GrnStarBird:
Einstein called the wavefunction collapse idea "spooky action at a distance" because the wavefunction could collapse everywhere in the universe.
Yet, one of the most sacred laws of physics as explained by Einstein is that nothing can travel faster than the speed of light in vacuum.
But this speed limit was "broken" in an experiment in which a laser pulse traveled at more than 300 times the speed of light. However, the laws of physics remain intact because Lijun Wang and colleagues at the NEC Research Institute in Princeton in the US are able to explain the results of their experiment in terms of the classical theory of wave propagation.
Special relativity prevents any object with mass travelling at the speed of light, and the principle of causality – the notion that the cause comes before the effect – is used to rule out the possibility of superluminal (faster-than-light) travel by light itself. However, a pulse of light can have more than one speed because it is made up of light of different wavelengths. The individual waves travel at their own phase velocity, while the pulse itself travels with the group velocity. In a vacuum all the phase velocities and the group velocity are the same. In a dispersive medium, however, they are different because the refractive index is a function of wavelength, which means that the different wavelengths travel at different speeds. Wang and colleagues report evidence for a negative group velocity of -310
c, where
c (=300 million metres per second) is the speed of light in vacuum.
Their experimental set-up is remarkably similar to that used to slow light to a speed of just
17 metres per second last year. It relies on using two lasers and a magnetic field to prepare a gas of caesium atoms in an excited state. This state exhibits strong amplification or gain at two wavelengths, and highly anomalous dispersion – that is, the refractive index changes rapidly with wavelength – in the region between these two peaks.
Wang and colleagues began by using a third continuous-wave laser to confirm that there are two peaks in the gain spectrum and that the refractive index does indeed change rapidly with wavelength in between. Next they send a 3.7-microsecond long laser pulse into the caesium cell, which is 6 centimetres long, and show that, at the correct wavelength, it emerges from the cell 62 nanoseconds sooner than would be expected if it had travelled at the speed of light. 62 nanoseconds might not sound like much, but since it should only take 0.2 nanoseconds for the pulse to pass through the cell, this means that the pulse has been travelling at 310 times the speed of light. Moreover, unlike previous superluminal experiments, the input and output pulse shapes are essentially the same.
The observed superluminal light pulse propagation is not at odds with causality or special relativity. In
fact, the very existence of the lossless anomalous dispersion region given is a result of the Kramers ± Kronig relation which itself is based on the causality requirements of electromagnetic response . Remarkably, the signal velocity of a light pulse, determined as the velocity at which the half point of the pulse front travels, also exceeds the speed of light in a vacuum, c, in the present experiment. It has also been suggested that the true speed at which information is carried by a light pulse should be determined as the ``frontal'' velocity of a step-function-shaped signal which has been shown not to exceed c.
A step function shaped signal - easypointzblogspot
There is no widespread agreement among physicists about the speed at which information is carried by pulses in such experiments. One definition is that it is the speed at which the point of half the maximum intensity on the leading edge of the pulse travels, but this velocity is superluminal in the Princeton experiment. The Wang team intends to analyze this further, including cases in which the pulse contains just a few photons.
The large dephasing rate in graphene offers also offers the feasibility of superluminal propagation of ultrashort light pulses. Additionally, the dynamical behavior of dispersion and absorption of a weak probe field in a closed-type graphene system has been investigated, and it is found that the absorption and dispersion can be dramatically affected by both the relative phase of applied fields and the Rabi frequencies* in such a way that a large transient gain can be achieved and a transient absorption can be completely eliminated.
Graphene, as the thinnest material known in the universe, consists of carbon atoms in a two-dimensional (2D) hexagonal lattice with unusual Dirac-like electronic** excitations. It holds many records related to mechanical, thermal, electrical and optical properties. Besides, its band-gap structure can be tuned by voltage or chemical doping, through which conductivity and transmission are changed. Subsequently, this feature can endow graphene with a capability of operation in both terahertz and optical frequency ranges. In addition to the interest in fundamental research of optoelectronic and condensed matter physics,
1,4graphene is gaining attention owing to its various technological applications. Moreover, extant literature has reported investigations concerning the optical properties of graphene. Not only do the investigations provide insights into the underlying nature of graphene’s excited states, but they also open up interesting perspectives for emerging photonic and optoelectronic applications.
Research has shown that magneto-optical properties of the graphene and thin graphite layer lead to multiple absorption peaks and unique selection rules for the allowed transitions. Furthermore, non-equidistant Landau-levels (LLs) and the selection rules make graphene an excellent candidate for LL laser. Moreover, its optical nonlinearity features have been exploited in multi-wave mixing, entangled photons and third harmonic generation. These achievements demonstrate the feasibility of graphene for applications such as chip-scale high-speed optical communications, all-optical signal processing, photonics and optoelectronics.
