Quantum • Environment-Induced Decoherence • Browser-only

Quantum Decoherence Time Calculator

Estimate how quickly a spatial superposition washes out because of collisions with its environment. Set pressure, temperature, particle size, Δx, and choose presets to see why everyday objects look classical.

Particle mass (kg) Particle radius (nm) for cross-section Superposition separation Δx (m) Environment temperature (K) Pressure (Pa) Environment particle mass (kg) (air ~4.65e-26, water ~2.99e-26)

Results

Collision rate

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nσv (1/s)

Decoherence rate Γ

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Scaled by Δx vs thermal λ_dB

Decoherence time τ

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τ = 1/Γ

Gas thermal λ_dB

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h / √(2π m kT)

Higher Γ → shorter τ. When τ is microseconds or less, the state looks classical almost instantly.

Decoherence intuition bites

Δx matters

Γ roughly scales with (Δx / λ_dB)². Large, well-separated states decohere much faster than tightly overlapped ones.

Separation scaling

Pressure dominates

Going from 1 atm to 10⁻⁸ Pa (typical qubit fridge) cuts the collision rate by ~13 orders of magnitude.

Vacuum helps

Warm baths kill coherence

Thermal speed v ∝ √T. Hotter environments both move faster and carry shorter λ_dB, ramping up Γ.

Temperature

Macroscopic objects

For a grain of dust in air with Δx ~ micron, τ is effectively zero—explaining why you never see everyday superpositions.

Why classical?

Coherence is local

Cold, shielded, small Δx systems (ions, superconducting qubits) can maintain coherence for µs–ms—long enough to compute.

Quantum devices

How this sample model works

This calculator uses a simple collisional decoherence picture: background particles with number density n = P / (k_BT) and thermal speed v = √(8k_BT / πm) hit a target of cross-section σ = πr². The collision rate is nσv. To model how well a collision distinguishes the two branches of a spatial superposition separated by Δx, we scale that rate by (Δx / λ_dB)², capped at 1, where λ_dB is the thermal de Broglie wavelength of the bath particle.

The result is a back-of-the-envelope decoherence rate Γ and time τ = 1/Γ. Real systems include additional channels (phonons, photons, electrical noise, surface loss), and isolation strategies (shielding, cooling, error correction). Still, the scaling explains why you don’t see Schrödinger cats in your living room but do see quantum interference in cryogenic, high-vacuum labs.

Use the presets to jump between everyday air, liquid water, a superconducting qubit fridge, and interstellar gas. Change Δx to see how microscopic separation keeps coherence alive longer than macroscopic ones.

Educational value: why decoherence kills everyday quantum weirdness

Decoherence is the missing link between the strange rules of quantum mechanics and the commonsense classical world. Students often ask, “If electrons can be in superposition, why don’t we see tables in two places at once?” This tool offers an accessible, numbers-first way to answer that question. By entering pressure, temperature, particle size, and Δx, you immediately see how enormous the collision rate is in everyday air, and how quickly Γ blows up when the separation between branches grows. A single glance at τ in the “air preset” shows that macroscopic superpositions decohere in effectively zero time, grounding the intuition that classicality is an emergent, environment-driven phenomenon.

The calculator also highlights the role of de Broglie wavelength. When you compare Δx to λ_dB, you see that even tiny separations can be “measured” by a warm bath because the bath particles carry short wavelengths. That teaches why cooling and vacuuming both matter in quantum experiments: colder particles move slower and have longer λ_dB, so they resolve spatial detail less sharply, reducing how much “which-branch” information leaks out per collision. Switching to the cryogenic vacuum preset demonstrates how many orders of magnitude τ can grow just by lowering P and T, mirroring the engineering that makes superconducting qubits viable.

Educators can use the dust-grain-in-air vs ion-in-fridge contrast to show scaling laws. The cross-section σ scales with r², so a tenfold increase in radius means a hundredfold rise in collision rate. Combine that with Δx dependence and you can build quick thought experiments: shrink Δx to atomic scales and coherence becomes plausible; expand Δx to microns and it disappears instantly. This directly supports lessons on why interference experiments (double-slit electrons, neutrons, C₆₀ molecules) demand high vacuum and shielding.

The space preset is equally instructive. Even in interstellar gas, where pressures can be ~10⁻¹⁵ Pa, decoherence eventually happens—but on timescales so long that a macroscopic object might effectively stay coherent compared with human observation. That contrast helps students appreciate that “quantum vs classical” is not binary; it is a continuum governed by rates and environment. It also opens discussions about quantum communication across free space, satellite experiments, and how gravitational decoherence or cosmic radiation might enter a more complete picture.

Because everything runs in the browser and updates instantly, the tool invites playful experimentation. Ask learners to halve the temperature, or to replace nitrogen with heavier argon (larger m) to see how thermal speed and λ_dB shift Γ. Have them vary Δx to mimic wavepacket spreading in a trap. Every tweak becomes a mini lab that reinforces the core lesson: coherence is fragile, environment-dependent, and tunable. Those insights are foundational for understanding why quantum error correction, cryogenics, shielding, and material science are all critical ingredients in building practical quantum technologies.