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Higher order coherence

Higher order coherence is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Higher order coherence rather than just read about it. In short: In quantum optics, correlation functions are used to characterize the statistical and coherence properties – the ability of waves to interfere – of electromagnetic radiation, like optical light. Higher order coherence or n-th order coherence (for any positive integer n>1) extends the concept of coherence to quantum optics and coincidence experiments.

Higher order coherence — main illustration
Higher order coherence — illustration

Key takeaways

  • Higher order coherence belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Higher order coherence to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Higher order coherence from memory before moving on to harder problems.

Reference excerpt

In quantum optics, correlation functions are used to characterize the statistical and coherence properties – the ability of waves to interfere – of electromagnetic radiation, like optical light. Higher order coherence or n-th order coherence (for any positive integer n>1) extends the concept of coherence to quantum optics and coincidence experiments. It is used to differentiate between optics experiments that require a quantum mechanical description from those for which classical fields suffice. Classical optical experiments like Young's double slit experiment and Mach-Zehnder interferometry are characterized only by the first order coherence. The 1956 Hanbury Brown and Twiss experiment brought to light a different kind of correlation between fields, namely the correlation of intensities, which correspond to second order coherences. Coherent waves have a well-defined constant phase relationship. Coherence functions, as introduced by Roy Glauber and others in the 1960s, capture the mathematics behind the intuition by defining correlation between the electric field components as coherence. These correlations between electric field components can be measured to arbitrary orders, hence leading to the concept of different orders or degrees of coherence. Orders of coherence can be measured using classical correlation functions or by using the quantum analogue of those functions, which take quantum mechanical description of electric field operators as input. The underlying mechanism and description of the physical processes are fundamentally different because quantum interference deals with interference of possible histories while classical interference deals with interference of physical waves. Analogous considerations apply to other wave-like systems. For example the case of Bose–Einstein correlations in condensed matter physics.

Introduction

First order coherence The normalized first order correlation function is written as:

γ ( 1 ) ( r 1 , t 1 ; r 2 , t 2 ) = ⟨ E ∗ ( r 1 , t 1 ) E ( r 2 , t 2 ) ⟩ [ ⟨ | E ( r 1 , t 1 ) | 2 ⟩ ⟨ | E ( r 2 , t 2 ) | 2 ⟩ ] 1 2 , {\displaystyle \gamma ^{(1)}(\mathbf {r} _{1},t_{1};\mathbf {r} _{2},t_{2})={\frac {\left\langle E^{*}(\mathbf {r} _{1},t_{1})E(\mathbf {r} _{2},t_{2})\right\rangle }{\left[\left\langle \left|E(\mathbf {r} _{1},t_{1})\right|^{2}\right\rangle \left\langle \left|E(\mathbf {r} _{2},t_{2})\right|^{2}\right\rangle \right]^{\frac {1}{2}}}},}

… excerpt ends here. Continue reading the full article.

Illustrations

Higher order coherence: Figure 1. Schematic diagram for the setup of the Young's Double Slit Experiment.
Figure 1. Schematic diagram for the setup of the Young's Double Slit Experiment.
Higher order coherence: Plot of g(2) as a function of the delay normalized to the coherence length τ/τc. The blue curve is for a coherent state (an ideal laser or a single frequency). The red curve is for Lorentzian chaotic light (e.g. collision broadened). The green curve is for Gaussian chaotic light (e.g. Doppler broadened). The chaotic light is super-Poissonian and bunched.
Plot of g(2) as a function of the delay normalized to the coherence length τ/τc. The blue curve is for a coherent state (an ideal laser or a single frequency). The red curve is for Lorentzian chaotic light (e.g. collision broadened). The green curve is for Gaussian chaotic light (e.g. Doppler broadened). The chaotic light is super-Poissonian and bunched.
Higher order coherence: Figure 2. A schematic diagram for the setup for Hanbury Brown and Twiss's original experiment.
Figure 2. A schematic diagram for the setup for Hanbury Brown and Twiss's original experiment.
Higher order coherence: Figure 3. The second order coherence for stellar light as measured in the Hanbury Brown and Twiss experiment as a function of the time delay introduced between the signals τ / τ 0 {\displaystyle \tau /\tau _{0}} , where τ 0 {\displaystyle \tau _{0}} is the coherence length.
Figure 3. The second order coherence for stellar light as measured in the Hanbury Brown and Twiss experiment as a function of the time delay introduced between the signals τ / τ 0 {\displaystyle \tau /\tau _{0}} , where τ 0 {\displaystyle \tau _{0}} is the coherence length.
Higher order coherence: Figure 4. The second order coherence for thermal, stellar and coherent light as a function of time delay. τ 0 {\displaystyle \tau _{0}} is the coherence length of the light beam.
Figure 4. The second order coherence for thermal, stellar and coherent light as a function of time delay. τ 0 {\displaystyle \tau _{0}} is the coherence length of the light beam.

Worked examples

Example 1 — a first encounter with Higher order coherence

Start with the simplest possible case. Write down what Higher order coherence claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Higher order coherence before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Higher order coherence ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Higher order coherence

In research
Higher order coherence appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Higher order coherence in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Higher order coherence is common in secondary-school and first-year university syllabi. It links to neighbouring topics Optical quantities, Quantum optics, so understanding it makes those chapters shorter.
In everyday life
Look for Higher order coherence outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Higher order coherence in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Higher order coherence means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Higher order coherence out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Higher order coherence in simple terms?

In quantum optics, correlation functions are used to characterize the statistical and coherence properties – the ability of waves to interfere – of electromagnetic radiation, like optical light. Higher order coherence or n-th order coherence (for any positive integer n>1) extends the concept of coh…

Why does Higher order coherence matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Higher order coherence?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Higher order coherence.

Tags

  • Optical quantities
  • Quantum optics

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