The antimatter object 3I/ATLAS exists as an Anti-Bose-Einstein Condensate (Anti-BEC) - a macroscopic quantum coherent structure with inverted electromagnetic topology. This state is protected by topological quantum numbers (Chern number C = -1 for antimatter versus C = +1 for matter) that only change through discontinuous transitions when the energy gap Δ between ground and excited states closes. This gap sits at Δ ~ 10⁻⁶⁰ eV per particle - the electromagnetic binding energy scale. For gap closure across all ~10³⁹ antimatter atoms requires E_gap ~ 10²¹-10²² joules. In the 3-kelvin interstellar environment where kᵦT << Δ, spontaneous decay is thermodynamically impossible, giving inherent billion-year stability.
The antimatter object 3I/ATLAS exists as an Anti-Bose-Einstein Condensate (Anti-BEC) - a macroscopic quantum coherent structure with inverted electromagnetic topology. This state is protected by topological quantum numbers (Chern number C = -1 for antimatter versus C = +1 for matter) that only change through discontinuous transitions when the energy gap Δ between ground and excited states closes. This gap sits at Δ ~ 10⁻⁶⁰ eV per particle - the electromagnetic binding energy scale. For gap closure across all ~10³⁹ antimatter atoms requires E_gap ~ 10²¹-10²² joules. In the 3-kelvin interstellar environment where kᵦT << Δ, spontaneous decay is thermodynamically impossible, giving inherent billion-year stability.
We demonstrate that a topology-induced Bose-Einstein condensation (BEC) takes place in a complex network. As a model topology, we consider the deterministic Apollonian network which exhibits scale-free, small-world, and hierarchical properties. Within a tight-binding approach for noninteracting bosons, we report that the BEC transition temperature and the gap between the ground and first excited states follow the same finite-size scaling law. An anomalous density dependence of the transition temperature is reported and linked to the structure of gaps and degeneracies of the energy spectrum. The specific heat is shown to be discontinuous at the transition, with low-temperature modulations as a consequence of the fragmented density of states.
This thesis is devoted to the rigorous study of dilute Bose gases with two-body and three-body interactions at zero temperature in two and three dimensions. Bose gases are many-body quantum systems composed of bosons, which notably do not obey the Pauli exclusion principle. As a consequence, at extremely low temperatures, a macroscopic fraction of the particles can occupy the same one-body quantum state. This phenomenon, known as Bose–Einstein condensation, was predicted in the 1920s by Bose and Einstein for noninteracting Bose gases, and first realised experimentally by the groups of Cornell and Wieman, and Ketterle, earning them the Nobel Prize for Physics in 2001. However, proving the occurrence of Bose–Einstein condensation in general interacting bosonic systems remains a major open problem and constitutes a central theme in this thesis. Another important property of bosonic matter is that it is generally more unstable than fermionic matter. In particular, for systems interacting via the Coulomb force, the Pauli exclusion principle is essential for explaining the stability of the second kind, which states that the energy and volume scale linearly with the number of particles. Nonetheless, bosonic systems with attractive but less singular interactions can also be stable, and the rigorous proof of this fact forms a second focus of this thesis. In three dimensions, we consider predominantly repulsive interactions. Firstly, we prove a leading order upper bound on the thermodynamic ground state energy of Bose gases with hard-core three-body interactions, which matches an existing lower bound. In addition, we obtain a simpler proof for integrable potentials. Secondly, we derive the leading order of the thermodynamic ground state energy of Bose gases with combined two-body and three-body interactions. More specifically, we show that, at the leading order, the ground state energy is entirely characterised by the scattering length of the two-body potential and the scattering hypervolume of the three-body potential. Thirdly, we study the time evolution of Bose–Einstein condensates with three-body interactions in the so-called Gross–Pitaevskii regime. We show that Bose–Einstein condensation is preserved under many-body evolution and that the condensate wavefunction evolves according to the quintic Gross–Pitaevskii equation. In particular, we show that the effective coupling constant is universal in the sense that it depends only on the scattering hypervolume of the interaction potential. As a by-product of our proof, we derive a stability of the second kind result for Bose gases with attractive two-body interactions and repulsive three-body interactions. In two dimensions, we consider trapped Bose gases with mean-field-type interactions, including the purely attractive case. We prove the stability of the second kind of the system and the convergence of the ground state energy per particle to that of a non-linear Schrödinger energy functional. As a consequence of the stability of the second kind, we also obtain Bose–Einstein condensation for the many-body ground states.
