Space-time crystal

A space-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]

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 arXiv:1206.4772 Tongcang Li, Zhe-Xuan Gong, Zhang-Qi Yin, H. T. Quan, Xiaobo Yin, Peng Zhang, L.-M. Duan, Xiang Zhang. Phys. Rev. Lett. 109, 163001. 21 June 2012 "Space-time crystals of trapped ions".
  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". Retrieved 4 May 2013.
  7. ↑ Bruno, Patrick (March 2013). "Comment on ‘‘Quantum Time Crystals’’". Phys. Rev. Lett. 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 (07): 070402. arXiv:1306.6275. Bibcode:2013PhRvL.111g0402B. doi:10.1103/PhysRevLett.111.070402. Retrieved 26 November 2013.
  9. ↑ Lisa Zyga (9 July 2015). "Physicists propose new definition of time crystals—then prove such things don't exist".
  10. ↑ Watanabe, Haruki; Oshikawa, Masaki (24 June 2015). "Absence of Quantum Time Crystals". Physical Review Letters 114 (25). doi:10.1103/PhysRevLett.114.251603.
  11. ↑ Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick (8 January 2016). "Symmetric Satellite Swarms and Choreographic Crystals". Physical Review Letters 116 (1). arXiv:1407.5876. doi:10.1103/PhysRevLett.116.015503.

Further reading

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