Time crystal
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In
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 the 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. As the laws of physics are symmetrical under continuous translations in time as well as space, the question arose in 2012 as to whether it is possible to break symmetry temporally, and thus create a "time crystal" that is resistant to entropy.[1]
If a discrete time-translation symmetry is broken (which may be realized in periodically driven systems), 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 only occur in non-equilibrium systems.[5] Discrete time crystals have in fact been observed in physics laboratories as early as 2016 (published in 2017). One example of a time crystal, which demonstrates non-equilibrium, broken time symmetry is a constantly rotating ring of charged ions in an otherwise lowest-energy state.[6]
Concept
Ordinary (non-time) crystals form through spontaneous symmetry breaking related to a spatial symmetry. Such processes can produce materials with interesting properties, such as
Time-translation symmetry
Symmetries in nature lead directly to conservation laws, something which is precisely formulated by Noether's theorem.[8]
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.[9] This symmetry implies the conservation of energy.[10]
Broken symmetry in normal crystals
Common 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. However, if we hold fixed the atoms of a crystal, the dynamics of an electron or other particle in the crystal depend on how it moves relative to the crystal, and particle momentum can change by interacting with the atoms of a crystal — for example in
Time crystals show a broken symmetry analogous to a discrete space-translation symmetry breaking. For example,[citation needed] the molecules of a liquid freezing on the surface of a crystal can align with the molecules of the crystal, but with a pattern less symmetric than the crystal: it breaks the initial symmetry. This broken symmetry exhibits three important characteristics:[citation needed]
- the system has a lower symmetry than the underlying arrangement of the crystal,
- the system exhibits spatial and temporal long-range order (unlike a local and intermittent order in a liquid near the surface of a crystal),
- it is the result of interactions between the constituents of the system, which align themselves relative to each other.
Broken symmetry in discrete time crystals (DTC)
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. (According to Philip Ball, DTC are so-called because "their periodicity is a discrete, integer multiple of the driving period".[13])
The initial symmetry, which is the discrete time-translation symmetry () with , is spontaneously broken to the lower discrete time-translation symmetry with , where is time, the driving period, an integer.[14]
Many systems can show behaviors of spontaneous time-translation symmetry breaking but may not be discrete (or Floquet) time crystals:
However, discrete (or Floquet) time crystals are unique in that they follow a strict definition of discrete time-translation symmetry breaking:[15]
- 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[15] (which is not the case of convection cells, oscillating chemical reactions and aerodynamic flutter),
- the system exhibits long-range order – the oscillations are in phase (synchronized) over arbitrarily long distances and time.
Moreover, the broken symmetry in time crystals is the result of many-body interactions: the order is the consequence of a collective process, just like in spatial crystals.[14] This is not the case for NMR spin echos.
These characteristics makes discrete time crystals analogous to spatial crystals as described above and may be considered a novel type or phase of nonequilibrium matter.[14]
Thermodynamics
Time crystals do not violate the laws of thermodynamics: energy in the overall system is conserved, such a crystal does not spontaneously convert thermal energy into mechanical work, and it cannot serve as a perpetual store of work. But it may change perpetually in a fixed pattern in time for as long as the system can be maintained. They possess "motion without energy"[16]—their apparent motion does not represent conventional kinetic energy.[17] Recent experimental advances in probing discrete time crystals in their periodically driven nonequilibrium states have led to the beginning exploration of novel phases of nonequilibrium matter.[14]
Time crystals do not evade the Second Law of Thermodynamics,[18] although they spontaneously break "time-translation symmetry", the usual rule that a stable object will remain the same throughout time. In thermodynamics, a time crystal's entropy, understood as a measure of disorder in the system, remains stationary over time, marginally satisfying the second law of thermodynamics by not decreasing.[19][20]
History
The idea of a quantized time crystal was theorized in 2012 by
In response to Wilczek and Zhang, Patrick Bruno (European Synchrotron Radiation Facility) and Masaki Oshikawa (University of Tokyo) published several articles stating that space–time crystals were impossible.[25][26]
Subsequent work developed more precise definitions of time-translation symmetry-breaking, which ultimately led to the Watanabe–Oshikawa "no-go" statement that quantum space–time crystals in equilibrium are not possible.[27][28] Later work restricted the scope of Watanabe and Oshikawa: strictly speaking, they showed that long-range order in both space and time is not possible in equilibrium, but breaking of time-translation symmetry alone is still possible.[29][30][31]
Several realizations of time crystals, which avoid the equilibrium no-go arguments, were later proposed.[32] In 2014 Krzysztof Sacha at Jagiellonian University in Kraków predicted the behaviour of discrete time crystals in a periodically driven system with "an ultracold atomic cloud bouncing on an oscillating mirror".[33][34]
In 2016, research groups at Princeton and at Santa Barbara independently suggested that periodically driven quantum spin systems could show similar behaviour. in March 2017.
