The Theory
In 2012, an American theoretical physicist, mathematician and Nobel Laureate named Frank Wilczek proposed the idea of a Time Crystal. Frank Wilczek is a Professor of Physics at Massachusetts Institute of Technology (MIT) and 2004 Physics Nobel prize winner for his discovery of asymptotic freedom. He has helped reveal and develop axions, anyons, the colour superconducting phases of quark matter, and other aspects of quantum field theory. He has worked on condensed matter physics, astrophysics, and particle physics. In 2018, he and Qing-Dong Jiang calculated that the so-called “quantum atmosphere” of materials should theoretically be capable of being probed using existing technology such as diamond probes with nitrogen-vacancy centres.
In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion. The system cannot lose energy to the environment and come to rest because it is already in its quantum ground state. Whereas in common crystals the atoms are arranged periodically in space, the atoms in a time crystal are arranged periodically in both space and time.
The existence of crystals in nature is a manifestation of spontaneous symmetry breaking, which occurs when the lowest-energy state of a system is less symmetrical than the equations governing that system. In the crystal ground state, the continuous translational symmetry in space is broken and replaced by the lower discrete symmetry of the periodic crystal. Ordinarily this is related to spatial symmetry, giving rise to the production of materials with interesting properties; such as diamonds, salt crystals and ferromagnetic metals.
As the laws of physics are symmetrical under continuous translations in time as well as space, the question arose in 2012 by Wilczek as to whether it is possible to also break symmetry temporally, and thus create a “time crystal” that is resistant to entropy. If a discrete time-translation symmetry is broken, then the system is referred to as a discrete time crystal. A discrete time crystal never reaches thermal equilibrium, as it is a type (or phase) of non-equilibrium matter. Breaking of time symmetry can occur only in non-equilibrium systems. While an ordinary crystal is periodic (has a repeating structure) in space, a time crystal has a repeating structure in time. A time crystal is periodic in time in the same sense that the pendulum in a pendulum-driven clock is periodic in time. Unlike a pendulum, a time crystal “spontaneously” self-organizes into robust periodic motion (breaking a temporal symmetry). These exotic systems, though predicted in 2012, were not demonstrated until 2016.
Experimental Realization of Discrete Time Quasicrystals
Conventional time crystals are created by subjecting a collection of particles to an external driving force that is periodic in time. In this instance, a quasiperiodic drive in the form of a structured but non-repeating sequence of microwave pulses was used. The researchers applied this quasiperiodic drive to an ensemble of strongly interacting spins associated with structural defects, known as nitrogen-vacancy centres, in diamond. They then tracked the resulting dynamics of these spins using a laser microscope.
Time crystals seem to break time-translation symmetry and have repeated patterns in time even if the laws of the system are invariant by translation of time. The time crystals that are experimentally realized show discrete time-translation symmetry breaking, not the continuous one: they are periodically driven systems oscillating at a fraction of the frequency of the driving force.
However, discrete (or Floquet) time crystals are unique in that they follow a strict definition of discrete time-translation symmetry breaking:
- it is a broken symmetry – the system shows oscillations with a period longer than the driving force,
- the system is in crypto-equilibrium – these oscillations generate no entropy, and a time-dependent frame can be found in which the system is indistinguishable from an equilibrium when measured stroboscopically,
- the system exhibits long-range order – the oscillations are in phase (synchronized) over arbitrarily long distances and time.
Floquet (periodically driven) systems can give rise to unique non-equilibrium phases of matter without equilibrium analogues. The most prominent example is the aforementioned realization of discrete time crystals. This study explores quantum systems subjected to a quasiperiodic drive. By leveraging a strongly interacting spin ensemble in diamond, the emergence of long-lived discrete time quasicrystals becomes apparent. Unlike conventional time crystals, time quasicrystals exhibit robust subharmonic responses at multiple incommensurate frequencies. The multifrequency nature of the quasiperiodic drive allows for the formation of diverse patterns associated with different discrete time quasicrystalline phases.
Crystal formation is a well-known example of spontaneous symmetry breaking. Traditionally, long-range order and periodicity were thought to be closely linked in crystalline phases. Conversely, quasicrystals exhibit long-range order without visible periodicity (the spins formed a structured but non-repeating pattern in time). This is a conceptually new phase of matter, the discrete time quasicrystal (DTQC), which extends time crystals into a quasiperiodic regime.
Diamond nitrogen-vacancy centres were used to experimentally demonstrate and explore the DTQC; revealing that the system maintains robust quasiperiodic order in time. Subsequently due to the strong interactions of spins working against external perturbations. Thirdly, it demonstrates that the quasiperiodic nature of the DTQC enables more complex patterns of order compared to conventional time crystals, breaking time-translation symmetry in an entirely new way.
This remarkable discovery expands our understanding of out-of-equilibrium quantum systems. The next logical step for researchers is to construct these states using alternative platforms, such as ultracold atoms, superconducting quantum bits or spin defects in two-dimensional materials. Consequently leading to numerous practical applications, such as multifrequency time references for precise measurements and advanced signal processing. This work opens new possibilities for exploring and exploiting the properties of time crystals and quasicrystals, with exciting implications for future technologies in both quantum computing and sensing.
Full Article
Experimental Realization of Discrete Time Quasicrystals
Guanghui He, Bingtian Ye, Ruotian Gong, Changyu Yao, Zhongyuan Liu, Kater W. Murch, Norman Y. Yao, and Chong Zu