The problem of understanding how a coherent, macroscopic Bose- Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering achievement of BEC in weakly interacting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the BEC number, as well as the development of its coherence. More recently, there has been interest in connecting such experiments to universal aspects of nonequilibrium phase transitions, in terms of both static and dynamical critical exponents. Here, the spontaneous formation of topological structures such as vortices and solitons in quenched cold-atom experiments has enabled the verification of the Kibble-Zurek mechanism predicting the density of topological defects in continuous phase transitions, first proposed in the context of the evolution of the early universe. This chapter reviews progress in the understanding of BEC formation and discusses open questions and future research directions in the dynamics of phase transitions in quantum gases. Introduction The equilibrium phase diagram of the dilute Bose gas exhibits a continuous phase transition between condensed and noncondensed phases. The order parameter characteristic of the condensed phase vanishes above some critical temperature T c and grows continuously with decreasing temperature below this critical point. However, the dynamical process of condensate formation has proved to be a challenging phenomenon to address both theoretically and experimentally. This formation process is a crucial aspect of Bose systems and of direct relevance to all condensates discussed in this book, despite their evident system-specific properties. Important questions leading to intense discussions in the early literature include the time scale for condensate formation and the role of inhomogeneities and finite-size effects in “closed” systems. These issues are related to the concept of spontaneous symmetry breaking, its causes, and implications for physical systems (see, for example, Chapter 5 by Snoke and Daley). In this chapter, we give an overview of the dynamics of condensate formation and describe the present understanding provided by increasingly well-controlled cold-atom experiments and corresponding theoretical advances over the past twenty years. We focus on the growth of BECs in cooled Bose gases, which, from a theoretical standpoint, requires a suitable nonequilibrium formalism.
Large Chern-number topological phase is always an important topic in modern physics. Here we investigate the topological superfluids in a coupled-layer system, in which transitions between different topological superfluids can be realized by controlling the binding energy, interlayer tunneling, and layer asymmetry, etc. These topological transitions are characterized by energy gap closing and reopening at the critical points at zero momentum, where the Chern number and sign of Pfaffian undergo a discontinuous change. Topological protected edge modes at the boundaries are ensured by the bulk-edge correspondence. In a trapped potential the edge modes are spatially localized at the interfaces between distinct topological superfluids, where the number of edge modes is equal to the Chern-number difference between the left and right superfluids. These topological transitions can be detected by spin texture at or near zero momentum, which changes discretely across the critical points due to band inversion. The model can be generalized to a multilayer system in which the Chern number can be equal to any positive integer. These large Chern-number topological superfluids provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.
The phenomenon of Bose-Einstein condensation (BEC), first predicted by Einstein 70 years ago, has finally been observed in the laboratory. In this elusive state of matter the concept of individual particles ceases to have meaning: the atoms condense into the same quantum state and act as a single entity that displays quantum mechanical behaviour on a macroscopic scale. The condensate was observed when Eric Cornell, Carl Wieman and colleagues at the Joint Institute for Laboratory Astrophysics in Boulder, Colorado, cooled a dilute gas of rubidium atoms, confined in a magnetic trap, to a temperature of just a few nanoKelvin (M H Anderson et al. 1995 Science 269 198).
With the announcement of the recent successful production of a Bose-Einstein condensate (BEC) of photons (2010), a circle has been completed which started in 1925 with the vision of Albert Einstein and Sateyendra Nath Bose - a sustained macroscopic condensed state of matter where all atoms are in the same lowest quantum state. The creation of an all-optical BEC, involving a surprisingly straightforward tabletop method, amenable now even to amateur researchers, which bypasses the normally requisite laser/evaporative cooling equipment and ultra-high vacuum chambers necessary for the production of the standard delicate atomic BEC, elevates this phenomenon to a new level well beyond its current perception as mere laboratory curiosity. Accordingly, this development certainly heralds the eventual incorporation of atomic and photon BECs as standard operating components of energy-efficient mechanical, optical and electrical systems, implying novel ingeneious engineering protocols amenable to all the tools of of non-linear and quantum optics. Pointing towards such a promising technological future are the suggestion that a photon BEC could serve as a new high-energy ultra-violet (UV) laser photon source, as well as the recent unprecedented implementation of a closed-loop atom circuit (toroidal atomic BEC - 2011) demonstrating precise control of superfluid current flow, forecasting the coveted development of an atomic SQUID. Perhaps, more significantly, the new highly robust and manageable optical BEC will allow heretofore unfathomable precise probing of the atomic and nano-levels of nature, affording novel high-quality testing procedures for the major foundations of quantum mechanics itself. Such a primary advancement, providing a clearer glimpse into the microscopic realms, may present us as never before with an unprecedented view of the quantum engine that underpins physical reality itself and help place the contextual nature of entanglement and quantum coherence on a firmer foundation(see also companion paper vixra:1112.0068). Thus further progress in achieving mastery over the precise flexible manipulation of exotic BEC states could demonstrate that quantum contextuality might be an unsusupected over-arching archetypal principle in nature, leading to new insight in regards to the interpretation of quantum mechanics at all levels of nature. Moreover, it will be shown that this concealed and hence heretofore unsuspected contextual aspect of natural laws, as exemplified by the dynamics underlying BEC structure, could be brought to bear to account for physical anomalies inexplicable using current paradigms, such as the claimed energy yields from low-energy nuclear reactions(as represented by the process of so-called cold fusion, directly related to recent commercial advancements in this field - the Andrea Rossi E-Cat, for example), making this phenomenon more tractable and rendered less controversial.