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A time crystal or space-time crystal is a structure that repeats periodically in time, as well in space. Normal three-dimensional crystals have a repeating pattern in space, but remain unchanged with respect to time; time crystals repeat themselves in time as well, leading the crystal to change from moment to moment. A time crystal never reaches thermal equilibrium as it is a type of non-equilibrium matter - a form of matter proposed in 2012, and first observed in 2017. This state of matter cannot be isolated from its environment - it is an open system in non-equilibrium.

The idea of a time crystal was first described by Nobel laureate and MIT professor Frank Wilczek in 2012. Subsequent work developed a more precise definition for time crystals, ultimately leading to a proof that they cannot exist in equilibrium. Then in 2016, Norman Yao and colleagues at the University of California at Berkeley proposed a way to create non-equilibrium time crystals, which Christopher Monroe and Mikhail Lukin independently confirmed in their labs. Both experiments were published in Nature in 2017.



The idea of a space-time crystal was first put forward by Frank Wilczek, a professor at MIT and Nobel laureate, in 2012.[1]

Xiang Zhang, a nanoengineer at University of California, Berkeley, and his team proposed creating a time crystal in the form of a constantly rotating ring of charged ions.[2]

In response to Wilczek and Zhang, Patrick Bruno, a theorist at the European Synchrotron Radiation Facility in Grenoble, France, published several papers claiming to show that space-time crystals were impossible. Also later Masaki Oshikawa from the University of Tokyo showed that time crystals would be impossible at their ground moreover he implied any matter can not exist in non-equilibrium in its ground state.[3][4]

Subsequent work developed more precise definitions of time translation symmetry-breaking which ultimately led to a 'no-go' proof that quantum time crystals in equilibrium are not possible.[5][6]

Several realizations of time crystals, which avoid the equilibrium no-go arguments, were later proposed.[7] Krzysztof Sacha at Jagiellonian University in Krakow predicted the behaviour of discrete time crystals in a periodically driven many-body system.[8] Work with spin systems[9] suggested periodically driven quantum systems could show similar behavior. And Norman Yao at Berkeley studied a different model of time crystals.[10]

Yao's blueprint was successfully used by two teams: a group led by Mikhail Lukin at Harvard[11] and a group led by Christopher Monroe at University of Maryland.[12]

Time translation symmetryEdit

Symmetries in nature lead directly to conservation laws, something which is precisely formulated by the Noether theorem.[13]

The basic idea of time-translation symmetry is that a translation in time has no effect on physical laws, i.e. that the laws of nature that apply today were the same in the past and will be the same in the future.[14] This symmetry implies the conservation of energy.[15]

Broken symmetry in normal crystalsEdit

Figure 2. Normal process (N-process) and Umklapp process (U-process). While the N-process conserves total phonon momentum, the U-process changes phonon momentum.

Normal crystals exhibit broken translation symmetry: they have repeated patterns in space, and are not invariant under arbitrary translations or rotations. The laws of physics are unchanged by arbitrary translations and rotations, but if we hold fixed the atoms of a crystal, the dynamics of electrons or other particles in the crystal depends on how it moves relative to the crystal, and particles' momentum can change by interacting with the atoms of a crystal—for example in Umklapp processes.[16] Quasimomentum[17], however, is conserved in a perfect crystal.

Broken symmetry in time crystalsEdit

Time crystals seem to break time-translation symmetry, and have repeated patterns in time. Fields or particles may change their energy by interacting with a time crystal, just as they can change their momentum by interacting with a spatial crystal.


Because a time crystal is a driven (i.e., open) quantum system that is in perpetual motion, it does not violate the laws of thermodynamics:[18] Energy is conserved, it does not spontaneously convert thermal energy into mechanical work, and it cannot serve as a perpetual store of work. But as long as it is driven by an outside force, it may change perpetually in with a fixed pattern in time.[19]

It has been proven that a time crystal cannot exist in thermal equilibrium. Recent years have seen more studies of non-equilibrium quantum fluctuations.[20]


In October 2016, Christopher Monroe at the University of Maryland, claimed to have created the world's first discrete time crystal. Using the idea from Yao's proposal, his team trapped a chain of 171Yb+ (ytterbium) ions in a Paul trap, confined by radio frequency electromagnetic fields. One of the two spin states was selected by a pair of laser beams. The lasers were pulsed, with the shape of the pulse controlled by an acousto-optic modulator, using the Tukey window to avoid too much energy at the wrong optical frequency. The hyperfine electron states in that setup, 2S1/2 |F=0, mF = 0⟩ and |F = 1, mF = 0⟩, have very close energy levels, separated by 12.642831 GHz. Ten Doppler-cooled ions were placed in a line 0.025 mm long and coupled together. The researchers observed a subharmonic oscillation of the drive. The experiment showed "rigidity" of the time crystal, where the oscillation frequency remained unchanged even when the time crystal was perturbed, that is it gained a frequency of its own and vibrated according to it. However, once the perturbation or frequency of vibration grew too strong, the time crystal "melted" and lost its oscillation and returned to the same state where it moved with the induced frequency.

Later in 2016, Mikhail Lukin at Harvard also reported the creation of a driven time crystal. His group used a diamond crystal doped with a high concentration of nitrogen-vacancy centers, which have strong dipole-dipole coupling and relatively long-lived spin coherence. By driving this strongly-interacting dipolar spin system with microwave fields and reading out the ensemble spin state with an optical (laser) field, it was observed that the spin polarization evolved at half the frequency of the microwave drive. The oscillations persisted for over 100 cycles. This sub-harmonic response to the drive frequency is seen as a signature of time-crystalline order.

Related conceptsEdit

A similar idea called a choreographic crystal has been proposed.[21]


Academic papersEdit

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