CAVITY QUANTUM ELECTRODYNAMICS HAROCHE PDF
Cavity Quantum Electrodynamics be greatly suppressed or enhanced by placing the atoms between mirrors or in cavities. Serge Haroche; Daniel Kleppner. With further refinement of this technology, cavity quantum electrodynamic (QED) In one of us (Haroche), along with other physicists at Yale University. Atomic cavity quantum electrodynamics reviews: J. Ye., H. J. Kimble, H. Katori, Science , (). S. Haroche & J. Raimond, Exploring the Quantum.
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We are making the text of this article freely available for 30 days because author Serge Haroche is one of the winners of the Nobel Prize in Physics. The full article with images, which appeared in the April issue, is available for purchase here.
Fleeting, spontaneous transitions are ubiquitous in the quantum world.
Cavity Quantum Electrodynamics |
Once they are under way, they seem as uncontrollable and as irreversible as the explosion of fireworks. Excited atoms, for example, discharge their excess energy in the form of photons that escape to infinity at the speed of light. Yet during the past decade, this inevitability has begun to yield. Atomic physicists have created devices that can slow spontaneous transitions, halt them, accelerate them or even reverse them entirely.
Recent advances in the fabrication of small superconducting cavities and other microscopic structures as well as novel techniques for laser manipulation of atoms make such feats possible.
By placing an atom in a small box with reflecting walls that constrain the wavelength of any photons it emits or absorbs—and thus the changes in state that it may undergo—investigators can cause single atoms to emit photons ahead of schedule, stay in an excited state indefinitely or block the passage of a laser beam. With further refinement of this technology, cavity quantum electrodynamic QED phenomena may find use in the generation and precise measurement of electromagnetic fields consisting of only a handful of photons.
Cavity QED processes engender an intimate correlation between the states of the atom and those of the field, and so their study provides new insights into quantum aspects of the interaction between light and matter. To understand the interaction between an excited atom and a cavity, one must keep in mind two kinds of physics: The emission of light by an atom bridges both worlds. Light waves are moving oscillations of electric and magnetic fields.
In this respect, they represent a classical event.
But light can also be described in terms of photons, discretely emitted quanta of energy. Sometimes the classical model is best, and sometimes the quantum one offers more understanding. When an electron in an atom jumps from a high energy level to a lower one, the atom emits a photon that carries away the difference in energy between the two levels.
This photon typically has a wavelength of a micron or less, corresponding to a frequency of a few hundred terahertz and an energy of about one electron volt. Any given excited state has a natural lifetime—similar to the half-life of a radioactive element—that determines the odds that the excited atom will emit a photon during a given time interval.
The probability that an atom will remain excited decreases along an exponential curve: In classical terms, the outermost electron in an excited atom is the equivalent of a small antenna, oscillating at frequencies corresponding to the energy of transitions to less excited states, and the photon is simply the antenna’s radiated field. When an atom absorbs light and jumps to a higher energy level, it acts as a receiving antenna instead.
If the antenna is inside a reflecting cavity, however, its behavior changes—as anyone knows who has tried to listen to a radio broadcast while driving through a tunnel.
Cavity Quantum Electrodynamics
As the car and its receiving antenna pass underground, they enter a region where the long wavelengths of the radio waves are cut off. The incident waves interfere destructively with those that bounce off the steel-reinforced concrete walls of the tunnel. In fact, the radio waves cannot propagate unless the tunnel walls are separated by more than half a wavelength.
This is the minimal width that permits a standing wave with at least one crest, or field maximum, to build up—just as the vibration of a violin string reaches a maximum at the middle of the string and vanishes at the ends.
What is true for reception also holds for emission: An excited atom in a small cavity is precisely such as antenna, albeit a microscopic one. If the cavity is small enough, the atom will be unable to radiate because the wavelength of the oscillating field it would “like” to produce cannot fit within the boundaries. As electrodnamics as the atom cannot emit a photon, it must remain in the same energy level; the excited state acquires an infinite lifetime. In research groups at the University of Washington and at the Massachusetts Institute of Technology demonstrated suppressed emission.
The group in Seattle inhibited the radiation of a single electron inside an electromagnetic trap, whereas the Quantmu.
The atoms remained in the same state without radiating as long as they were between the plates. Millimeter-scale structures are much too wide to alter the behavior of conventionally excited atoms emitting micron or submicron radiation; consequently, the M. An atom in electrorynamics Rydberg state has almost enough energy to lose an electron completely. Because this outermost electron is bound only weakly, it can assume any of a great number of closely spaced energy levels, and the photons it emits while jumping form one to another have wavelengths ranging from a fraction of a millimeter to a few centimeters.
Rydberg atoms are prepared by irradiating ground-state atoms with laser light of appropriate wavelengths and are widely used in cavity QED experiments. The suppression of spontaneous emission at an optical frequency requires much smaller cavities. In one of us Harochealong with other physicists at Yale University, made a micron-wide structure by stacking two optically flat mirrors separated by extremely thin metallic spacers. The workers sent atoms through this passage, thereby preventing them from radiating for as long as 13 times the normal excited-state lifetime.
Researchers at the University of Rome used similar micron-wide gaps to inhibit emission by excited dye molecules. The experiments performed on atoms between two flat mirrors have an interesting twist. Such a structure, with no sidewalls, constrains the wavelengths only of photons electrodynaics polarization is parallel to the mirrors.
As a result, emission is inhibited only if the atomic dipole antenna oscillates along the plane of mirrors. It was essential, for example, to prepare the electrodynaimcs atoms with this dipole orientation in the M.
The Yale researchers demonstrated these polarization-dependent effects by rotating the atomic dipole between the mirrors with the help of a magnetic field. When the dipole orientation was tilted with respect to the mirrors’ plane, the excited-state lifetime dropped substantially. Suppressed emission also takes place in solid-state cavities—tiny regions of semiconductor bounded by layers of disparate substances.
