We provide strong evidence that the effective spin-spin interaction in a multimodal confocal optical cavity gives rise to a self-induced glassy phase, which emerges exclusively from the peculiar Euclidean correlations and is not related to the presence of disorder as in standard spin glasses. As recently shown, this spin-spin effective interaction is both nonlocal and nontranslational invariant, and randomness in the atoms' positions produces a spin glass phase. Here we consider the simplest feasible disorder-free setting, where atoms form a one-dimensional regular chain and we study the thermodynamics of the resulting effective Ising model. We present extensive results showing that the system has a low-temperature glassy phase. The model depends on the adimensional parameter α=(a/w_{0})^{2}, a being a lattice spacing and w_{0} an interaction length scale. Notably, for rational values of α=p/q, the number of metastable states at low temperature grows exponentially with q and the problem of finding the ground state rapidly becomes computationally intractable, suggesting that the system develops high-energy barriers and ergodicity breaking occurs.
We provide strong evidence that the effective spin-spin interaction in a multimodal confocal optical cavity gives rise to a self-induced glassy phase, which emerges exclusively from the peculiar Euclidean correlations and is not related to the presence of disorder as in standard spin glasses. As recently shown, this spin-spin effective interaction is both nonlocal and nontranslational invariant, and randomness in the atoms' positions produces a spin glass phase. Here we consider the simplest feasible disorder-free setting, where atoms form a one-dimensional regular chain and we study the thermodynamics of the resulting effective Ising model. We present extensive results showing that the system has a low-temperature glassy phase. The model depends on the adimensional parameter α=(a/w_{0})^{2}, a being a lattice spacing and w_{0} an interaction length scale. Notably, for rational values of α=p/q, the number of metastable states at low temperature grows exponentially with q and the problem of finding the ground state rapidly becomes computationally intractable, suggesting that the system develops high-energy barriers and ergodicity breaking occurs.
In the context of ultracold atoms in multimode optical cavities, the appearance of a quantum-critical glass phase of atomic spins has been predicted recently. Due to the long-range nature of the cavity-mediated interactions, but also the presence of a driving laser and dissipative processes such as cavity photon loss, the quantum optical realization of glassy physics has no analog in condensed matter and could evolve into a ``cavity glass microscope'' for frustrated quantum systems out of equilibrium. Here we develop the nonequilibrium theory of the multimode Dicke model with quenched disorder and Markovian dissipation. Using a unified Keldysh path integral approach, we show that the defining features of a low-temperature glass, representing a critical phase of matter with algebraically decaying temporal correlation functions, are seen to be robust against the presence of dissipation due to cavity loss. The universality class, however, is modified due to the Markovian bath. The presence of strong disorder leads to an enhanced equilibration of atomic and photonic degrees of freedom, including the emergence of a common low-frequency effective temperature. The imprint of the atomic spin-glass physics onto the photon subsystem realizes a ``photon glass'' state and makes it possible to detect the glass state by standard experimental techniques of quantum optics. We provide an unambiguous characterization of the superradiant and glassy phases in terms of fluorescence spectroscopy, homodyne detection, and the temporal photon correlation function ${g}^{(2)}(\ensuremath{\tau})$.
We show that the effective spin-spin interaction between three-level atoms confined in a multimode optical cavity is long-ranged and sign changing, like the RKKY interaction; therefore, ensembles of such atoms subject to frozen-in positional randomness can realize spin systems having disordered and frustrated interactions. We argue that, whenever the atoms couple to sufficiently many cavity modes, the cavity-mediated interactions give rise to a spin glass. In addition, we show that the quantum dynamics of cavity-confined spin systems is that of a Bose-Hubbard model with strongly disordered hopping but no on-site disorder; this model exhibits a random-singlet glass phase, absent in conventional optical-lattice realizations. We briefly discuss experimental signatures of the realizable phases.
"Spatially modulated ordered states, such as crystals, liquid crystals, and antiferromagnets, are ubiquitous in nature but relatively difficult to realize in ultracold atomic systems. In the present work, we present a scheme for generating controllable cavity-mediated interactions between atoms, and show that these interactions give rise to a crystallization transition in the case of a transversely pumped optical cavity. We focus on the case of multimode cavities, in which the interactions are relatively local and the range of possible ordered configurations (and consequently of low-energy fluctuations) is large; as we show, the crystallization transition for a Bose-Einstein condensate in a multimode cavity is driven first-order by fluctuations, through the Brazovskii effect. The ordered state to which this crystallization transition gives rise is a ""supersolid,"" possessing both superfluid and solid order. We address the crystallization transition and the properties of the ordered state, discuss the experimental feasibility of observing these, and finally show how ordering in layered systems of atoms is geometrically frustrated. We then introduce a more straightforward realization of frustrated cavity-mediated interactions, viz. systems of randomly-positioned spins in multimode cavities. We show by means of a mapping to a variant of the Hopfield associative-memory model that such systems exhibit a spin-glass phase. Finally, we consider a different ultracold-atomic setting---that of spin-orbit-coupled Bose gases---in which the Brazovskii effect has a profound influence on the low-temperature phases, leading to a universal preference for stripe-like ordering at zero temperature and bosonic pair condensation at nonzero temperatures."