In the past three decades, controlling group velocity of light has attracted a lot of interest owing to its potential applications, such as tunable optical buffers, optical memory and enhancing the nonlinear effect. Thus, numerous experimental and theoretical works have been devoted to control it in materials such as atomic medium, alexandrite crystal,
33optomechanical system
34 and superconducting phase quantum circuit system. Slow light can be used in telecommunication applications such as controllable optical delay lines, optical buffers, true time delay methods for synthetic aperture radar, development of spectrometers with enhanced spectral resolution and optical memories. On the other hand, the question of wave velocity has been studied since the advent of Einstein’s special theory of relativity. The key issue is whether the speed of light in vacuum,
c, is an upper limit to the group velocity. Theoretical works have shown that the group velocity is not limited and a great deal of experiments confirmed that it is possible for optical or electrical wave pulses to travel through absorbing, attenuating or gain materials with group velocities greater than
c. Another interesting scenario in light propagation concerns the situation where the group velocity of light can even become negative. It is worth mentioning that the superluminal light propagation does not violate Einstein’s theory of special relativity since the energy and information flow do not exceed
c. By using the principle of such propagation, one can improve the speed of information transfer in telecommunication. An ideal condition for practical light propagation is a region in which the light pulse should not attenuate or amplify, primarily due to fact that pulse propagation does not possible in the presence of a large absorption. Besides, gain may add some noise to the system. Moreover, going towards superluminal propagation of shorter pulses is highly desirable; in this context, graphene potentially facilitates superluminal propagation of such pulses because of its large dephasing rate, about 30 ps−1, and high optical nonlinearity.
As mentioned above, considerable attention was paid to optical properties of graphene, however, superluminal light propagation in such system has received scant study to date. Despite the achievement of superluminal light propagation in graphene in only a few studies, it is accompanied by considerable absorption so that the pulse propagation does not possible, resulting in a drawback of practical applications. In this paper, we report a gain-assisted superluminal light propagation in a Landau-quantized graphene and show that the slope of dispersion can change from positive to negative just by adjusting the intensities of the coupling or controlling fields. Additionally, many works have focused on transient properties of probe field absorption, gain and enhancement of dispersion in both atomic and solid-state systems. Despite the importance of the transient behavior, there is a little study on this phenomenon in graphene. In fact, no study has been reported to date on transient optical properties of a closed-type graphene system.
Look at the role of the relative phase of applied fields on the transient optical properties of a graphene monolayer system. Motivated by a recent study on phase sensitivity of optical bistability and multistability in graphene, the transient optical properties of the Landau-quantized graphene monolayer system interacting with three laser fields has been investigated. The effects of both Rabi frequencies and relative phase of applied fields on the probe field absorption and dispersion, again, have been investigated. It is shown that the absorption and dispersion can be dramatically affected by the relative phase and the Rabi frequencies so that the transient absorption can be completely eliminated and a large transient gain can be achieved just by choosing the proper relative phase.
See:
https://www.researchgate.net/publication/12401462_Gain-assisted_superluminal_light_propagation
* Rabi frequencies - is the frequency of oscillation for a given
atomic transition in a given light field. It also gives the measure of the fluctuation of population between the levels. 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 occur at the Rabi frequency. The Rabi frequency is a semiclassical concept as it is based on a
quantum atomic transition and a
classical light field.
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 radiofrequency field. (Note that this is distinct from the
Larmor frequency, which characterizes the precession of a transverse nuclear magnetization about a static magnetic field.)
See:
https://www.formulasearchengine.com/wiki/Rabi_frequency
** Dirac-like electronic properties: the low energy fermionic excitations of a wide range of materials, including high temperature d- wave superconductors, topological insulators, 2, 3 graphene, and bulk semi-metallic systems like Cd,As2,5, behave as massless Dirac particles instead of fermions that obey the Schrödinger Hamiltonian. These materials would display seemingly universal properties that would be a direct consequence of the linear or Dirac spectrum of their quasi-particles, such as a power-law temperature dependence for their fermionic contribution to the heat capacity. Furthermore, the linear electronic dispersion around their Dirac or Weyl nodes and the nature of their electronic wave functions lead to remarkable electrical transport properties such as the observation of Klein tunneling, weak antilocalization, and unconventional Landau levels in graphene.
See:
https://arxiv.org/pdf/2102.01793.pdf
A pulse of light or "wave packet" (a cluster made up of many separate interconnected waves of different frequencies) is drastically reconfigured as it passes through the vapor as shown above. Some of the component waves are stretched out, others compressed. Yet at the end of the chamber, they recombine and reinforce one another to form exactly the same shape as the original pulse, it's essentially called 'rephasing.'
The key finding is that the reconstituted pulse re-forms before the original intact pulse could have gotten there by simply traveling though empty space. The peak of the pulse is, in effect, extended forward in time. Consequently, detectors attached to the beginning and end of the vapor chamber show that the peak of the exiting pulse leaves the chamber about 62 billionths of a second before the peak of the initial pulse finishes going in.
That is not the way things usually work. Ordinarily, when sunlight--which, like the pulse in the experiment, is a combination of many different frequencies--passes through a glass prism, the prism disperses the white light’s components. This happens because each frequency moves at a different speed in glass, smearing out the original light beam. Blue is slowed the most, and thus deflected the farthest; red travels fastest and is bent the least. That phenomenon produces the familiar rainbow spectrum.
The experimental work above may result in dramatic improvements in optical transmission rates.
Hartmann352