Abstract The year 2024 marks the 100th anniversary of the first article on Bose statistics. Bose breathed life into the Planck distribution of radiation by a microscopic derivation (Bose 1924Z. Phys.26178), adding a new insight, namelyindistinguishabilityinto the then evolving quantum theory. Einstein recognized the importance of this article and got it published. Using Bose statistics Einstein wrote an article on the theory (Einstein 1924Sutzungsber. Preuss. Akad. Wiss Phys.-Math Kl.261) of an ideal Bose gas and Bose–Einstein condensation. The groundbreaking discovery of Bose, an unveiling of a secret of quantum mechanics, continues to reverberate after a century. Bose’s paper is considered the fourth important paper in old quantum theory, following Planck’s (1900) article (Planck 1900Verh. Disch Phys. Ges.2202), Einstein’s (1905) photoelectric effect (Einstein 1905Ann. Phys., Lpz.17132) and Bohr’s model (1913) of the atom (Bohr 1913London, Edinburgh Dublin Phil. Mag. J. Sci.261). Dirac (1926Proc. R. Soc.A112661) coined the namebosonfor one of the two families of indistinguishable particles, the other family being fermion. The edifice of modern quantum field theory, many-body quantum theory, quantum-information and quantum-computing are built on bosons, fermions and anyons. The ever-blooming quantum garden of bosons has photons, gluons, W-bosons, mesons, Higgs-bosons, gravitons, phonons, magnons, excitons, plasmons, polaritons and so on. We present a brief historical account of Bose’s life and his discovery, followed by a bird’s eye view of the impacts of bosons in modern science and technology: from Bose’s distribution of 3-degree background radiation reaching us in the form of cosmic microwave background from the big bang era toboson sampling, a novel quantum computing method. Bosogenesis before Baryogenesis?: And God said, Let there be light: and there was light (Genesis, 1:4)
Abstract The year 2024 marks the 100th anniversary of the first article on Bose statistics. Bose breathed life into the Planck distribution of radiation by a microscopic derivation (Bose 1924Z. Phys.26178), adding a new insight, namelyindistinguishabilityinto the then evolving quantum theory. Einstein recognized the importance of this article and got it published. Using Bose statistics Einstein wrote an article on the theory (Einstein 1924Sutzungsber. Preuss. Akad. Wiss Phys.-Math Kl.261) of an ideal Bose gas and Bose–Einstein condensation. The groundbreaking discovery of Bose, an unveiling of a secret of quantum mechanics, continues to reverberate after a century. Bose’s paper is considered the fourth important paper in old quantum theory, following Planck’s (1900) article (Planck 1900Verh. Disch Phys. Ges.2202), Einstein’s (1905) photoelectric effect (Einstein 1905Ann. Phys., Lpz.17132) and Bohr’s model (1913) of the atom (Bohr 1913London, Edinburgh Dublin Phil. Mag. J. Sci.261). Dirac (1926Proc. R. Soc.A112661) coined the namebosonfor one of the two families of indistinguishable particles, the other family being fermion. The edifice of modern quantum field theory, many-body quantum theory, quantum-information and quantum-computing are built on bosons, fermions and anyons. The ever-blooming quantum garden of bosons has photons, gluons, W-bosons, mesons, Higgs-bosons, gravitons, phonons, magnons, excitons, plasmons, polaritons and so on. We present a brief historical account of Bose’s life and his discovery, followed by a bird’s eye view of the impacts of bosons in modern science and technology: from Bose’s distribution of 3-degree background radiation reaching us in the form of cosmic microwave background from the big bang era toboson sampling, a novel quantum computing method. Bosogenesis before Baryogenesis?: And God said, Let there be light: and there was light (Genesis, 1:4)
We discuss another of Einstein’s statistical contributions to quantum theory: his work on quantum statistics. It was prompted by a paper that S. Bose sent to him in 1924 when the physics community had finally accepted the photon idea upon the discovery and analysis of Compton scattering. We present in detail Bose’s derivation of Planck’s distribution, using a particle approach. Einstein extended Bose’s analysis of radiation to systems of matter particles. Here he made the discovery of the astounding phenomenon of Bose–Einstein condensation. The ultimate understanding of Planck’s spectral distribution came about in modern quantum mechanics with its notion of indistinguishable particles, and the connection between spin and statistics. We also provide a modern discussion of Bose–Einstein condensation.
