Dephasing
Encyclopedia
Dephasing is a name for the mechanism that recovers classical
behavior from a quantum system. It is an important effect in condensed matter physics
, particularly in the study of mesoscopic devices. The reason can be understood easily if we can see conduction in metals as a typical classical phenomenon with quantum effects all embedded into an effective mass that can be computed quantum mechanically as also happens to resistance that can be seen as a scattering effect of conduction electrons. When the temperature is lowered and the dimension of the device are meaningfully reduced, this classical behavior should disappear and the laws of quantum mechanics should govern the behavior of conducting electrons seen as waves that ballistically move inside the conductor without any kind of dissipation. Most of the time this is what one observes. But it appeared as a surprise to uncover that the so called dephasing time, that is the time it takes for the conducting electrons to lose their quantum behavior, becomes finite rather than infinite when the temperature approaches zero in mesoscopic devices violating the expectations of the theory of Altshuler, Aronov and Khmelnitskii (see citation below). This kind of saturation of the dephasing time at low temperatures is presently an open problem even as several proposals have been put forward.
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Dephasing is a process in which coherence
in a substance caused by perturbation decays over time, and the system returns to the state before perturbation.
The coherence of a sample is explained by the off-diagonal elements of a density matrix. An external electric
or magnetic field
can create coherence between two quantum states in a sample if the frequency
corresponds to the energy gap between the two states. The coherence terms decay with the dephasing time, T2.
After coherence is created in a sample by light, the sample emits a polarization wave, the frequency of which is equal to and the phase
of which is inverted from the incident light. In addition, the sample is excited by the incident light and a population of molecules in the excited state is generated. The light passing through the sample is absorbed because of these two processes, and it is expressed by an absorption spectrum. The coherence decays with the time constant, T2, and the intensity of the polarization wave is reduced. The population of the excited state also decays with the time constant of the longitudinal relaxation
, T1. The time constant T2 is usually much smaller than T1, and the bandwidth of the absorption spectrum is related to these time constants by the Fourier transform
, so the time constant T2 is a main contributor to the bandwidth. Recently, the time constant T2 has been measured with ultrafast time-resolved spectroscopy
directly, such as in photon echo experiments.
What is the dephasing rate of a particle that has an energy E if it is subject to a fluctuating environment that has a temperature T? In particular what is the dephasing rate close to equilibrium (E~T), and what happens in the zero temperature limit? This question has fascinated the mesoscopic community during the last two decades (see references below).
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...
behavior from a quantum system. It is an important effect in condensed matter physics
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...
, particularly in the study of mesoscopic devices. The reason can be understood easily if we can see conduction in metals as a typical classical phenomenon with quantum effects all embedded into an effective mass that can be computed quantum mechanically as also happens to resistance that can be seen as a scattering effect of conduction electrons. When the temperature is lowered and the dimension of the device are meaningfully reduced, this classical behavior should disappear and the laws of quantum mechanics should govern the behavior of conducting electrons seen as waves that ballistically move inside the conductor without any kind of dissipation. Most of the time this is what one observes. But it appeared as a surprise to uncover that the so called dephasing time, that is the time it takes for the conducting electrons to lose their quantum behavior, becomes finite rather than infinite when the temperature approaches zero in mesoscopic devices violating the expectations of the theory of Altshuler, Aronov and Khmelnitskii (see citation below). This kind of saturation of the dephasing time at low temperatures is presently an open problem even as several proposals have been put forward.
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Dephasing is a process in which coherence
Coherence (physics)
In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....
in a substance caused by perturbation decays over time, and the system returns to the state before perturbation.
The coherence of a sample is explained by the off-diagonal elements of a density matrix. An external electric
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
or magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
can create coherence between two quantum states in a sample if the frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
corresponds to the energy gap between the two states. The coherence terms decay with the dephasing time, T2.
After coherence is created in a sample by light, the sample emits a polarization wave, the frequency of which is equal to and the phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
of which is inverted from the incident light. In addition, the sample is excited by the incident light and a population of molecules in the excited state is generated. The light passing through the sample is absorbed because of these two processes, and it is expressed by an absorption spectrum. The coherence decays with the time constant, T2, and the intensity of the polarization wave is reduced. The population of the excited state also decays with the time constant of the longitudinal relaxation
Vibrational energy relaxation
Vibrational energy relaxation, or vibrational population relaxation, is a process in which the population distribution of molecules in quantum states of high energy level caused by an external perturbation returns to the Maxwell-Boltzmann distribution....
, T1. The time constant T2 is usually much smaller than T1, and the bandwidth of the absorption spectrum is related to these time constants by the Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
, so the time constant T2 is a main contributor to the bandwidth. Recently, the time constant T2 has been measured with ultrafast time-resolved spectroscopy
Time-resolved spectroscopy
In physics and physical chemistry, time-resolved spectroscopy is the study of dynamic processes in materials or chemical compounds by means of spectroscopic techniques. Most often, processes are studied that occur after illumination of a material, but in principle, the technique can be applied to...
directly, such as in photon echo experiments.
What is the dephasing rate of a particle that has an energy E if it is subject to a fluctuating environment that has a temperature T? In particular what is the dephasing rate close to equilibrium (E~T), and what happens in the zero temperature limit? This question has fascinated the mesoscopic community during the last two decades (see references below).