Time crystal

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A time crystal is a hypothetical quantum system that has periodic oscillations of one or more physical measurands in its ground state . The temporal- periodic ground state is thus analogous to the spatial- periodic state of a conventional crystal . Both states can also be understood as a consequence of spontaneous symmetry breaking . While in the conventional crystal the continuous translational symmetry of space is broken spontaneously, the oscillations in a time crystal result from a spontaneous break in the time translation symmetry . It is now known that time crystals are not possible in systems with continuous time translation symmetry, but there are indications of an analogous phenomenon - the “discrete time crystal” - in periodically excited systems with discrete time translation symmetry.

Theoretical research

Frank Wilczek

Basic concept

In 2012, the American Nobel Prize winner Frank Wilczek proposed the concept of a time crystal. In his first work with Alfred Shapere , he showed that a classical system with a certain energy - momentum relation can exhibit oscillations in the ground state. However, since physical realizations of this relation were not found, this idea was initially not pursued any further. In a second work he hypothesized that quantum mechanical systems can also have a time-crystalline ground state. A short time later, a physical realization of this idea was proposed: a ring-shaped chain of ions in an ion trap that should rotate spontaneously in a magnetic field .

Harmonics of a fundamental oscillation

No-go theorem

The French theorist Patrick Bruno showed, however, that systems that rotate spontaneously in the ground state can not exist in thermodynamic equilibrium, and that Wilczek's basic idea is therefore unsustainable. Subsequent work by other theorists confirmed and generalized Bruno's argument.

Discrete time crystals

However, further theoretical investigations showed that periodically excited, interacting quantum many-body systems can develop stable states with oscillations whose frequency is not identical to the excitation frequency, as usual, but corresponds to a discrete sub- harmonic (i.e. an integer fraction) of this frequency. Since the oscillations spontaneously break through the temporal periodicity of the excited system, such systems were called “discrete time crystals” in analogy to Wilczek's original concept. The stability of these states is based on the phenomenon of “many-particle localization”, which counteracts the absorption of energy from the excitation and thus a heating of the system.

Experimental research

The theoretical work motivated several experiments in which a targeted search for time-crystalline states was carried out. The atomic physicist Chris Monroe and his group found evidence of oscillations in optically excited chains of ytterbium ions with the behavior predicted for discrete time crystals. In particular, the oscillations proved to be robust with respect to variations in the excitation frequency. Further experimental confirmations resulted from nuclear magnetic resonance experiments on diamond defect centers and on molecular crystals that were excited by microwave radiation . The various observations of "discrete time crystals" indicate that it is a general phenomenon that manifests itself in different experimental systems - regardless of their special characteristics.

Review article

Individual evidence

  1. ↑ Alfred Shapere, Frank Wilczek: Classical Time Crystals . In: Physical Review Letters . tape 109 , no. 16 , October 15, 2012, p. 160402 , doi : 10.1103 / PhysRevLett.109.160402 ( aps.org [accessed December 22, 2018]).
  2. ^ Frank Wilczek: Quantum Time Crystals . In: Physical Review Letters . tape 109 , no. 16 , October 15, 2012, p. 160401 , doi : 10.1103 / PhysRevLett.109.160401 ( aps.org [accessed December 22, 2018]).
  3. ↑ Tongcang Li, Zhe-Xuan Gong, Zhang-Qi Yin, HT Quan, Xiaobo Yin: Space-Time Crystals of Trapped Ions . In: Physical Review Letters . tape 109 , no. 16 , October 15, 2012, p. 163001 , doi : 10.1103 / PhysRevLett.109.163001 ( aps.org [accessed December 22, 2018]).
  4. ↑ Patrick Bruno: Impossibility of Spontaneously Rotating Time Crystals: A No-Go Theorem . In: Physical Review Letters . tape 111 , no. 7 , August 14, 2013, p. 070402 , doi : 10.1103 / PhysRevLett.111.070402 ( aps.org [accessed December 22, 2018]).
  5. ↑ Haruki Watanabe, Masaki Oshikawa: Absence of Quantum Time Crystals . In: Physical Review Letters . tape 114 , no. 25 , June 24, 2015, p. 251603 , doi : 10.1103 / PhysRevLett.114.251603 ( aps.org [accessed December 22, 2018]).
  6. ↑ Vedika Khemani, Achilleas Lazarides, Roderich Moessner , S. L. Sondhi: Phase Structure of Driven Quantum Systems . In: Physical Review Letters . tape 116 , no. 25 , June 21, 2016, p. 250401 , doi : 10.1103 / PhysRevLett.116.250401 ( aps.org [accessed December 22, 2018]).
  7. ↑ N. Y. Yao, A. C. Potter, I.-D. Potirniche, A. Vishwanath: Discrete Time Crystals: Rigidity, Criticality, and Realizations . In: Physical Review Letters . tape 118 , no. 3 , January 18, 2017, p. 030401 , doi : 10.1103 / PhysRevLett.118.030401 ( aps.org [accessed December 22, 2018]).
  8. ↑ C. Monroe, NY Yao, A. Vishwanath, AC Potter, I.-D. Potirniche: Observation of a discrete time crystal . In: Nature . tape 543 , no. 7644 , March 2017, ISSN  1476-4687 , p. 217–220 , doi : 10.1038 / nature21413 ( nature.com [accessed December 22, 2018]).
  9. ↑ Mikhail D. Lukin, Eugene Demler, Norman Y. Yao, Curt von Keyserlingk, Vedika Khemani: Observation of discrete time-crystalline order in a disordered dipolar many-body system . In: Nature . tape 543 , no. 7644 , March 2017, ISSN  1476-4687 , p. 221–225 , doi : 10.1038 / nature21426 ( nature.com [accessed December 22, 2018]).
  10. ↑ Jared Rovny, Robert L. Blum, Sean E. Barrett: Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System . In: Physical Review Letters . tape 120 , no. 18 , May 1, 2018, p. 180603 , doi : 10.1103 / PhysRevLett.120.180603 ( aps.org [accessed December 22, 2018]).