Dispersive probes / Causal control
When can atoms passing through a cavity reveal its photon number, and when can delayed feedback keep that number steady? Once enough atoms have passed, as long as no two candidate numbers give the same phase shift. Each atom crosses without absorbing a photon and picks up a phase set by the photon number; weak contrast and missed atoms only mean more atoms are needed. Feedback holds the number only if it acts before more photons leak out; a slow controller corrects a number that has already changed.
Send Ramsey probe atoms through a cavity one after another. Record which of two states each atom is found in and infer the photon-number distribution. Then apply delayed feedback and use a fresh run of atoms to check whether the number stays stable.
Schematic scale and motion; the plots show simulated records.
Glowing atoms illustrate the probe beam; each retained event appears in the plots. Atoms travel left to right through both Ramsey zones and the gap between the cavity mirrors, then enter the state detector. The stored microwave axis is perpendicular to the atom beam. The glowing slider represents the calibrated dispersive coupling; its position and brightness do not show the hidden photon number.
Atoms cross the same cavity one by one
If you continue control after verification, a fresh cavity is prepared. The photon-number filter starts with equal weights on every number from zero to nine. It uses only the observed atom states, the phase settings and the calibrated transitions. The prepared number and whether each hidden actuator pulse succeeded never enter the inference.
Ready. Predict first, then acquire.
Space: acquire or stop. Right arrow: one atom. Escape: stop. Shortcuts apply only when the workbench has focus; ordinary controls retain their native keys.
Raw readout of each atom
Teal: control atoms. Violet: fresh verification atoms. Gray: missed detection. Phase is retained in every raw row; the plot shows the most recent three hundred probes.
Inferred photon number; the true value is not shown
Feedback with a finite delay
Green pulses add one photon probabilistically; gold pulses remove one. The controller propagates the calibrated probability, never the hidden success. A single queued command waits for its full delay. Decisions require eight probes and a posterior peak above fifty-five percent.
Values computed from the records alone
Retained probes
Control posterior mean
Control target probability
Control uncertainty / bits
Fresh verifier target probability
Saved target probability
The posterior target probability assumes this calibrated photon-number model. It is not a measured preparation fidelity, and it does not measure phase coherence. Verification starts from a fresh flat prior, cancels every queued pulse and freezes the control posterior. The cavity keeps losing photons during verification.
Latest raw records; the CSV has every row
| Probe | Purpose | Phase / rad | State | Pulse | Issued after |
|---|
Saved run, model limits and sources
No saved run. Saving preserves the exact random state, record streams, posteriors and queued pulses in memory.
Zero temperature is assumed. Number is bounded from zero through nine; attempted boundary jumps stay at the boundary. Feedback is a stochastic number-jump teaching model, rather than the coherent microwave displacement of the historical apparatus.
Physics tutorial
BackgroundSend Ramsey probe atoms through a cavity one after another. Record which of two states each atom is found in and infer the photon-number distribution. Then apply delayed feedback and use a fresh run of atoms to check whether the number stays stable.
Why it mattersAn absorbing photodetector uses up the photons it counts. A far-detuned atom instead picks up a phase that depends on the photon number, and a second Ramsey pulse plus a state-selective detector read that phase out.
Start with the essentials
The Ramsey probabilities of the two observed energy states add up to one. Alternating the analysis phase gives both quadratures, but photon numbers whose phase shifts differ by exactly a whole number of turns still look the same.
The predicted distribution already accounts for the known photon loss and for commanded actions that succeed at random. The filter never sees the prepared or the simulated photon number. A missed atom leaves the predicted distribution unchanged.
At zero temperature this loss map is exact, and several photons can disappear between two probes. The mean photon number decays exponentially. Thermal jumps up to higher photon numbers are left out.
A command to add or remove a photon succeeds with a known probability. The controller carries this whole probability map forward and never learns whether a command actually succeeded. Commands take effect only after the chosen delay. Sayrin and colleagues used a coherent displacement, not this actuator.
Typical misconceptionIn a QND experiment, the cavity cannot lose photons.
Better mental modelThe probe itself leaves the photon number unchanged. Cavity damping and the feedback actuator do exchange energy with the field, and both the simulator and the inference filter include those transitions.
Typical misconceptionIf the inferred photon number is sharp, the full state of the field must have been preserved.
Better mental modelThe displayed state contains only photon-number populations, so it cannot show phase coherence or cat-state interference. Measuring the number generally disturbs the phase, and the Lab makes no claim that the phase survives.
Typical misconceptionThe verification run measures a final photon number that is perfectly frozen.
Better mental modelVerification starts a new inference from new atoms and a fresh prior, but it probes the same cavity, which keeps evolving. Photons are still lost, all pending commands are canceled, and the controller's posterior is frozen for comparison.
Choose Count without loss and acquire a sequence. Compare the two-state atom outcomes, the posterior and the missed readouts.
What to observe: Each detected atom changes what we know about the photon number. The dispersive probe itself does not change the simulated photon number.Choose Parity alias, acquire, and look at every peak left in the posterior. Then try Weak / missed probes.
What to observe: Photon numbers with identical likelihoods all remain as candidates. A high posterior mean is not a precise measurement of the photon number.Choose Repair photon loss. Watch each command join the queue after an atom is recorded and take effect at a later probe number. Save the run, then compare it with Late controller.
What to observe: The inference can notice a photon loss only some time after it happens. A slow actuator may act on an estimate that is already out of date. The target probability is inferred from the records under this model; it is not a measured fidelity.Press Stop, then Fresh verification. Queued commands are canceled and feedback is frozen. A separate filter, starting from a flat prior, processes only the new atoms.
What to observe: Given the physical field and the calibrated model, the verification posterior does not depend on the control records. The cavity still loses photons during verification, so this is not a measurement of a frozen final state.Save the run, change the settings, then restore and export it. Press Stop midway to keep a partial acquisition, and use One atom to step through the sequence.
What to observe: Restoring brings back the parameters, the random-number state, both posteriors, every raw outcome and the queue of pending commands. The CSV export holds the observed records and commands, never the hidden true photon number.Quantum evidence · Reading path
Articles on this path that use this experiment, followed by the other experiments they suggest.