Later, time crystals in open systems, so called dissipative time crystals, were proposed in several platforms breaking a discrete [39][40][41][42] and a continuous[43][44] time-translation symmetry. A dissipative time crystal was experimentally realized for the first time in 2021 by the group of Andreas Hemmerich at the Institute of Laser Physics at the University of Hamburg.[45] The researchers used a Bose–Einstein condensate strongly coupled to a dissipative optical cavity and the time crystal was demonstrated to spontaneously break discrete time-translation symmetry by periodically switching between two atomic density patterns.[45][46][47] In an earlier experiment in the group of Tilman Esslinger at ETH Zurich, limit cycle dynamics[48] was observed in 2019,[49] but evidence of robustness against perturbations and the spontaneous character of the time-translation symmetry breaking were not addressed.
In 2019, physicists Valerii Kozin and Oleksandr Kyriienko proved that, in theory, a permanent quantum time crystal can exist as an isolated system if the system contains unusual long-range multiparticle interactions. The original "no-go" argument only holds in the presence of typical short-range fields that decay as quickly as r−α for some α > 0. Kozin and Kyriienko instead analyzed a spin-1/2 many-body Hamiltonian with long-range multispin interactions, and showed it broke continuous time-translational symmetry. Certain spin correlations in the system oscillate in time, despite the system being closed and in a ground energy state. However, demonstrating such a system in practice might be prohibitively difficult,[50][51] and concerns about the physicality of the long-range nature of the model have been raised.[52]
In 2022, the Hamburg research team, supervised by Hans Keßler and Andreas Hemmerich, demonstrated, for the first time, a continuous dissipative time crystal exhibiting spontaneous breaking of continuous time-translation symmetry.[53][54][55][56]
In February 2024, a team from Dortmund University in Germany built a time crystal from indium gallium arsenide that lasted for 40 minutes, nearly 10 million times longer than the previous record of around 5 milliseconds. In addition, the lack of any decay suggest the crystal have lasted even longer, stating that it could last "at least a few hours, perhaps even longer".[57][58][59][60]https://phys.org/news/2024-02-physicists-highly-robust-crystal.html
Experiments
In October 2016, Christopher Monroe at the
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, and that it gained a frequency of its own and vibrated according to it (rather than only the frequency of the drive). However, once the perturbation or frequency of vibration grew too strong, the time crystal "melted" and lost this subharmonic oscillation, and it returned to the same state as before where it moved only with the induced frequency.[38]
Also 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. This strongly interacting dipolar spin system was driven with microwave fields, and the ensemble spin state was determined 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 subharmonic response to the drive frequency is seen as a signature of time-crystalline order.[37]
In May 2018, a group in
In February 2021 a team at Max Planck Institute for Intelligent Systems described the creation of time crystal consisting of magnons and probed them under scanning transmission X-ray microscopy to capture the recurring periodic magnetization structure in the first known video record of such type.[63][64]
In July 2021, a team led by Andreas Hemmerich at the Institute of Laser Physics at the University of Hamburg presented the first realization of a time crystal in an open system, a so-called dissipative time crystal using ultracold atoms coupled to an optical cavity. The main achievement of this work is a positive application of dissipation – actually helping to stabilise the system's dynamics.[45][46][47]
In November 2021, a collaboration between Google and physicists from multiple universities reported the observation of a discrete time crystal on Google's Sycamore processor, a quantum computing device. A chip of 20 qubits was used to obtain a many-body localization configuration of up and down spins and then stimulated with a laser to achieve a periodically driven "Floquet" system where all up spins are flipped for down and vice-versa in periodic cycles which are multiples of the laser's frequency. While the laser is necessary to maintain the necessary environmental conditions, no energy is absorbed from the laser, so the system remains in a protected eigenstate order.[20][65]
Previously in June and November 2021 other teams had obtained virtual time crystals based on floquet systems under similar principles to those of the Google experiment, but on
In February 2022, a scientist at UC Riverside reported a dissipative time crystal akin to the system of July 2021 but all-optical, which allowed the scientist to operate it at room temperature. In this experiment injection locking was used to direct lasers at a specific frequency inside a microresonator creating a lattice trap for solitons at subharmonic frequencies.[70][71]
In March 2022, a new experiment studying time crystals on a quantum processor was performed by two physicists at the university of Melbourne, this time using IBM's Manhattan and Brooklyn quantum processors observing a total of 57 qubits.[72][73][74]
In June 2022, the observation of a continuous time crystal was reported by a team at the Institute of Laser Physics at the University of Hamburg, supervised by Hans Keßler and Andreas Hemmerich. In periodically driven systems, time-translation symmetry is broken into a discrete time-translation symmetry due to the drive. Discrete time crystals break this discrete time-translation symmetry by oscillating at a multiple of the drive frequency. In the new experiment, the drive (pump laser) was operated continuously, thus respecting the continuous time-translation symmetry. Instead of a subharmonic response, the system showed an oscillation with an intrinsic frequency and a time phase taking random values between 0 and 2π, as expected for spontaneous breaking of continuous time-translation symmetry. Moreover, the observed limit cycle oscillations were shown to be robust against perturbations of technical or fundamental character, such as quantum noise and, due to the openness of the system, fluctuations associated with dissipation. The system consisted of a Bose–Einstein condensate in an optical cavity, which was pumped with an optical standing wave oriented perpendicularly with regard to the cavity axis and was in a superradiant phase localizing at two bistable ground states between which it oscillated.[53][54][55][56]
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Academic articles
- Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick (2016). "Symmetric Satellite Swarms and Choreographic Crystals". Physical Review Letters. 116 (1): 015503. S2CID 17918689.