Sign-changing interactions constitute a crucial ingredient in the creation of frustrated many-body systems such as spin glasses. We present here the demonstration of a photon-mediated sign-changing interaction between Bose-Einstein-condensed atoms in a confocal cavity. The interaction between two atoms is of an unusual, nonlocal form proportional to the cosine of the inner product of the atoms' position vectors. This interaction arises from the differing Gouy phase shifts of the cavity's degenerate modes. The interaction drives a nonequilibrium Dicke-type phase transition in the system leading to atomic checkerboard density-wave order. Because of the Gouy phase anomalies, the checkerboard pattern can assume either a sinelike or cosinelike character. This state is detected via the holographic imaging of the cavity's superradiant emission. Together with a companion paper [Y. Guo, V. D. Vaidya, R. M. Kroeze, R. A. Lunney, B. L. Lev, and J. Keeling, Emergent and broken symmetries of atomic self-organization arising from Gouy phases in multimode cavity QED, Phys. Rev. A 99, 053818 (2019)PLRAAN2469-992610.1103/PhysRevA.99.053818], we explore this interaction's influence on superradiant phase transitions in multimode cavities. Employing this interaction in cavity QED spin systems may enable the creation of artificial spin glasses and quantum neural networks.
In this paper, quantum algorithms are to be used to simulate glassy systems in toy models. To look for glassy behavior, the energy landscape and spin configurations of the transverse field Ising model in a longitudinal field are studied. The Variational Quantum Eigensolver (VQE) is used to obtain the ground-state energies and corresponding eigenstates for a 6×6 Ising lattice using 36 qubits and a 1-dimensional Ising chain of length 25. For the 8×8 Cellular Potts model, the original Hamiltonian is converted to an Ising formulation for the VQE to reduce to its ground state. The energy change during minimization is carefully analyzed to find whether the effects of interfacial tension among cells could probably induce glassiness in the cell system.
Bosonic excitations within long-range ordered, but strongly inhomogeneous phases have been studied in quite some detail. My thesis focuses instead on understanding the insulating, localized phase of disordered bosonic systems. In particular I study localization properties of strongly interacting bosons and spin systems in a disorder potential at zero temperature. I focus on simple, prototypical spin models (Ising model and XY model) in random fields on a Cayley tree with large connectivity. Regarding the nature of the quantum phase transition in strong disorder I find the following results: i) With a uniformly distributed disorder non-extensive excitations in the disordered phase are all localized. ii)Moreover, I find that the order arises due to a collective condensation, which is qualitatively distinct from a Bose Einstein condensation of single particle excitations into a delocalized state. In particular, in non-frustrated Bose glasses, I do not find evidence for a boson mobility edge in the Bose glass. These results are qualitatively different from claims in the recent literatures . Considering that (many body) localization of bosons is a kind of quantum glass transition, it is an interesting question to ask what phenomena occur, if the ingredients for more conventional (classical) glassy physics are added to a disordered bosons system, namely: random, frustrated interactions between the bosons. One can still think about such a system as bosons in a disordered potential, where the disordered potential is, at least partly, self-generated by random frustrated interactions between the bosons. This question takes us to the study of another type of disordered systems: glassy systems. Those are typically characterized by low temperature phases with an inhomogeneous density or magnetization pattern, which is extremely long-lived due to the occurrence of non-trivial ergodicity breaking. I study a solvable model of hard core bosons (pseudospins) subject to disorder and frustrating interactions. This solvable model provides insight into the possibility of coexistence of super uidity and glassy density order, as well as into the nature of the coexistence phase (the superglass). In particular, for the considered mean field model I prove the existence of a superglass phase. This complements the numerical evidence for such phases provided by quantum Monte Carlo investigations in finite dimensions and on random graphs. Those were, however, limited to finite temperature, and could thus not fully elucidate the structure of the phases at T = 0. In contrast, my analytical approach allows one to understand the quantum phase transition between glassy superfluid and insulator, and the non-trivial role played by glassy correlations. When the frustrated interactions are strong enough, the superfluid order may be destroyed. As I will show in a mean field model, this happens within the glass phase of the system, where a disorder induced superfluid-insulator phase transition takes place to give way to a frustrated Bose glass. The glassy background on top of which this happens leads to many interesting phenomena which seem not to have been noticed before. To understand the nature of the glassy superfluid-insulator quantum phase transition at zero temperature and the transport properties on the insulating, Bose glass side of the transition is the goal of the third part of my thesis. To address the above questions, I studied an exactly solvable model of a glassy superfluid-insulator quantum phase transition on a Bethe lattice geometry with high connectivity. My main results can be summarized as follows: i) I found that the superfluid-insulator transition is shifted to stronger hopping. This is a result of the pseudo gap in the density of states of the glass state, which tends to strongly disfavor the onset of superfluidity. ii) In the glassy insulator, the discrete local energy levels become broadened due to the quantum fluctuations.The level-broadening process appears as a phase transition which has strong similarities with an Anderson localization transition, and has implications on many body localization. By using the locator expansion for bosons I found that, the glassy insulator has a finite mobility edge for the bosonic excitations, which, however, does not close upon approaching the SI quantum phase transition point. This finding helps to understand the nature of the superfluid-to-frustrated Bose glass transition: the superfluid emerges as a collective phase ordering phenomenon at zero temperature, and not as a condensation in to a single particle delocalized state, in contrast to opposite predictions in the recent literatures. The existence of a mobility edge in the insulator suggests the possibility of phononless, activated transport in the bosonic insulator, which might be a candidate explanation for the experimentally seen activated transport, which has remained a mystery for a long time.