The Dicke model describes the cooperative interaction of an ensemble of two-level atoms with a single-mode photonic field and exhibits a quantum phase transition as a function of light–matter coupling strength. Extending this model by incorporating short-range atom–atom interactions makes the problem intractable but is expected to produce new physical phenomena and phases. Here, we simulate such an extended Dicke model using a crystal of ErFeO3, where the role of atoms (photons) is played by Er3+spins (Fe3+magnons). Through terahertz spectroscopy and magnetocaloric effect measurements as a function of temperature and magnetic field, we demonstrated the existence of a novel atomically ordered phase in addition to the superradiant and normal phases that are expected from the standard Dicke model. Further, we elucidated the nature of the phase boundaries in the temperature–magnetic-field phase diagram, identifying both first-order and second-order phase transitions. These results lay the foundation for studying multiatomic quantum optics models using well-characterized many-body solid-state systems.
The existence of quantum tricriticality and exotic phases are found in a tricritical Dicke triangle (TDT) where three cavities, each one containing an ensemble of three-level atoms, are connected to each other through the action of an artificial magnetic field. The conventional superradiant phase (SR) is connected to the normal phase through first- and second-order boundaries, with tricritical points located at the intersection of such boundaries. Apart from the SR phase, a chiral superradiant (CSR) phase is found by tuning the artificial magnetic field. This phase is characterized by a nonzero photon current and its boundary presents chiral tricritical points (CTCPs). Through the study of different critical exponents, we are able to differentiate the universality class of the CTCP and TCP from that of second-order critical points, as well as find distinctive critical behavior among the two different superradiant phases. The TDT can be implemented in various systems, including atoms in optical cavities as well as the circuit QED system, allowing the exploration of a great variety of critical manifolds.
more » « less- Award ID(s):
- 2207283
- NSF-PAR ID:
- 10382817
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Quantum Frontiers
- Volume:
- 1
- Issue:
- 1
- ISSN:
- 2731-6106
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract -
Both aliovalent doping and the charge state of multivalent lattice ions determine the oxygen non-stoichiometry ( δ ) of mixed ionic and electronic conductors (MIECs). Unfortunately, it has been challenging for both modeling and experiments to determine the multivalent ion charge states in MIECs. Here, the Fe charge state distribution was determined for various compositions and phases of the MIEC La 1−x Sr x FeO 3−δ (LSF) using the spin-polarized density functional theory (DFT)-predicted magnetic moments on Fe. It was found that electron occupancy and crystal-field-splitting-induced differences between the Fe 3d-orbitals of the square pyramidally coordinated, oxygen-vacancy-adjacent Fe atoms and the octahedrally-coordinated, oxygen-vacancy-distant-Fe atoms determined whether the excess electrons produced during oxygen vacancy formation remained localized at the first nearest neighbor Fe atoms (resulting in small oxygen vacancy polarons, as in LaFeO 3 ) or were distributed to the second-nearest-neighbor Fe atoms (resulting in large oxygen vacancy polarons, as in SrFeO 3 ). The progressively larger polaron size and anisotropic shape changes with increasing Sr resulted in increasing oxygen vacancy interactions, as indicated by an increase in the oxygen vacancy formation energy above a critical δ threshold. This was consistent with experimental results showing that Sr-rich LSF and highly oxygen deficient compositions are prone to oxygen-vacancy-ordering-induced phase transformations, while Sr-poor and oxygen-rich LSF compositions are not. Since oxygen vacancy induced phase transformations cause a decrease in the mobile oxygen vacancy site fraction ( X ), both δ and X were predicted as a function of temperature and oxygen partial pressure, for multiple LSF compositions and phases using a combined thermodynamics and DFT approach.more » « less
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Key points Vision plays a crucial role in guiding locomotion in complex environments, but the coordination between gaze and stride is not well understood.
The coordination of gaze shifts, fixations, constant gaze and slow gaze with strides in cats walking on different surfaces were examined.
It was found that gaze behaviours are coordinated with strides even when walking on a flat surface in the complete darkness, occurring in a sequential order during different phases of the stride.
During walking on complex surfaces, gaze behaviours are typically more tightly coordinated with strides, particularly at faster speeds, only slightly shifting in phase.
These findings indicate that the coordination of gaze behaviours with strides is not vision‐driven, but is a part of the whole body locomotion synergy; the visual environment and locomotor task modulate it. The results may be relevant to developing diagnostic tools and rehabilitation approaches for patients with locomotor deficits.
Abstract Vision plays a crucial role in guiding locomotion in complex environments. However, the coordination between the gaze and stride is not well understood. We investigated this coordination in cats walking on a flat surface in darkness or light, along a horizontal ladder and on a pathway with small stones. We recorded vertical and horizontal eye movements and 3‐D head movement, and calculated where gaze intersected the walkway. The coordination of gaze shifts away from the animal, gaze shifts toward, fixations, constant gaze, and slow gaze with strides was investigated. We found that even during walking on the flat surface in the darkness, all gaze behaviours were coordinated with strides. Gaze shifts and slow gaze toward started in the beginning of each forelimb's swing and ended in its second half. Fixations peaked throughout the beginning and middle of swing. Gaze shifts away began throughout the second half of swing of each forelimb and ended when both forelimbs were in stance. Constant gaze and slow gaze away occurred in the beginning of stance. However, not every behaviour occurred during every stride. Light had a small effect. The ladder and stones typically increased the coordination and caused gaze behaviours to occur 3% earlier in the cycle. At faster speeds, the coordination was often tighter and some gaze behaviours occurred 2–16% later in the cycle. The findings indicate that the coordination of gaze with strides is not vision‐driven, but is a part of the whole body locomotion synergy; the visual environment and locomotor task modulate it.
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