In 1924 the Indian physicist Satyendra Nath Bose sent Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein generalized Bose's theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved and, in the same year, predicted that at sufficiently low temperatures the particles would become locked together in the lowest quantum state of the system. We now know that this phenomenon, called Bose-Einstein condensation (BEC), only happens for “bosons” – particles with a total spin that is an integer multiple of h, the Planck constant divided by 2π.
Einstein is best known for relativity and his other 1905 breakthroughs – explaining the photoelectric effect and his work on Brownian motion – but his ideas also underpinned the development of the laser and the creation of a new state of matter called the Bose-Einstein condensate. These discoveries, which were made in 1916 and 1924, respectively, were based on Einstein's investigations into bosonic particles such as photons. Moreover, Bose – Einstein condensation was predicted to occur in one of the simplest physical systems: the ideal gas.
2025 is the year of Quantum Science and Technology. It celebrates 100 years since the invention of quantum theory (as previously mentioned, in 1925 Heisenberg published what is considered the first paper on quantum mechanics). How is quantum theory doing on her 100th birthday? It is thriving! Its successes continue in quantum chemistry, condensed matter, molecular, optical, nuclear and particle physics, and new areas of quantum information and quantum computation that utilize non-classical information theoretic properties of quantum systems have burst upon the scene, and many researchers are involved in the new area of quantum biology. The achievements of quantum theory are phenomenal, and there does not exist a single experiment that contradicts its basic tenets. As illustrated by the magic cube of physics, the structure of the fundamental framework of physics is completely dominated by quantum theory, which is intrinsically probabilistic and contextual, and by spacetime physics, which is not intrinsically probabilistic and it is not contextual. In the area of overlaps between quantum and spacetime physics, we find local quantum field theory, where spacetime appears as a glorified index of quantum fields—and yet is important in defining what we mean by locality, causality, etc. Nevertheless, local quantum field theory, especially in the form of effective field theory has scored (and continues to score) impressive successes in particle, nuclear and condensed matter and statistical physics, as well as in the realms of quantum field theory in curved but not dynamical backgrounds, including weakly gravitational fields and cosmology.
In 1995 two different research groups observed for the first time the Bose-Einstein condensation (BEC) in ultracold gases. When the confining magnetic trap was turned off the gas was left free to expand, and the velocity of the particles showed a clear peak: most of the particles were occupying the same single particle state, the one of lowest energy. The Bose-Einstein condensation had been predicted in 1925 by Einstein, written by inspiration of a work on the statistic of the photons by Bose (1924). In this work Bose described the behavior of an ensemble of photons, treating them as massless particles, with no number conservation associated. Einstein extended this approach to particles with a mass and with fixed number, creating what is now called the Bose-Einstein distribution. The particles that follow such a description are called ``bosons'', as opposed to the ``fermions'' of the Fermi-Dirac statistics. Einstein predicted that in a gas of bosons - under a critical temperature - a finite fraction of the total number of particles would have been in the ground state, and act as a single entity. This amusing theoretical discovery found its utility a few years later. In the late thirties, new techniques allowed to cool Helium-4 at few Kelvins above the absolute zero. The properties of the resulting liquid were a puzzlement to the scientific community: among others, it could flow without experiencing friction. The liquid was called a ``superfluid''. A first explanation was given by London in 1938, which linked the superfluid behavior to the presence of a BEC among the bosonic Helium particles. The fermions cannot condense by themselves. On the other hand, they can form bound pairs and act as bosons, as it happens in a metal at low temperature. Using this approach, in 1957 Bardeen, Cooper and Schrieffer created a successful model of superconductivity by describing a superconductor as a superfluid in a charged system. During the course of these years we explored the superfluid properties of Bosons and Fermions in different settings. The original contributions of the thesis are described starting from the third chapter, where we speak about the generation and stability of solitons in a periodic optical lattices, both fixed or in motion. In the fourth chapter we study the generation of giant vortices in cold fermions, by using a generalized hydrodynamical approach. In chapter 5 we study the effect of a quasiperiodic lattice and the glassy phase it produces on a gas of bosons. Finally, we study the interaction of normal matter and superfluids with gravitational waves. While this interaction is seen to be extremely small, we believe that the resulting formalism is interesting by itself.