Space-time crystal

A space-time crystal, time crystal, or four-dimensional crystal, is a theoretical structure periodic in time and space. It extends the idea of a crystal to four dimensions.[1][2] The idea was proposed by Frank Wilczek in 2012. His speculation was that a construct would have a group of particles that move and periodically return to their original state, perhaps moving in a circle, and form a time crystal. In order for this perpetual motion to work, the system must not radiate its rotational energy.[3] This type of motion is distinct from that of persistent currents in a superconductor, wherein the rotating Cooper pairs are not time crystals because their wave functions are homogenous, meaning time translational symmetry isn't broken.[4] Symmetry would be spontaneously broken in Wilczek's ring system if its ground state still involves continuous movement.

Tongcang Li and others proposed a system with beryllium ions circulating in a magnetic ion trap at about 10−9 K.[4] Wilczek also suggested that a computing device could be possible with different rotational states representing information, and maybe different kinds of ions. Since this construct is in the lowest energy state it could in principle survive the heat death of the universe and continue forever.[5]

In May 2013 researchers announced they will attempt to build a component of a space time crystal, by making a rotating ring of calcium ions. Their location will be confined by electric field, and rotation in a ground state will be forced by a magnetic field. Unwanted disturbances will be minimized by reducing the temperature to 1 μK by way of laser cooling. The ion trap will be 100 μm wide. Possible rotation of the ion ring will be demonstrated by using a laser to electronically excite one of the trapped ions.[6]

Patrick Bruno has criticized this concept, arguing that Wilczek's rotating state is not the ground state of the system. He derives the supposed true, non-rotating ground state.[7] In August 2013 Bruno presented arguments that indicated rotating ground-state systems are impossible.[8]

Haruki Watanabe and Masaki Oshikawa formalised the definition of space time crystals from a ground state only requirement to also include states in thermal equilibrium. The definition used the correlation of the local order parameter at different points in space and time. This correlation in a time crystal shows a periodic oscillation as a function of time difference even as volume is increased to infinity. Next they claimed to show that time translation symmetry cannot be broken thus proving that time crystal do not exist. With the extension of the definition to crystals with a finite temperature, the Lieb-Robinson bound is used to show that for small enough time intervals the correlation over a time difference has an upper bound that tends to 0 as the volume increases.[9][10]

A similar idea called a choreographic crystal has been proposed .[11]

In March 2016 researchers Else, Bauer and Nayak proposed that a non-equilibrium driven system called a "Floquet-many-body-localized driven system" could have broken time symmetry.[12]

Experimental Space-time crystals

In October 2016, researchers at the University of Maryland, College Park claim to have created the world's first discrete time crystal.[13] Using the idea from the March proposal, they 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 are called 2S1/2 |F=0, mF = 0⟩ and |F = 1, mF = 0⟩. The different energy levels of these are very close, separated by 12.642831 GHz. Ten Doppler cooled ions were used in a line 0.025 mm long. The ions were coupled together. The researchers observed a subharmonic oscillation of the drive. The experiment also showed "rigidity" of the time crystal, where the oscillation frequency remained unchanged even when the time crystal was perturbed. However if the perturbation drive was too great, the time crystal "melted" and lost its oscillation.[14]

References

  1. ↑ Yirka, Bob (9 July 2012). "Physics team proposes a way to create an actual space-time crystal". Phys.org. Retrieved 15 July 2012.
  2. ↑ Wolchover, Natalie (25 April 2013). "Perpetual Motion Test Could Amend Theory of Time". The Simons Foundation. Retrieved 29 April 2013.
  3. ↑ Kentucky, FC (26 June 2012). "How to Build A Space-Time Crystal". Technology Review. MIT. Retrieved 18 July 2012.
  4. 1 2 Li, Tongcang; et al. (15 October 2012). "Space-Time Crystals of Trapped Ions". Physical Review Letters. 109 (16): 163001. arXiv:1206.4772Freely accessible. Bibcode:2012PhRvL.109p3001L. doi:10.1103/PhysRevLett.109.163001.
  5. ↑ Aron, Jacob (6 July 2012). "Computer that could outlive the universe a step closer". New Scientist. Retrieved 17 July 2012.
  6. ↑ Hewitt, John (4 May 2013). "Creating time crystals with a rotating ion ring". phys.org. Retrieved 4 May 2013.
  7. ↑ Bruno, Patrick (March 2013). "Comment on Quantum Time Crystals". Physical Review Letters. 110 (11): 118901. Bibcode:2013PhRvL.110k8901B. doi:10.1103/PhysRevLett.110.118901. Retrieved 28 April 2013.
  8. ↑ Bruno, Patrick (August 2013). "Impossibility of Spontaneously Rotating Time Crystals: A No-Go Theorem". Phys. Rev. Lett. 111 (7): 070402. arXiv:1306.6275Freely accessible. Bibcode:2013PhRvL.111g0402B. doi:10.1103/PhysRevLett.111.070402. Retrieved 26 November 2013.
  9. ↑ Zyga, Lisa (9 July 2015). "Physicists propose new definition of time crystals—then prove such things don't exist". phys.org.
  10. ↑ Watanabe, Haruki; Oshikawa, Masaki (24 June 2015). "Absence of Quantum Time Crystals". Physical Review Letters. 114 (25): 251603. arXiv:1410.2143Freely accessible. Bibcode:2015PhRvL.114y1603W. doi:10.1103/PhysRevLett.114.251603. PMID 26197119.
  11. ↑ Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick (8 January 2016). "Symmetric Satellite Swarms and Choreographic Crystals". Physical Review Letters. 116 (1): 015503. arXiv:1407.5876Freely accessible. Bibcode:2016PhRvL.116a5503B. doi:10.1103/PhysRevLett.116.015503. PMID 26799028.
  12. ↑ Else, Dominic V.; Bauer, Bela; Nayak, Chetan (25 August 2016). "Floquet Time Crystals". Physical Review Letters. 117 (9): 090402. arXiv:1603.08001Freely accessible. Bibcode:2016PhRvL.117i0402E. doi:10.1103/PhysRevLett.117.090402. PMID 27610834.
  13. ↑ "Physicists Create World's First Time Crystal". MIT Technology Review. 2016-10-04.
  14. ↑ J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I.-D. Potirniche, A. C. Potter, A. Vishwanath, N. Y. Yao, and C. Monroe (27 September 2016). "Observation of a Discrete Time Crystal". 1609: arXiv:1609.08684. arXiv:1609.08684v1Freely accessible. Bibcode:2016arXiv160908684Z.

Further reading

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