PUMP / PAIR / LISTEN

Dynamical Casimir Photon Pairs

Modulate a superconducting boundary and examine two matched microwave modes. Rotate the receivers, compare equally bright thermal light, and collect the correlated fluctuations.

An effective two-mode squeezing model inspired by a SQUID-terminated waveguide. Energy comes from the prescribed pump. Equal thermal input occupations and symmetric vacuum loss; no broadband circuit solution, calibrated flux-to-gain conversion or pump depletion. The scene is schematic; the field mean is zero.

A MODULATED BOUNDARY. TWO MATCHED MODES.

JOINT NOISE / VACUUM REFERENCE

0

BRIGHTNESS OF EITHER OUTPUT MODE

0

01PUMP / SQUID

02FREQUENCY SORTER

03RECEIVERS A / B

Schematic chip. Envelope height scales with square root of photon occupation, above vacuum. Purple blocks mark loss. Curves are not instantaneous fields; selected frequencies sum to the pump frequency.

r=0.9

01 / JOINT FLUCTUATIONS

The shape tells you what brightness cannot.

Cyan density: model for the X setting. Gold dots: saved X records only. Drag horizontally to rotate both receivers; arrows change one degree. Square-root density colors, fixed scale.

$X_A\ \longrightarrow\quad X_B\ \uparrow$

02 / ROTATE THE LISTENING AXIS

Find the quiet direction.

Model joint noise versus shared receiver phase; gold marks the selected angle. The dashed reference is one. Both orthogonal measurement settings are required for the witness.

$\theta\ ({}^\circ)\ \longrightarrow\quad W$

PREPARE AGAIN. COLLECT AGAIN.

Listen together. Keep every sample.

0 / 20000

Independent matched-mode preparations, alternating the X and orthogonal P settings. Each trial jointly measures one quadrature per mode; incompatible quadratures are never measured on the same copy. Ideal homodyne reception after the declared loss. Fixed seed, all samples retained.

Recorded joint noise

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Sampling standard error

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Model joint noise

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Uncertainty check

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Narrow together, noisy alone.

Gold: recorded combinations, X difference and P sum pooled. Cyan: the model Gaussian with integrated bin probabilities. Outer bins include every tail beyond −5 and 5.

Latest 20 records · export all

Trial	Setting	A	B

Model, conventions and sources

The real pump phase defines zero. Both receivers rotate through the same angle. Each vacuum quadrature has variance one half. Separate X and P preparations give the two variances; a witness below one is sufficient for entanglement in this trusted ideal measurement model. A value above one at a poor angle does not prove separability.

a'=a\cosh r+b^\dagger\sinh r

X=(a+a^\dagger)/\sqrt2,\quad P=(a-a^\dagger)/(i\sqrt2)

W=\tfrac12[\operatorname{Var}(X_A-X_B)+\operatorname{Var}(P_A+P_B)]

W_\theta=1-\eta+\eta(2n_{\mathrm{th}}+1)[\cosh(2r)-\sinh(2r)\cos(2\theta)]

Effective two selected temporal-frequency modes: the exponential squeeze map is not the full broadband SQUID input–output calculation. The two input modes have equal occupation, which is not a claim of a common physical temperature at different frequencies. Symmetric attenuation mixes each output with independent vacuum. No amplifier noise, phase drift, bandwidth inversion, pump depletion or circuit calibration.

Start with the essentials

Focus question: Empty input. Correlated output.
One-sentence intuition: Each mode alone looks thermal. Their shared fluctuations reveal the pair process.

Core mathematical model

A quantitative signature

W=\frac{\operatorname{Var}(X_A-X_B)+\operatorname{Var}(P_A+P_B)}{2}

With vacuum variance one half per quadrature, separable states have W at least one. The two combinations are measured on different preparations.

Common difficulties

Respect the energy source

Typical misconceptionThe vacuum supplies free energy.

Better mental modelThe externally driven boundary supplies energy. Squeezing describes the effective quantum transformation.

Read the measurement contract

Typical misconceptionA displayed theoretical curve is already acquired evidence.

Better mental modelAn effective two-mode squeezing model inspired by a SQUID-terminated waveguide. Energy comes from the prescribed pump. Equal thermal input occupations and symmetric vacuum loss; no broadband circuit solution, calibrated flux-to-gain conversion or pump depletion. The scene is schematic; the field mean is zero.

Run the experiment

01
Predict the contrast
Compare the squeezed output with the equally bright thermal preset.
What to observe: Mean brightness agrees, while the joint cloud changes shape.
02
Break the effect
Rotate both receivers or add thermal input and loss.
What to observe: A poor measurement angle can hide correlations without changing the source brightness.
03
Collect and inspect
Collect trials, pin a run, alter one control and restore it. Export every record as CSV.
What to observe: The gold data come only from saved simulated records; cyan curves are model references.