Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous breaking of discrete time translation symmetry, in ultra-cold atoms bouncing on an oscillating mirror, still awaits experimental demonstration. Here, we perform a detailed analysis of the experimental conditions needed for the realization of such a discrete time crystal. Importantly, the considered system allows for the realization of dramatic breaking of discrete time translation symmetry where a symmetry broken state evolves with a period tens of times longer than the driving period. Moreover, atoms bouncing on an oscillating mirror constitute a suitable system for the realization of dynamical quantum phase transitions in discrete time crystals and for the demonstration of various non-trivial condensed matter phenomena in the time domain. We show that Anderson localization effects, which are typically associated with spatial disorder and exponential localization of eigenstates of a particle in configuration space, can be observed in the time domain when ultra-cold atoms are bouncing on a randomly moving mirror.
Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry. Recently, the concept of phase transitions has been extended to non-equilibrium dynamics of time-independent systems induced by a quantum quench, i.e. a sudden change of some parameter of the Hamiltonian. There, the return probability of a system to the ground state reveals singularities in time which are dubbed dynamical quantum phase transitions. We show that the quantum quench in a discrete time crystal leads to dynamical quantum phase transitions where the return probability of a periodically driven system to a Floquet eigenstate before the quench reveals singularities in time. It indicates that dynamical quantum phase transitions are not restricted to time-independent systems and can be also observed in systems that are periodically driven. We discuss how the phenomenon can be observed in ultra-cold atomic gases.
The Unruh effect is a quantum relativistic effect where the accelerated observer perceives the vacuum as a thermal state. Here we propose the experimental realization of the Unruh effect for interacting ultracold fermions in optical lattices by a sudden quench resulting in vacuum acceleration with varying interactions
Background: Strongly deformed oblate superheavy nuclei form an intriguing region where the toroidal nuclear structures may bifurcate from the oblate spheroidal shape. The bifurcation may be facilitated when the nucleus is endowed with a large angular moment about the symmetry axis with I = Iz. The toroidal high-K isomeric states at their local energy minima can be theoretically predicted using the cranked self-consistent Skyrme-Hartree-Fock method.Purpose: We use the cranked Skyrme-Hartree-Fock method to predict the properties of the toroidal high-spin isomers in the superheavy nucleus 304 120184.Method: Our method consists of three steps: first, we use the deformation-constrained Skyrme-Hartree-FockBogoliubov approach to search for the nuclear density distributions with toroidal shapes. Next, using these toroidal distributions as starting configurations we apply an additional cranking constraint of a large angular momentum I = Iz about the symmetry z-axis and search for the energy minima of the system as a function of the deformation. In the last step, if a local energy minimum with I = Iz is found, we perform at this point the cranked symmetry-and deformation-unconstrained Skyrme-Hartree-Fock calculations to locate a stable toroidal high-spin isomeric state in free convergence. Results:We have theoretically located two toroidal high-spin isomeric states of 304 120184 with an angular momentum I=Iz=81 (proton 2p-2h, neutron 4p-4h excitation) and I=Iz=208 (proton 5p-5h, neutron 8p-8h) at the quadrupole moment deformations Q20 = −297.7 b and Q20 = −300.8 b with energies 79.2 MeV and 101.6 MeV above the spherical ground state, respectively. The nuclear density distributions of the toroidal high-spin isomers 304 120184(Iz=81 and 208 ) have the maximum density close to the nuclear matter density, 0.16 fm −3 , and a torus major to minor radius aspect ratio R/d = 3.25. Conclusions:We demonstrate that aligned angular momenta of Iz=81 and 208 arising from multi-particlemulti-hole excitations in the toroidal system of 304 120184 can lead to high-spin isomeric states, even though the toroidal shape of 304 120184 without spin is unstable. Toroidal energy minima without spin may be possible for superheavy nuclei with higher atomic numbers, Z 122, as reported previously [7].
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