- Bruno, Patrick (2013a). "Comment on 'Quantum Time Crystals'". Physical Review Letters. 110 (11): 118901. S2CID 41459498.
- Bruno, Patrick (2013b). "Comment on "Space-Time Crystals of Trapped Ions"". Physical Review Letters. 111 (2): 029301. S2CID 1502258.
- Else, Dominic V.; Bauer, Bela; Nayak, Chetan (2016). "Floquet Time Crystals". Physical Review Letters. 117 (9): 090402. S2CID 1652633.
- Grifoni, Milena; Hänggi, Peter (1998). "Driven quantum tunneling" (PDF). Physics Reports. 304 (5–6): 229–354. S2CID 120738031. Archived from the original(PDF) on 2017-02-11.
- Guo, Lingzhen; Marthaler, Michael; Schön, Gerd (2013). "Phase Space Crystals: A New Way to Create a Quasienergy Band Structure". Physical Review Letters. 111 (20): 205303. S2CID 9337383.
- Guo, Lingzhen; Liang, Pengfei (2020). "Condensed matter physics in time crystals". New Journal of Physics. 22 (7): 075003. S2CID 218538401.
- Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich; Sondhi, S. L. (2016). "Phase Structure of Driven Quantum Systems". Physical Review Letters. 116 (25): 250401. S2CID 883197.
- Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012a). "Space-Time Crystals of Trapped Ions". Physical Review Letters. 109 (16): 163001. S2CID 8198228.
- Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012). "Reply to Comment on "Space–Time Crystals of Trapped Ions"". Unpublished. Bibcode:2012arXiv1212.6959L.
- Lindner, Netanel H.; Refael, Gil; Galitski, Victor (2011). "Floquet topological insulator in semiconductor quantum wells". Nature Physics. 7 (6): 490–495. S2CID 26754031.
- Mendonça, J. T.; Dodonov, V. V. (2014). "Time Crystals in Ultracold Matter". Journal of Russian Laser Research. 35 (1): 93–100. S2CID 122631523.
- Nozières, Philippe (2013). "Time crystals: Can diamagnetic currents drive a charge density wave into rotation?". EPL. 103 (5): 57008. S2CID 118662499.
- Robicheaux, F.; Niffenegger, K. (2015). "Quantum simulations of a freely rotating ring of ultracold and identical bosonic ions". Physical Review A. 91 (6): 063618. ISSN 2469-9926.
- Sacha, Krzysztof (2015). "Modeling spontaneous breaking of time-translation symmetry". Physical Review A. 91 (3): 033617. S2CID 118627872.
- Sacha, Krzysztof (2015). "Anderson localization and Mott insulator phase in the time domain". Scientific Reports. 5: 10787. PMID 26074169.
- Sacha, Krzysztof; Zakrzewski, Jakub (2018). "Time Crystals: a review". Reports on Progress in Physics. 81 (1): 016401. S2CID 28224975.
- Shirley, Jon H. (1965). "Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time". Physical Review. 138 (4B): B979–B987. ISSN 0031-899X.
- Smith, J.; Lee, A.; Richerme, P.; Neyenhuis, B.; Hess, P. W.; Hauke, P.; Heyl, M.; Huse, D. A.; Monroe, C. (2016). "Many-body localization in a quantum simulator with programmable random disorder". Nature Physics. 12 (10): 907–911. S2CID 53408060.
- Volovik, G. E. (2013). "On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order". JETP Letters. 98 (8): 491–495. S2CID 119100114.
- von Keyserlingk, C. W.; Khemani, Vedika; Sondhi, S. L. (2016). "Absolute stability and spatiotemporal long-range order in Floquet systems". Physical Review B. 94 (8): 085112. S2CID 118699328.
