. A laser differs from other sources of light in that it emits light that is coherence (physics), ''coherent''. Spatial coherence allows a laser to be focused to a tight spot, enabling uses such as optical communication, laser cutting, and Photolithography#Light sources, lithography. It also allows a laser beam to stay narrow over great distances (collimated light, collimation), used in laser pointers, lidar, and free-space optical communication. Lasers can also have high temporal coherence, which permits them to emit light ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Rabi Frequency
The Rabi frequency is the frequency at which the probability amplitudes of two atomic energy levels fluctuate in an oscillating electromagnetic field. It is proportional to the transition dipole moment of the two levels and to the amplitude (''not'' intensity) of the electromagnetic field. Population transfer between the levels of such a 2-level system illuminated with light exactly resonant with the difference in energy between the two levels will occur at the Rabi frequency; when the incident light is detuned from this energy difference (detuned from resonance) then the population transfer occurs at the generalized Rabi frequency. The Rabi frequency is a semiclassical concept since it treats the atom as an object with quantized energy levels and the electromagnetic field as a continuous wave. In the context of a nuclear magnetic resonance experiment, the Rabi frequency is the nutation frequency of a sample's net nuclear magnetization vector about a radio-frequency field. (Not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Precession
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called '' nutation''. In physics, there are two types of precession: torque-free and torque-induced. In astronomy, ''precession'' refers to any of several slow changes in an astronomical body's rotational or orbital parameters. An important example is the steady change in the orientation of the axis of rotation of the Earth, known as the precession of the equinoxes. Torque-free or torque neglected Torque-free precession implies that no external moment (torque) is applied to the body. In torque-free precession, the angular momentum is a constant, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate Rotation
Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point. Rotation can have a sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude. A rotation is different from other types of motions: translations, which have no fixed points, and (hyperplane) reflections, each of them having an entire -dimensional flat of fixed points in a - dimensional space. Mathematically, a rotation is a map. All rotations about a fixed point form a group under composition called the rotation group (of a particular space). But in mechanics and, more generally, in physics, this concept is frequently understood as a coordinate transformation (importantly, a transformation of an orthonormal basis), because for any motion of a body there is an inverse transformation whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotating Wave Approximation
The rotating-wave approximation is an approximation used in atom optics and magnetic resonance. In this approximation, terms in a Hamiltonian that oscillate rapidly are neglected. This is a valid approximation when the applied electromagnetic radiation is near resonance with an atomic transition, and the intensity is low. Explicitly, terms in the Hamiltonians that oscillate with frequencies \omega_L + \omega_0 are neglected, while terms that oscillate with frequencies \omega_L - \omega_0 are kept, where \omega_L is the light frequency, and \omega_0 is a transition frequency. The name of the approximation stems from the form of the Hamiltonian in the interaction picture, as shown below. By switching to this picture the evolution of an atom due to the corresponding atomic Hamiltonian is absorbed into the system ket, leaving only the evolution due to the interaction of the atom with the light field to consider. It is in this picture that the rapidly oscillating terms mentioned prev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