Solid-state physicists routinely produce structures of submicron dimensions by means of molecular-beam epitaxy, in which materials are built up one atomic layer at a time. Devices built to take advantage of cavity QED phenomena could engender a new generation of light emitters [see “Microlasers,” by Jack L. These experiments indicate a counterintuitive phenomenon that might be called “no-photon interference.
But this begs a philosophical question: How can the photon “know,” even before being emitted, whether the cavity is the right or wrong size? Part of the answer lies in yet another odd result of quantum mechanics. A cavity with no photon is in its lowest-energy state, the so-called ground state, but it is not really empty. The Heisenberg uncertainty principle sets a lower limit on the product of the electric and magnetic fields inside the cavity or anywhere else for that matter and thus prevents them from simultaneously vanishing.
This so-called vacuum field exhibits intrinsic fluctuations at all frequencies, from long radio waves down to visible, ultraviolet and gamma radiation, and is a crucial concept in theoretical physics. Indeed, spontaneous emission of a photon by an excited atom is in a sense induced by vacuum fluctuations. The no-photon interference effect arises because the fluctuations of the vacuum field, like the oscillations of more actual electromagnetic waves, are constrained by the cavity walls.
In a small box, boundary conditions forbid long wavelengths–there can be no vacuum fluctuations at low frequencies. An excited atom that would ordinarily emit a low-frequency photon cannot do so, because there are no vacuum fluctuations to stimulate its emission by oscillating in phase with it.
Small cavities suppress atomic transitions; slightly larger ones, however, can enhance them. When the size of a cavity surrounding an excited atom is increased to the point where it matches the wavelength of the photon that the atom would naturally emit, vacuum-field fluctuations at that wavelength flood the cavity and become stronger than they would be in free space. This state of affairs encourages emission; the lifetime of the excited state becomes much shorter than it would naturally be. If the resonant cavity has absorbing walls or allows photons to escape, the emission is not essentially different from spontaneous radiation in free space–it just proceeds much faster.
If the cavity walls are very good reflectors and the cavity is closed, however, novel effects occur.
These effects, which depend on intimate long-term interactions between the excited atom and the cavity, are the basis for a series of new devices that can make sensitive measurements of quantum phenomena.
Instead of simply emitting a photon and going on its way, an excited atom in such a resonant cavity oscillates back and forth between its excited and unexcited states. The emitted photon remains in the box in the vicinity of hroche atom and is promptly reabsorbed. The atom-cavity system oscillates between two states, one consisting of an excited atom and no photon, and the other caviy a de-excited atom and a photon trapped in the cavity.
The frequency of this oscillation depends on the transition energy, on the size of the atomic dipole and on the size of the cavity. This atom-photon exchange has a deep analogue in classical physics. If two identical pendulums are coupled by a weak spring and one of them is set in motion, the other will soon start swinging while the first gradually comes to rest.
At this point, the first pendulum starts swinging again, commencing an ideally endless exchange of energy. A state in which one pendulum is excited and the other is at rest is clearly not stationary, because energy electrodybamics continuously from one pendulum to the other. The system does have two steady states, however: The system’s oscillation in each of these “eigenmodes” differs because of the additional force imposed by the coupling–the pendulums oscillate slightly slower in phase and slightly faster out of phase.
Furthermore, the magnitude of the frequency difference between the two eigenmodes is precisely equal to the rate at which the two pendulums exchange their energy in the nonstationary states. Researchers harovhe the California Institute of Technology recently observed this “mode splitting” in an atom-cavity system.
They cavitu a weak laser beam through a cavity made of two spherical mirrors while cvity beam of cesium atoms also crossed the qkantum. The atomic beam was so tenuous that there was at most one atom at a time in the cavity. Although the cavity was not closed, the rate at which it exchanged photons with each atom exceeded the rate at which the atoms emitted photons cavit escaped the cavity; consequently, the physics was fundamentally the same as that in a closed resonator.
The spacing between the mirrors was an integral multiple of the wavelength of the transition between the first excited state of cesium and its ground state. Experimenters varied the wavelength and hence frequency of the laser and recorded its transmission across the cavity. When the cavity was empty, cacity transmission reached a sharp maximum at the resonant frequency of the cavity. When the resonator contained one atom on average, however, a symmetrical double peak appeared; its valley matched the position of the previous single peak.
The frequency splitting, about six megahertz, marked the rate of energy exchange between the atom and a single photon in the cavity. This apparatus is extremely sensitive: This phenomenon can be used to count atoms electrodyanmics the same way one currently counts cars or people intercepting an infrared light in front of a photodetector.
Although simple in principle, such an cavty is technically demanding. The cavity must be as small as electrodunamics because the frequency splitting is proportional to the vacuum-field amplitude, which is inversely proportional to the square root of the box’s volume.
At the same time, the mirrors must be very good reflectors so that the photon remains trapped for at least as long as it takes the atom and cavity to exchange a photon. The group at Caltech used mirrors that were coated to achieve In such a trap, a photon could bounce back and forth abouttimes over the course of a quarter of a microsecond before being transmitted through the mirrors.
Experimenters have been able to achieve even longer storage times–as great as several hundred milliseconds– by means of superconducting niobium cavities cooled to temperatures of about one kelvin or less. These cavities are ideal for trapping the photons emitted by Rydberg atoms, which typically range in wavelength from a few millimeters to a few centimeters corresponding to frequencies between 10 and gigahertz.
In a recent experiment in our laboratory at ENS, we excited rubidium atoms with lasers and sent them across a superconducting cylindrical cavity tuned to a transition connecting the excited state to another Rydberg level 68 gigahertz higher in energy.