"Observation of discrete time-crystalline order in a disordered dipolar many-body system" is a preprint posted to arXiv (1610.08057v1) on 25 October 2016 by Soonwon Choi, Joonhee Choi, Renate Landig and colleagues in Mikhail Lukin's group at Harvard, with sample makers in Japan and Germany and theorists at Princeton and Berkeley. It is among the first laboratory reports of a Discrete Time Crystal (DTC): a periodically kicked system whose collective response repeats at a whole multiple of the kick period, and keeps doing so even when the kicks are slightly wrong. The authors note that a closely related trapped-ion result with 10 ions appeared while they were preparing the manuscript.
What was claimed
The paper reports that a room-temperature ensemble of roughly 10^6 nitrogen-vacancy (NV) spin impurities in diamond, driven by repeated microwave pulses, settles into a response with twice the drive period. It argues that this rhythm is protected by the spins' mutual interactions rather than by precise control, that the authors could map where the behaviour starts and stops, and that its lifetime is limited only by the spins' coupling to their surroundings. In the authors' framing, the phase is one "nominally forbidden in equilibrium", citing the Watanabe–Oshikawa result discussed in Watanabe–Oshikawa No-Go Statement. What is broken here is the discrete time-translation symmetry of the drive, not the continuous symmetry of Wilczek's original proposal; see Spontaneous Time-Translation Symmetry Breaking.
The system and the drive
Each NV centre carries an electronic spin-1. An external magnetic field picks out one crystal orientation and two of the three spin levels, giving an effective two-level system that can be prepared and read out with a green 532 nm laser and steered with microwaves. The sample is dense, about 45 ppm of NV centres, so the selected spins sit about 8 nm apart on average and interact through magnetic dipolar coupling of typically 2π × 105 kHz. They are also strongly disordered: lattice strain, random NV positions and stray paramagnetic impurities give each spin a random local field with a spread of about 2π × 4.0 MHz. The probed region is a spot about 300 nm across in a diamond nanobeam, a three-dimensional volume holding the million or so spins.
One drive cycle, which Floquet Theory treats as a repeating unit, has two steps. First the spins are held along one axis by a strong microwave field (Rabi frequency 2π × 54.6 MHz) for a time τ1, during which their interactions act. Then a short, strong pulse (2π × 41.7 MHz) rotates them by an angle θ close to π, flipping them. After n cycles the polarisation is measured, and its Fourier spectrum shows which frequencies dominate. A response at ν = 1/2, in units of the drive frequency, is the period-doubling signature.
What was measured
The key comparison is between short and long interaction times. With τ1 = 92 ns and an essentially perfect flip, the polarisation alternated sign each cycle, but the authors call this trivial: a perfect π pulse alone produces it. Changing the flip to θ = 1.034π destroyed the half-frequency peak and split it into two peaks that tracked the pulse error. With the same imperfect pulse but τ1 = 989 ns, the sharp ν = 1/2 peak returned and the oscillation lasted beyond about 100 cycles. That restoration under a deliberate error is what the paper identifies as time-crystalline order.
To map the phase, the authors defined a "crystalline fraction", the share of late-time spectral power (cycles 50 to 100) in the half-frequency peak, and set the boundary at 10%. With τ1 = 92 ns the fraction fell off once θ strayed by about 0.02π; with τ1 = 275 ns it stayed large over 0.86π < θ < 1.13π. The robust region grew with τ1 and levelled off near 400 ns. A simple self-consistent model, in which each spin's neighbours supply a rotation that compensates the pulse error, roughly matches the boundary for short and moderate τ1 but overestimates it at long ones.
They also showed a three-period version. Using all three NV spin levels and two pulses per cycle, the response locked to ν = 1/3 with τ1 = 387 ns despite pulse perturbations as large as 17%, whereas at τ1 = 35 ns the peaks shifted with every perturbation.
Limits the paper itself reports
The order is not permanent. Pulse imperfections of about 1% (0.5% from uneven microwave fields, 0.9% from on-site disorder) make even the trivial signal fade after about 50 periods. In the time-crystalline regime the half-frequency signal shows a fast initial decay and then a slow one. That slow decay speeds up sharply near the boundary at θ = 1.086π. At θ = 1.034π the fitted lifetime grows with τ1 but levels off at the independently measured spin lifetime, T1ρ = 60 ± 2 µs, set by the environment. A tilted starting state gave a lifetime of 47.6 ± 2.4 µs, close to the 49.2 ± 3.3 µs of the standard one, which the authors read as insensitivity to initial conditions.
The paper is also frank that its result is not explained. Early theory tied discrete time crystals either to many-body localisation, where strong disorder freezes a system's memory, or to a long-lived "pre-thermal" window. The authors argue that neither fits: three-dimensional dipolar spins are not expected to localise, and their fully polarised starting state should show no pre-thermal order. They suggest that slow, "critical" thermalisation may keep the spins from even reaching a pre-thermal state, call for more theory, and do not rule out that the drive itself induces localisation. The model used to map the phase treats each spin's neighbour field as a classical number and ignores entanglement; the authors expect this to fail at long interaction times.
Place in the dossier
The Discrete Time Crystal (DTC) page summarises this experiment in one line, from secondary reporting, as spin polarisation at half the drive frequency persisting for over 100 cycles. The paper supports that figure but adds the context that matters. The order lasts tens of microseconds, not indefinitely. It appears only with enough interaction relative to pulse error, in a disordered, room-temperature solid. Its theoretical basis was open at the time of writing. The authors' closing outlook, that such phases might one day help with quantum metrology, is a suggestion, not a demonstrated application. Nothing in the experiment bears on wider claims about energy or time that the name "time crystal" sometimes attracts; see Time Crystal.
Source notes & attribution
- https://arxiv.org/pdf/1610.08057