A time crystal or space-time crystal is a hypothetic structure that repeats periodic 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
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.
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.[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]
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]
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 crystals
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.
Thermodynamics
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]
Experiments
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. However, once the perturbation grew too strong, the time crystal "melted" and lost its oscillation.
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 concepts
A similar idea called a choreographic crystal has been proposed.[21]
Enz, Charles P. (1974). "Is the Zero-Point Energy Real?". In Enz, C. P.; Mehra, J. (eds.). Physical Reality and Mathematical Description. Dordrecht: D. Reidel Publishing Company. pp. 124–132.
doi:
10.1007/978-94-010-2274-3_8.
ISBN978-94-010-2274-3.
A time crystal or space-time crystal is a hypothetic structure that repeats periodic 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
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.
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.[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]
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]
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 crystals
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.
Thermodynamics
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]
Experiments
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. However, once the perturbation grew too strong, the time crystal "melted" and lost its oscillation.
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 concepts
A similar idea called a choreographic crystal has been proposed.[21]
Enz, Charles P. (1974). "Is the Zero-Point Energy Real?". In Enz, C. P.; Mehra, J. (eds.). Physical Reality and Mathematical Description. Dordrecht: D. Reidel Publishing Company. pp. 124–132.
doi:
10.1007/978-94-010-2274-3_8.
ISBN978-94-010-2274-3.