Magnet-Free Quantum Isolator: Phasor-Diagram View (2D)

Isolator

Coupling ratio g_d/g_c 1.00

Interference phase φ 90°

Amplifier noise rate 50%

Live Readouts

Forward transmission

0.0 dB

Reverse isolation

45.0 dB

Qubit coherence

100%

How the phasor diagram works

This 2D view replaces the 3D scene's flowing particles with the actual mathematics: a live phasor (Argand) diagram. The direct coherent coupling is drawn as a unit vector A on the complex plane; the dissipative coupling routed through the lossy auxiliary mode is drawn as a second vector B of length r = g_d/g_c, tacked on tip-to-tail. Their vector sum C = A + B is the actual complex transmission amplitude — its length is read directly off the diagram, not looked up from a formula.

B's angle, forward:  φ − 90°   →  |C_fwd| = √(r²+1+2r·sinφ) / (1+r)
B's angle, reverse:  φ + 90°   →  |C_rev| = √(r²+1−2r·sinφ) / (1+r)
Isolation(dB) = −20·log₁₀ |C_rev|   (capped ~45 dB)

Flipping B's angle by 180° between the forward and reverse diagrams is the nonreciprocity — same two vectors, same lengths, but the auxiliary mode's dissipative path contributes with opposite relative sign depending on which way the signal travels through it. At r = 1, φ = 90° the reverse vectors point exactly opposite and cancel to a point while the forward vectors align and add fully.

The scrolling wave trace below shows the same interference as ordinary sinusoid superposition: y_sum(t) = cos(ωt) + r·cos(ωt + angle) is itself a single cosine whose peak height is exactly |C| — the dashed horizontal guides mark that computed peak so you can watch the trace confirm it in real time.

Isolator ON/OFF — off forces r = 0: only vector A remains, fully reciprocal, so forward and reverse diagrams become identical.
Coupling ratio r — the two path vectors must be equal length (r = 1) for exact reverse cancellation.
Interference phase φ — must sit at 90° so B is exactly perpendicular to A in the forward diagram; drift reopens a reverse leak.
Amplifier noise rate — how often the amplifier port launches a noise packet back toward the qubit along the bottom strip.

Real-world relevance: this reservoir-engineered, magnet-free approach (after Metelmann & Clerk) is used in real superconducting-qubit labs to build on-chip isolators and directional amplifiers where a centimeter-scale ferrite circulator won't fit.

Direct path A / forward signal Dissipative path B / leaked noise Resultant sum C / cancelled noise