Quantum contrasts / Light in superposition
How can one wave packet of light end up in several places at once? Kerr evolution twists a coherent light field into a superposition of two or three coherent pieces sitting at different places in phase space. Where the pieces interfere, the Wigner function turns negative. Measuring photon-number parity shows it: odd photon numbers outnumber even ones there, though each outcome still has an ordinary probability. Phase noise washes the interference out.
Let the Kerr effect turn one coherent light field into a superposition of two or three coherent states. Move a probe across the Wigner function, which can dip below zero, and count how often the photon number comes out even or odd. Then compare photon loss with phase noise, and see whether the interference between branches fades before the stored energy does.
Phase space · height is five times the signed Wigner value · drag to rotate
Measure the state, keep every outcome
Each parity trial returns even or odd. A negative Wigner estimate means more odd outcomes.
Move the displacement probe
Background: model Wigner values on a fixed color scale. Outlined dots: recorded parity estimates. The gold cross is the probe; this is not a tomographic reconstruction.
Even or odd: raw outcomes
Interval: 95% Wilson interval from the raw parity counts. It describes sampling uncertainty only. Every trial starts from a fresh identical field.
Prepare, store, displace, then read the parity
The field starts in a coherent state and evolves under the ideal Kerr Hamiltonian. Then the Kerr term is switched off, and the field is stored while it loses photons to the vacuum. Gaussian phase uncertainty acts last, as a separate channel. The surface, the energy and the two parity probabilities all come from this same final density matrix.
The teal curve is the fraction of mean energy retained. The coral curve is the environment-overlap factor that multiplies the cross terms between the two coherent branches; it applies only to the half-revival cat without phase noise. This analytic reference is the untruncated limit of the same preparation and loss channel. It is not the purity, a sum of Fock off-diagonal elements, a measured visibility or a fidelity. When the branches overlap strongly, it cannot be read as the coherence of a cat with distinguishable branches. Both curves are model references; the outlined parity samples above are the acquired data.
The energy lifetime is one over the loss rate. For well-separated branches, the cross terms start out decaying faster than the energy by a factor of twice the initial mean photon number. The plot uses the exact finite-time factor above instead of stretching that short-time approximation. For the vacuum there is no energy ratio, because the initial energy is zero.
The basis size truncates the prepared quantum state itself, not a camera or a detector. The probability of the coherent state that falls outside the basis is reported before normalization. Above 0.1%, acquisition is blocked; enlarge the basis before trusting a cat prediction. The model leaves out thermal photons, Kerr and loss acting at the same time, pulse errors, detector inefficiency and state reconstruction.
Positive Kerr coefficient in a frame rotating with the linear cavity frequency. The initial coherent amplitude has adjustable magnitude and angle. Time is a fraction of the full revival. After preparation Kerr is switched off. Vacuum photon loss acts during a separate storage interval, followed by independent Gaussian phase uncertainty; the two noise channels commute. This is not simultaneous dissipative Kerr evolution or a fitted decoherence rate.
The plot axes are dimensionless real and imaginary coherent amplitudes. This Wigner convention integrates to one over that plane. The probe means displace by minus its coordinate, then measure parity. The samples are ideal binary readouts; the smooth surface always comes from the density matrix. The input is projected onto the selected Fock support and normalized; its omitted probability is reported. The exact finite-support annihilation-loss map preserves trace and positivity, with no integration time step. No drive, thermal bath, ancilla pulse or detector model.
Albert et al. · vacuum photon loss, equations 1.3–1.6 · Kirchmair et al. · Kerr evolution and fractional revivals · Banaszek et al. · displaced parity
Physics tutorial
BackgroundLet the Kerr effect turn one coherent light field into a superposition of two or three coherent states. Move a probe across the Wigner function, which can dip below zero, and count how often the photon number comes out even or odd. Then compare photon loss with phase noise, and see whether the interference between branches fades before the stored energy does.
Why it mattersThis Lab shows how a coherent superposition differs from a mixture. Under photon loss, you can compare how long the energy lasts with how long the interference between branches lasts.
Start with the essentials
The Kerr interaction is switched off before photons start leaking into vacuum. The cross-term factor applies only to the two-branch cat at the half revival with zero phase uncertainty. It is not a measured visibility, nor a sum of coherences in the photon-number basis. Branches that overlap strongly do not form a distinguishable cat.
Each photon number picks up its own phase, which shears the field in phase space. At fractions of the revival period this forms superpositions of coherent states, and after a full period every Fock component is back in phase.
This noise channel keeps the diagonal populations unchanged. It does not model energy loss.
Each shot uses a freshly prepared copy of the same state. The state is displaced by minus the probe coordinate and then read out as even or odd. Wilson intervals show the uncertainty that comes from a finite number of shots.
Typical misconceptionThe smooth Wigner surface was reconstructed from the shots shown on screen.
Better mental modelThe coherent input first goes through ideal Kerr evolution. Storage is a separate later step in which photons leak into vacuum, with an optional Gaussian phase spread. The photon-number basis is cut off at an adjustable maximum, and the page reports how much input probability lies above it. Kerr evolution and loss never act at the same time, and drive errors and detector inefficiency are left out. The Wigner surface comes from the model, not from measured data, and its negative values are not negative probabilities.
Choose Energy leaks; coherence fades. Compare the fraction of energy kept with the branch cross-term factor, then find a negative valley and collect parity outcomes. Stop a run partway, pin it, resume it, export it and restore it.
What to observe: At amplitude two and a loss dose of one quarter, about 78% of the energy remains, but the cross-term factor is only about 17%. Phase noise on its own leaves the energy unchanged. These numbers are model predictions that you can compare with the collected parity data; they are not a reconstruction of the state.Start at Prepare, then choose Halfway or One third. Rotate the surface to see its positive and negative parts.
What to observe: Positive lobes appear together with negative interference valleys. At a full revival the field returns to a single coherent packet.Move the probe into a negative valley and collect 500 parity outcomes. Pin the run and export the raw CSV.
What to observe: Odd outcomes outnumber even ones, and once the interval is narrow enough it lies entirely below zero. No single outcome has a negative probability.Increase the phase uncertainty, compare the curves, then restore the pinned preparation.
What to observe: The noise lowers the purity and changes the interference, but the photon-number populations stay the same.Quantum evidence · Reading path
Articles on this path that use this experiment, followed by the other experiments they suggest.