- Wang, Y. H.; Steinberg, H.; Jarillo-Herrero, P.; Gedik, N. (2013). "Observation of Floquet-Bloch States on the Surface of a Topological Insulator". Science. 342 (6157): 453–457. S2CID 29121373.
- Wilczek, Frank (2013a). "Wilczek Reply" (PDF). Physical Review Letters. 110 (11): 118902. PMID 25166586.
- Wilczek, Frank (2013). "Superfluidity and Space–Time Translation Symmetry Breaking". Physical Review Letters. 111 (25): 250402. S2CID 7537145.
- Yoshii, Ryosuke; Takada, Satoshi; Tsuchiya, Shunji; Marmorini, Giacomo; Hayakawa, Hisao; Nitta, Muneto (2015). "Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions". Physical Review B. 92 (22): 224512. S2CID 118348062.
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Books
- Sacha, Krzysztof (2020). Time Crystals. Springer Series on Atomic, Optical, and Plasma Physics. Vol. 114. Springer. S2CID 240770955.
Press
- Ball, Philip (20 September 2021). "Focus: Turning a Quantum Computer into a Time Crystal". Physics. 14. APS Physics: 131. .
- Ball, Philip (8 January 2016). "Focus: New Crystal Type is Always in Motion". physics.aps.org. APS Physics. Archived from the original on 3 February 2017.
- Coleman, Piers (9 January 2013). "Quantum physics: Time crystals". Nature. 493 (7431): 166–167. S2CID 205075903.
- Cowen, Ron (27 February 2012). ""Time Crystals" Could Be a Legitimate Form of Perpetual Motion". scientificamerican.com. Scientific American. Archived from the original on 2 February 2017.
- Gibney, Elizabeth (2017). "The quest to crystallize time". Nature. 543 (7644): 164–166. S2CID 4460265.
- Grossman, Lisa (18 January 2012). "Death-defying time crystal could outlast the universe". newscientist.com. New Scientist. Archived from the original on 2 February 2017.
- Hackett, Jennifer (22 February 2016). "Curious Crystal Dances for Its Symmetry". scientificamerican.com. Scientific American. Archived from the original on 3 February 2017.
- Hannaford, Peter; Sacha, Krzysztof (17 Mar 2020). "Time crystals enter the real world of condensed matter". physicsworld.com. Institute of Physics.
- Hewitt, John (3 May 2013). "Creating time crystals with a rotating ion ring". phys.org. Science X. Archived from the original on 4 July 2013.
- Johnston, Hamish (18 January 2016). "'Choreographic crystals' have all the right moves". physicsworld.com. Institute of Physics. Archived from the original on 3 February 2017.
- Joint Quantum Institute (22 March 2011). "Floquet Topological Insulators". jqi.umd.edu. Joint Quantum Institute.
- Ouellette, Jennifer (31 January 2017). "World's first time crystals cooked up using new recipe". newscientist.com. New Scientist. Archived from the original on 1 February 2017.
- Powell, Devin (2013). "Can matter cycle through shapes eternally?". Nature. S2CID 181223762. Archived from the originalon 3 February 2017.
- University of California, Berkeley (26 January 2017). "Physicists unveil new form of matter—time crystals". phys.org. Science X. Archived from the original on 28 January 2017.
- Weiner, Sophie (28 January 2017). "Scientists Create A New Kind Of Matter: Time Crystals". popularmechanics.com. Popular mechanics. Archived from the original on 3 February 2017.
- Wood, Charlie (31 January 2017). "Time crystals realize new order of space-time". csmonitor.com. Christian Science Monitor. Archived from the original on 2 February 2017.
- Yirka, Bob (9 July 2012). "Physics team proposes a way to create an actual space-time crystal". phys.org. Science X. Archived from the original on 15 April 2013.
- Zyga, Lisa (20 February 2012). "Time crystals could behave almost like perpetual motion machines". phys.org. Science X. Archived from the original on 3 February 2017.
- Zyga, Lisa (22 August 2013). "Physicist proves impossibility of quantum time crystals". phys.org. Space X. Archived from the original on 3 February 2017.
- Zyga, Lisa (9 July 2015). "Physicists propose new definition of time crystals—then prove such things don't exist". phys.org. Science X. Archived from the original on 9 July 2015.
- Zyga, Lisa (9 September 2016). "Time crystals might exist after all (Update)". phys.org. Science X. Archived from the original on 11 September 2016.
External links
- Christopher Monroe at University of Maryland
- Frank Wilczek
- Lukin Group at Harvard University
- Norman Yao at the University of California at Berkeley
- Krzysztof Sacha at Jagiellonian University in Kraków
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