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arXiv:1904.05719

Density Wave Superradiance of Photonic Fluid in Frustrated Triangle Lattice Cavity Arrays

Feng Chao, Yu Chen

Published Apr 11, 2019• 0 citations
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Abstract

The spontaneously broken of translational symmetry is usually due to the competition between local interactions and long-range interactions. However, in this paper, we show how a crystalline order can be generated by the competition between local interaction and long-range correlation by frustration. Here we propose a positive hopping Bose Hubbard model on triangle lattices with a pair creation term which comes from frustrated linked cavity arrays with degenerate quantum gases in them. We find by increasing the strength of pair creation term against local interaction strength, two kinds of density wave ordered superradiant photonic fluid phase can be realized and a first order transition between two different density wave ordered states is found. This proposal shows us a new way to produce coherent "solid" phase without the help of long range interactions.

DOI
10.48550/arxiv.1904.05719

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The spontaneously broken of translational symmetry is usually due to the competition between local interactions and long-range interactions. However, in this paper, we show how a crystalline order can be generated by the competition between local interaction and long-range correlation by frustration. Here we propose a positive hopping Bose Hubbard model on triangle lattices with a pair creation term which comes from frustrated linked cavity arrays with degenerate quantum gases in them. We find by increasing the strength of pair creation term against local interaction strength, two kinds of density wave ordered superradiant photonic fluid phase can be realized and a first order transition between two different density wave ordered states is found. This proposal shows us a new way to produce coherent "solid" phase without the help of long range interactions.
Frustration occurs when a system cannot find a lowest-energy configuration due to conflicting constraints. We show that a frustrated superradiant phase transition occurs when the ground-state superradiance of cavity fields due to local light-matter interactions cannot simultaneously minimize the positive photon hopping energies. We solve the Dicke trimer model on a triangle motif with both negative and positive hopping energies and show that the latter results in a sixfold degenerate ground-state manifold in which the translational symmetry is spontaneously broken. In the frustrated superradiant phase, we find that two sets of diverging time and fluctuation scales coexist, one governed by the mean-field critical exponent and another by a novel critical exponent. The latter is associated with the fluctuation in the difference of local order parameters and gives rise to site-dependent photon number critical exponents, which may serve as an experimental probe for the frustrated superradiant phase. We provide a qualitative explanation for the emergence of unconventional critical scalings and demonstrate that they are generic properties of the frustrated superradiant phase at the hand of a one-dimensional Dicke lattice with an odd number of sites. The mechanism for the frustrated superradiant phase transition discovered here applies to any lattice geometries where the antiferromagnetic ordering of neighboring sites are incompatible and therefore our work paves the way toward the exploration of frustrated phases of coupled light and matter.
Understanding how frustration and symmetry breaking shape collective behavior is a central problem in quantum many-body systems. In this work, we investigate this problem in large one- and two-dimensional arrays of coupled Dicke models on a periodic lattice, where strong light-matter coupling gives rise to a superradiant phase and competition between neighboring order parameters induces spontaneous translational symmetry breaking. Such Dicke lattice models constitute a fundamentally new class of quantum many-body systems, as they simultaneously realize the thermodynamic limit associated with the lattice size and an intrinsic thermodynamic limit arising from collective on-site interactions with quantum emitters. We show that frustration drives photonic density-wave ordering, and that the resulting broken periodicity can be predicted from the excitation spectrum of the symmetric phase, without requiring computationally prohibitive thermodynamic energy minimization. Furthermore, we demonstrate that an emergent Nambu-Goldstone mode arises near the critical point in a one-dimensional chain despite the presence of only discrete symmetry, and uncover the mechanism that enables this otherwise forbidden gapless excitation. We also find quasi-periodic ordering in the superradiant phase, reminiscent of quasicrystals, and demonstrate that synthetic magnetic flux provides a powerful knob to control the nature of translational symmetry breaking. Our results establish a new direction in quantum many-body physics where the coexistence of local and global thermodynamic limits gives rise to unconventional symmetry breaking and emergent collective behavior.
Abstract Density order is usually a consequence of the competition between long-range and short-range interactions. Here we report a density ordered superfluid emergent from a homogeneous Mott insulator due to the competition between frustrations and local interactions. This transition is found in a Bose–Hubbard model on a frustrated triangle lattice with an extra pairing term. Furthermore, we find a quantum phase transition between two different density ordered superfluids, which is beyond the Landau–Ginzburg (LG) paradigm. A U(1) symmetry is emergent at the critical point, while the symmetry in each density ordered superfluid is Z 2 × Z 3. We call the transition a ‘shamrock transition’, due to its degenerate ground state in the parameter space being a shamrock-like curve rather than a circle in an LG-type transition. Effective low energy theories are established for the two transitions mentioned above and we find their resemblance and differences with clock models.
Geometrical frustration and long-range couplings are key contributors to create quantum phases with different properties throughout physics. We propose a scheme where both ingredients naturally emerge in a Raman induced subwavelength lattice. We first demonstrate that Raman-coupled multicomponent quantum gases can realize a highly versatile frustrated Hubbard Hamiltonian with long-range interactions. The deeply subwavelength lattice period leads to strong long-range interparticle repulsion with tunable range and decay. We numerically demonstrate that the combination of frustration and long-range couplings generates many-body phases of bosons, including a range of density-wave and superfluid phases with broken translational and time reversal symmetries, respectively. Our results thus represent a powerful approach for efficiently combining long-range interactions and frustration in quantum simulations.
The complex dynamical phases of quantum systems are dictated by atomic interactions that usually evoke an emergent periodic order. Here, we study a quantum many-body system with two competing and substantially different long-range interaction potentials where the dynamical instability towards density order can give way to a disordered amorphous solid, which exhibits local density modulations but no long-range periodic order. We consider a two-dimensional Bose-Einstein condensate in the Rydberg-dressing regime coupled to an optical standing wave resonator. The dynamic pattern formation in this system is governed by the competition between the two involved interaction potentials: repulsive soft-core interactions arising due to Rydberg dressing and infinite-range sign changing interactions induced by the cavity photons. The amorphous phase is found when the two interaction potentials introduce incommensurate length scales. The dynamic formation of this peculiar phase can be attributed to frustration induced by the two competing interaction energies and length scales.
Coherent light-matter interactions between a quantum gas and light in a high-finesse cavity can drive self-ordering phase transitions. To date, such phenomena have involved exclusively single-atom coupling to light, resulting in coupled charge-density or spin-density wave and superradiant order. In this work, we engineer simultaneous coupling of cavity photons to both single atoms and fermionic pairs, which are also mutually coupled due to strong correlations in the unitary Fermi gas. This interplay gives rise to an interference between the charge-density wave and a pair-density wave, where the short-range pair correlation function is spontaneously modulated in space. We observe this effect by tracking the onset of superradiance as the photon-pair coupling is varied in strength and sign, revealing constructive or destructive interference of the three orders with a coupling mediated by strong light-matter and atom-atom interactions. Our observations are compared with mean-field theory where the coupling strength between atomic- and pair-density waves is controlled by higher-order correlations in the Fermi gas. These results demonstrate the potential of cavity quantum electrodynamics to produce and observe exotic orders in strongly correlated matter, paving the way for the quantum simulation of complex quantum matter using ultracold atoms. Cavity-mediated interactions lead to collective effects and ordering in ultracold atomic systems. Here, the authors demonstrate the interplay of different ordered states of ultracold Fermi gases in a cavity, resulting from an intriguing coexistence of photon coupling with both atoms and atom-pairs.