A pendulum receives a kick but returns to its starting position not after one period, but after two. That is how a discrete time crystal behaves: a phase of matter that spontaneously breaks discrete time-translation symmetry and oscillates with a period that is a multiple of the driving period. Previously, such phases were stabilized by disorder, which induced many-body localization and prevented the system from heating into a featureless state. However, disorder complicates control and scaling. The new work takes a different route: instead of disorder or a linear potential gradient, it uses a power-law gradient in the interaction strength between neighboring spins.

Consider a one-dimensional chain of L spin-1/2 particles. The interaction between neighboring spins has the form j^α $σ_j^z$ $σ_{j+1}^z$, where j is the site index and α is a tunable exponent. The system is subjected to periodic instantaneous kicks that rotate the spins about the x-axis by an angle close to π/2. The evolution over one period is described by a Floquet operator. Numerical analysis using matrix product states shows that for a wide range of α from 0.5 to 1.5, the system exhibits period doubling. The lifetime of the time crystal grows exponentially with size: t* ~ exp(1.99(2)L) for α=0.5 and t* ~ exp(2.15(9)L) for α=1.5. This means that already for a few dozen spins, the state persists almost indefinitely.

The same system works as a quantum battery. The stored energy in the time-crystal phase scales as E ~ $L^{2.042(2)}$ for α=1, that is, superlinearly. However, after normalizing the Hamiltonian, the power becomes almost independent of system size. The true advantage of the battery is not superlinear power but robustness: the charge is preserved under imperfections and does not require precise synchronization with the optimal moment. For the quantum sensor, the quantum Fisher information grows faster than linearly, indicating a quantum advantage. The exponent $β_s$ depends on α sub-polynomially: $β_s$ ~ $α^{0.37(3)}$. Under Markovian dephasing, the quantum Fisher information still grows with time as $F_Q$ ~ $n^{1.8}$ for α=0.5 and $F_Q$ ~ $n^{2.3}$ for α=1.5, indicating that the quantum advantage persists in an open system.

Previously, it was unclear whether a time crystal could be stabilized without disorder, using only an interaction gradient, and whether such a crystal could be useful for practical energy storage and sensing. Now it is shown that a power-law interaction gradient stabilizes a time crystal with period doubling, and this crystal works as a robust quantum battery and a sensor with quantum advantage. A model of a spin chain with power-law growing interactions and periodic kicks was constructed; the conditions for period doubling were derived analytically, and stability and performance metrics were verified numerically. The results can be implemented on existing platforms with trapped ions or Rydberg atoms to create prototypes of quantum batteries and high-precision sensors. A pendulum that returns to its starting position after every second kick turns out to be not just a curiosity but a tool for storing energy and measuring time with quantum precision.