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Bulletin of the American Physical Society

Super-quasicrystal stripe phases in optical superlattices with Raman-assisted tunneling

Junpeng Hou, Haiping Hu, Kuei Sun, Chuanwei Zhang

Published Aug 29, 2017• 0 citations
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Abstract

Quasicrystal is a class of ordered structures defying conventional classification of solid crystals and may carry classically forbidden (e.g., 5-fold) rotational symmetries. In view of long-sought supersolids, a nature question is whether the quasicrystal order can also coexist with superfluidity, forming super-quasicrystals, which spontaneously break $U(1)$ symmetry due to superfluidity and forms quasicrystalline order that is not possessed by the underlying Hamiltonian. Here we show that a super-quasicrystal stripe state with the minimum 5-fold rotational symmetry can be realized as the ground state of a Bose-Einstein condensate in an optical superlattice with Raman-assisted tunneling. There exists a rich phase diagram consisting of various super-quasicrystal, supersolid, plane-wave phases, and their phase transitions. Our scheme can be generalized for generating other higher-order (e.g., 7-fold) quasicrystal states, and provides a platform for investigating such new exotic quantum matter.

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Quasicrystal is a class of ordered structures defying conventional classification of solid crystals and may carry classically forbidden (e.g., 5-fold) rotational symmetries. In view of long-sought supersolids, a nature question is whether the quasicrystal order can also coexist with superfluidity, forming super-quasicrystals, which spontaneously break U(1)U(1)U(1) symmetry due to superfluidity and forms quasicrystalline order that is not possessed by the underlying Hamiltonian. Here we show that a super-quasicrystal stripe state with the minimum 5-fold rotational symmetry can be realized as the ground state of a Bose-Einstein condensate in an optical superlattice with Raman-assisted tunneling. There exists a rich phase diagram consisting of various super-quasicrystal, supersolid, plane-wave phases, and their phase transitions. Our scheme can be generalized for generating other higher-order (e.g., 7-fold) quasicrystal states, and provides a platform for investigating such new exotic quantum matter.
A quasicrystal is a class of ordered structures defying conventional classification of solid crystals and may carry classically forbidden (e.g., fivefold) rotational symmetries. In view of long-sought supersolids, a natural question is whether a superfluid can spontaneously form quasicrystalline order that is not possessed by the underlying Hamiltonian, forming "superfluid-quasicrystals." Here we show that a superfluid-quasicrystal stripe state with the minimal fivefold rotational symmetry can be realized as the ground state of a Bose-Einstein condensate within a practical experimental scheme. There exists a rich phase diagram consisting of various superfluid-quasicrystal, supersolid, and plane-wave phases. Our scheme can be generalized for generating other higher-order (e.g., sevenfold) quasicrystal states, and provides a platform for investigating such new exotic quantum matter.
The discovery of quasicrystals with crystallographically forbidden rotational symmetries has changed the notion of the ordering in materials, yet little is known about the dynamical emergence of such exotic forms of order. Here we theoretically study a nonequilibrium cavity-QED setup realizing a zero-temperature quantum phase transition from a homogeneous Bose-Einstein condensate to a quasicrystalline phase via collective superradiant light scattering. Across the superradiant phase transition, collective light scattering creates a dynamical, quasicrystalline optical potential for the atoms. Remarkably, the quasicrystalline potential is "emergent" as its eightfold rotational symmetry is not present in the Hamiltonian of the system, rather appears solely in the low-energy states. For sufficiently strong two-body contact interactions between atoms, a quasicrystalline order is stabilized in the system, while for weakly interacting atoms the condensate is localized in one or few of the deepest minima of the quasicrystalline potential.
We study the emergence of quasicrystal configurations in the ground-state phase diagram of bosonic systems interacting through pair potentials of Lifshitz's type. By using a variational mean-field approach, we determine the relevant features of the corresponding potential interaction kind stabilizing such quasicrystalline states in two dimensions. Unlike their classical counterpart, in which the interplay between only two wave vectors determines the resulting symmetries of the solutions, the quantum picture relates in a more complex way to the instabilities of the excitation spectrum. Moreover, the quantum quasicrystal patterns are found to emerge as the ground state with no need of moderate thermal fluctuations. The study extends to the exploration of the excitation properties and the possible existence of superquasicrystals, i.e., supersolidlike quasicrystalline states in which the long-range nonperiodic density profile coexists with a nonzero superfluid fraction. Our calculations suggest that, in an intermediate region between the homogeneous superfluid and the normal quasicrystal phases, these exotic states indeed exist at zero temperature. Comparison with full numerical simulations provides a solid verification of the variational approach adopted in this paper.
Superfluids under specific conditions can exhibit spontaneous breaking of continuous translation symmetries and form exotic spatially ordered states of matter known as supersolids. Despite its early theoretical prediction, it took over half-a-centrury to experimentally demonstrate the supersolid phase in ultracold atomic Bose-Einstein condensates, forming due to long-range interatomic interactions. Here we propose as a promising new platform for supersolidity exciton-polariton superfluids, confined in annular optically induced traps. The supersolid phase emerges due to effective attractive interactions, mediated by the normal excitonic component of the system. Experimental demonstration of spontaneously formed spatially ordered phase is in agreement with detailed mean-field theoretical analysis and numerical simulation. The spontaneous character of the observed supersolid transition is further evidenced by the formation of specific zero-energy Nambu-Goldstone modes in the collective excitation spectrum.
We study the emergence of Bose glass phases in self sustained bosonic quasicrystals induced by a pair interaction between particles of Lifshitz–Petrich type. By using a mean-field variational method designed in momentum space as well as Gross–Pitaevskii simulations we determine the phase diagram of the model. The study of the local and global superfluid fraction allows the identification of supersolid, super quasicrystal, Bose glass and insulating phases. The Bose glass phase emerges as a quasicrystal phase in which the global superfluidity is essentially zero, while the local superfluidity remains finite in certain ring structures of the quasicrystalline pattern. Furthermore, we perform continuous space Path Integral Monte Carlo simulations for a case in which the interaction between particles stabilizes a quasicrystal phase. Our results show that as the strength of the interaction between particles is increased the system undergoes a sequence of states consistent with the super quasicrystal, Bose glass, and quasicrystal insulator thermodynamic phases.
We study the ground-state phase diagram and the quantum phase transitions in spin-1 Bose gases with Raman-induced spin-orbit coupling. In addition to the Bose-Einstein condensates with uniform density, three types of stripe condensation phases that simultaneously break the U(1) symmetry and the translation symmetry are identified. The transitions between these phases are investigated, and the occurrences of the various tricritical points are predicted. The excitation spectra in the plane-wave phase and the zero-momentum phase show rich roton-maxon structures, and their instabilities indicate the tendency to develop the crystalline order. We propose the atomic gas of 23Na^{23}\mathrm{Na}23Na could be a candidate for observing the stripe condensate with high contrast fringes.