Historical research guide · 0722 · 2026

Subcycle tomography of quantum light

Geehyun Yang · Matthias Kizmann · Alfred Leitenstorfer · Andrey S. Moskalenko

In one minute

Quantum optics normally describes light in modes with a well-defined frequency, which means every picture of a quantum state is an average smeared over many oscillations of the wave. Geehyun Yang and Andrey Moskalenko at KAIST, with Matthias Kizmann and Alfred Leitenstorfer at Konstanz, work out how to take the picture faster than one cycle. Their probe is a light pulse shorter than half a cycle of the field under study; sweeping its delay and its carrier phase builds what they call a time-resolved Wigner function — a snapshot of the field’s quantum state at one instant rather than an average over the wave. On paper they make ultrashort squeezed vacuum in a thin zinc telluride crystal, optionally subtract a single photon using an avalanche photodiode, and watch the phase-space picture squeeze, rotate, and for the photon-subtracted state go negative, which is the signature no classical light can imitate. They also show the picture can be rebuilt from three quadrature measurements rather than millions.

Connection

Chapter 2 rests on the vacuum being a real medium you can read rather than a bookkeeping device, and electro-optic sampling is how it gets read; this paper carries that reading from variances up to full state tomography, inside a single oscillation of the field. It belongs to chapter 1 too, because it names the price of the evidence — how many measurements a subcycle snapshot actually costs — and then cuts it by orders of magnitude.

From the source

The central construction is the time-resolved Wigner function. Normalising the two time-delayed detection quadratures so that they satisfy the canonical commutation relation, the authors define a characteristic function from the density matrix and Fourier transform it. The result captures the complete information contained in the positive-frequency part of the electric-field operator, with a temporal resolution equal to the duration of the probe pulse, and since its centre of gravity along each axis gives the real and imaginary parts of the classical field at that delay, it can be read as a generalisation of the classical field phasor.Section II, Results, equations 1 and 2
The proposed apparatus is fully specified. A strong linearly polarised mid-infrared half-cycle pulse drives a second-order nonlinear process in a generating crystal — zinc telluride thinner than 15 micrometres, thin enough to be treated as effectively dispersionless — producing an ultrashort squeezed-vacuum pulse at the perpendicular polarisation, which a polarising beam splitter separates from the drive. An optional avalanche photodiode behind a high-reflectance beam splitter postselects the subtraction of a single photon, imposing non-Gaussian structure on the output. Detection is pulsed balanced homodyning with a unipolar local oscillator shorter than the drive, its delay set by an adjustable mirror and its carrier-envelope phase by a phase shifter; the authors note the same statistics are obtainable by electro-optic sampling.Section II, Results, Figure 1 and the accompanying description
A pulsed squeezed vacuum is not one mode but a few. Through the Bloch-Messiah reduction the state decomposes into temporally localised principal modes, and treating every mode with a squeezing parameter below one thousandth as vacuum, four modes suffice for the driving used here, with squeezing parameters 0.281, 0.046, 0.005 and 0.004. The time-dependent squeezing that the tomography sees therefore comes mainly from the first localised mode, with most of the remainder from the second.Section II, Results, equation 3 and the paragraph following it
What each mode contributes is set by transmission coefficients — the squared projections of the gated detection mode onto the principal modes — which for the first two modes closely follow the temporal shape of those modes. With a Gaussian probe of 5.8 femtoseconds the first two are captured while the rapid oscillations of the third and fourth are washed out. Near a delay of minus 14 femtoseconds, where the driving field becomes significant in the effective conformal time flow inside the generating crystal, the tomogram shows strong squeezing. The product of the two quadrature variances slightly exceeds one quarter, which the authors attribute mainly to a time-dependent portion of thermal photons reaching the detection mode, a phenomenon related to one reported for a rapidly switched Unruh-DeWitt detector.Section II, Results, equations 4 to 6 and Figure 2
Temporal resolution and quantum visibility trade against each other, and the paper puts numbers on the trade. Expanding the probe pulse to about 24.5 femtoseconds gives the highest metrological power for the squeezed state, 0.643, and the largest negativity of the time-resolved Wigner function at the origin for the photon-subtracted state, minus 0.232. A probe that is too short contaminates the reading with vacuum contributions from higher-order principal modes; a longer one lowers both quantities. The quantum features nevertheless remain pronounced while the probe stays considerably shorter than the period of the field driving the quantum light.Section II, Results, equation 9 and Figure 4 with its caption
The reconstruction is made affordable. Rather than the inverse Radon transform, which needs the full quadrature distribution at many carrier-envelope phases and then at many delays, the tomogram can be approximated to the Nth order of a Gram-Charlier expansion from N plus 1 phase-rotated quadratures. At second order — three phase-rotated quadratures, giving two variances and one covariance — the reconstruction matches the exact result to a Hilbert-Schmidt distance of 0.0007 for the pulsed squeezed state and 0.0551 for the photon-subtracted state, at the least favourable delays in each case, and still captures the non-Gaussianity and the orientation of the distribution. The authors set this against the millions of repetitions state-of-the-art experiments need to capture the statistics of a single quadrature at a single instant.Section II, Results, equation 8 and Figure 3; summary paragraph

The way in

https://doi.org/10.1103/m5ln-m31l

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

Published as Physical Review A 113, 043703 (2026) under the APS default licence. The preprint is on arXiv as 2307.12812, version 1 posted 24 July 2023, under the arXiv.org perpetual non-exclusive distribution licence, which grants arXiv distribution rights and nothing further — checked on the arXiv record on 2026-09-08, where no Creative Commons statement appears, and the preprint carries none. So this sheet holds the summary, the claims and the authors’ own abstract and sends the reader to the source; the claims are read against that preprint, whose section numbering is used in the locators. Geehyun Yang and Andrey Moskalenko write from the Department of Physics at KAIST in Daejeon; Matthias Kizmann from the University of California, Irvine and the University of Konstanz; Alfred Leitenstorfer from the Department of Physics and Center for Applied Photonics at Konstanz. The companion sheet in this library is Back action in quantum electro-optic sampling of electromagnetic vacuum fluctuations by Guedes, Vakulchyk, Seletskiy, Leitenstorfer, Moskalenko and Burkard, Physical Review Research 5, 013151 (2023), which is reproduced there in full under CC BY and which prices the disturbance the probe itself causes.

How to cite it

Geehyun Yang, Matthias Kizmann, Alfred Leitenstorfer, Andrey S. Moskalenko (2026) Subcycle tomography of quantum light doi:10.1103/m5ln-m31l

Where it sits in the curriculum

What the vacuum is