6. Superposition & Interference
Reading time: ~35 minutes | Pages: 7
Your Progress
Course: 0% complete
Superposition is the heart of quantum mechanics: a system can exist in multiple states simultaneously until measured. This leads to the famous interference effects that distinguish quantum from classical physics.
Video Lecture
Quantum Superposition Explained - Double Slit Experiment
Excellent explanation of quantum superposition using the iconic double-slit experiment, showing how particles exhibit wave-like interference
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
The Double-Slit Experiment
Young's Double-Slit Experiment
— Thomas Young
Demonstrated that light exhibits wave-like interference by passing through two slits, creating alternating bright and dark fringes
Significance: First direct evidence that light is a wave, contradicting Newton's corpuscular theory
Electron Diffraction
— Davisson & Germer
Observed that electrons (particles!) create interference patterns just like light waves when scattered from a crystal
Significance: Confirmed de Broglie's wave-particle duality: matter has wave properties
Single-Electron Double-Slit
— Claus Jönsson
Performed double-slit with electrons sent one at a time. Pattern builds up gradually, proving each electron interferes with itself
Significance: Most direct demonstration that superposition is a property of individual quantum particles, not ensembles
Which-Path Information Destroys Interference
— Dürr, Nonn, Rempe
Experimentally demonstrated quantum complementarity: measuring which-path information eliminates interference pattern
Significance: Proved that wave-particle duality is fundamental: you cannot observe both aspects simultaneously
Principle of Superposition
Linearity of quantum mechanics: If $|\psi_1\rangle$ and $|\psi_2\rangle$ are valid states, so is any linear combination:
for any $c_1, c_2 \in \mathbb{C}$ with normalization $|c_1|^2 + |c_2|^2 = 1$
Key insight: The system is NOT in state 1 OR state 2. It's in a genuinely new state—a superposition—that exhibits properties of both.
💡 Application: Quantum Computing
A quantum bit (qubit) exists in superposition $|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$, simultaneously representing both 0 and 1. This allows quantum computers to explore exponentially many states in parallel—the basis of quantum speedup for certain problems.
Double-Slit Experiment
A quantum particle passes through two slits. Before measurement, it exists in a superposition:
Probability density at the screen:
Interference term: $2\text{Re}(\psi_1^*\psi_2)$ creates the alternating bright/dark fringes
If you instead know which slit the particle went through (e.g., by placing a detector), the state becomes:
No interference term → no pattern, just two overlapping blobs
Video Lecture
Quantum Double-Slit Experiment Visualized
Beautiful animations showing how the interference pattern emerges as individual particles are detected one by one
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
📝 Worked Example: Interference Fringe Spacing
Problem: Electrons (λ = 1 nm) pass through two slits separated by d = 100 nm. A screen is placed L = 1 m away. What is the spacing between bright fringes?
Step 1: Path difference for constructive interference
Small angle approximation: sin θ ≈ θ for small angles
Step 2: Angular position of bright fringes
Step 3: Linear position on screen
Step 4: Fringe spacing
💡 Result: Bright fringes are spaced 1 cm apart—easily observable!
Coherence & Phase
Coherent superposition: Requires definite phase relationship between components
Phase $\phi$ determines fringe positions. Interference requires stable $\phi$
Decoherence: Environment entangles with system, destroying phase coherence:
This is why we don't see macroscopic objects in superposition—they decohere almost instantly
🤔 Self-Check Question
Question: In the double-slit experiment, if you place a detector at one slit to see if the particle passes through, the interference pattern disappears. Why?
Show Answer
Answer: The detector measurement collapses the superposition. Before detection, the state was:
After detecting the particle at slit 1, the state collapses to $|\text{slit 1}\rangle$. There's no longer a superposition, so no interference term in the probability distribution.
Key principle: Quantum complementarity—you can observe wave behavior (interference) OR particle behavior (which-path), but not both simultaneously.
Which-Path Information & Complementarity
Bohr's Complementarity Principle: Wave and particle aspects of quantum systems are complementary—mutually exclusive but both necessary for complete description.
The trade-off is quantitative:
where $\mathcal{V}$ = visibility (interference) and $\mathcal{D}$ = distinguishability (which-path info)
Interpretation: Perfect interference ($\mathcal{V} = 1$) requires zero which-path information ($\mathcal{D} = 0$), and vice versa.
Video Lecture
Wave-Particle Duality and Quantum Complementarity
In-depth discussion of complementarity, delayed-choice experiments, and what quantum mechanics tells us about the nature of reality
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
💡 Application: Quantum Cryptography
Quantum key distribution (QKD) protocols like BB84 exploit superposition and measurement-induced collapse to detect eavesdropping. An eavesdropper measuring photon polarization collapses superpositions, introducing detectable errors.
Example: Alice sends $|\psi\rangle = \frac{1}{\sqrt{2}}(|H\rangle + |V\rangle)$. Eve measures in H/V basis, collapsing it. Bob's subsequent measurement shows anomalies, revealing Eve's presence.
📝 Worked Example: Visibility Calculation
Problem: In a double-slit experiment, the maximum intensity is $I_{\text{max}} = 9I_0$ and minimum is $I_{\text{min}} = I_0$. Calculate the visibility (fringe contrast).
Step 1: Recall visibility definition
This quantifies how "visible" the interference pattern is
Step 2: Substitute values
💡 Result: Visibility is 0.8 (80%), indicating strong but not perfect interference. Maximum distinguishability is $\mathcal{D} = \sqrt{1 - 0.8^2} = 0.6$.
Schrödinger's Cat: Macroscopic Superposition
The infamous thought experiment: a cat in a box with a quantum-triggered poison is in superposition:
Why don't we see macroscopic superpositions?
Decoherence: The cat interacts with ~10²³ air molecules/second. Each interaction entangles the cat with its environment, rapidly destroying quantum coherence. The timescale is ~10⁻²³ seconds—far too fast to observe.
🤔 Self-Check Question
True or False: A quantum system in superposition $|\psi\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ is "really" in state |0⟩ or |1⟩, we just don't know which until we measure.
Show Answer
False! This is a common misconception. The system is NOT in a definite state that we're simply ignorant about (hidden variable).
Proof: If it were truly in |0⟩ or |1⟩ pre-measurement, you couldn't observe interference effects. Experiments (Bell tests) show violations of Bell inequalities, ruling out all local hidden variable theories.
Correct view: The system genuinely exists in a superposition—a new kind of state that has no classical analog. Measurement doesn't "reveal" a pre-existing value; it creates the value.
📝 Chapter Summary
Key Equations
Key Concepts
- Superposition is a genuine quantum state, not ignorance
- Interference requires coherent superposition
- Which-path information destroys interference
- Wave-particle duality is complementary
- Decoherence explains classical limit
- Measurement collapses superposition
Superposition lies at the heart of quantum weirdness. It's not that particles are "sometimes waves, sometimes particles"—they're always quantum objects exhibiting both aspects, with complementarity determining which aspect we can observe. Understanding superposition and interference is essential for modern quantum technologies and fundamental tests of reality itself.
🔗 Related Topics:Measurement & Collapse • Decoherence • Bell Inequalities