method

coherent spectroscopy

Spectroscopy using coherent light-matter interactions to probe quantum states.
34 related articles · 2 formulas

Description

Coherent spectroscopy is a family of techniques that use light with a well-defined phase relationship — coherent light, typically from lasers — to probe the quantum states of matter. Unlike conventional spectroscopy, which simply measures how much light is absorbed or emitted at each frequency, coherent spectroscopy exploits the wave nature of light and matter to extract information about quantum superpositions, energy-level structures, and dynamical processes. It is the foundation of many modern quantum technologies, from atomic clocks to quantum computing.

History

The field emerged in the 1960s and 1970s with the development of lasers and the theoretical work on coherent transients by Richard Brewer and others. The technique of photon echoes, a cornerstone of coherent spectroscopy, was first predicted by Erwin Hahn in 1950 and demonstrated in optics by I. D. Abella, N. A. Kurnit, and S. R. Hartmann in 1966.

How it works

The key idea is that a coherent light pulse can prepare a quantum system in a superposition of states. A second pulse, delayed in time, can then interfere with the first, creating an echo or a beat signal that reveals the system's coherence properties. By varying the time delay and frequency of the pulses, researchers can map out the energy landscape of the system with high precision, even in the presence of noise or disorder.

In practice

Coherent spectroscopy is used in atomic clocks, quantum memory devices, and in the characterization of semiconductor nanostructures and molecular dynamics.

Fun fact

The photon echo, a key phenomenon in coherent spectroscopy, is the optical analogue of the spin echo used in MRI machines.

Concept graph →

Formulas

$$C_{l m l' m'} = \langle a_{l m} a^*_{l' m'} \rangle$$
Defines correlation coefficients of spherical harmonic coefficients.
What is in the formula
C_{lm l'm'}variableAngular power spectrum coefficients — angular power spectrum
a_{lm}variableSpherical harmonic coefficients of temperature map — spherical harmonic coefficient kelvin
⟨ ⟩operatorEnsemble average over realizations — ensemble average
*operatorComplex conjugation — complex conjugate
c_{lml'm'}\equiv\langlea_{lm}a^*_{l'm'}\rangle · 2606.24886
$$C_{xy}(f) = \frac{|P_{xy}(f)|^2}{P_{xx}(f) P_{yy}(f)}$$
Measures the linear correlation between two signals at frequency f.
What is in the formula
C_{xy}(f)variableMagnitude squared coherence at frequency f — coherence
P_{xy}(f)variableCross-spectral density between signals x and y at frequency f — cross spectral density watt per hertz
P_{xx}(f)variablePower spectral density of signal x at frequency f — power spectral density watt per hertz
P_{yy}(f)variablePower spectral density of signal y at frequency f — power spectral density watt per hertz
| \cdot |operatorMagnitude (absolute value) of a complex number — absolute value
c_{xy}(f)=\frac{|p_{xy}(f)|^2}{p_{xx}(f)p_{yy}(f)} · 2607.18136v3

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