Quantum information with ultracold quantum gases 6 hu berlin, 18. The early experiments on bose einstein condensation in dilute atomic gases accomplished three longstanding goals. A gapless theory of boseeinstein condensation in dilute gases at finite temperature. The quest to realize bec in a dilute weakly interacting gas was pursued in at least three different directions. Boseeinstein condensation in a dilute, trapped gas at.
Perfect periodic structure phonon free with variable lling. 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. Meanfield theory provides a framework to understand the main features of the. The theory of boseeinstein condensation of dilute gases. Wolfgang ketterle born 21 october 1957 is a german physicist and professor of physics at the massachusetts institute of technology mit. We prove this fact theoretically for bosons with twobody repulsive interaction potentials in the dilute limit. Since the experimental demonstration of bose einstein condensation in dilute atomic gases there has been an explosion of interest in the properties of this novel macroscopic quantum system. Received on 8 february, 2004 the material presented here consists of lecture notes written for. Since an atomic bose einstein condensate, predicted by einstein in 1925, was first produced in the laboratory in 1995, the study of ultracold bose and fermi gases has become one of the most active areas in contemporary physics. The study of boseeinstein condensates in dilute gases encompasses a number of.
It is an excellent text, a broad survey with some indepth discussions. Pdf the mathematical theory of dilute gases applied mathematical sciences download online. This advance has paved the way to the precise control of the quantum behavior of ultracold atomic systems. The statistical mechanics of bosons were developed by satyendra nath bose for a photon gas, and extended to massive particles by albert einstein who realized that an ideal gas of bosons would form a. Theory of boseeinstein condensation in trapped gases. Although first proposed by einstein in 1924, bose einstein condensation bec in a gas was not achieved until 1995 when, using a combination of laser cooling and trapping, and magnetic trapping and evaporation, it was first observed in rubidium and then in lithium and sodium, cooled down to extremely low temperatures. Bose einstein condensates in dilute atomic gases, which were. Pdf theory of boseeinstein condensation in trapped gases.
The nature of superfuidity and bose einstein condensation. These microscopic interactions manifest themselves in twobody correlations and dictate the mesoscopic and macroscopic properties of the condensate. Einstein then extended bose s ideas to matter in two other papers. Review bose einstein condensation in dilute gases is an excellent and muchneeded text of the theory of these condensates although progress continues at a cracking pace, there is now a set of basic notions that it is sensible to teach postgraduates, including the way that condensates are made and their physical properties as macroscopic quantum systems. This gaseous state, a bose einstein condensate, was produced in the laboratory for the first time in 1995 and investigating such condensates has become one of the. The nature of superfuidity and boseeinstein condensation core.
So far, both have remained apart with no quantum mechanical description of gravity available. We study the occurrence of a bose einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. Bose einstein condensation in dilute gases in 1925 einstein predicted that at low temperatures particles in a gas could. Boseeinstein condensation of exciton polaritons nature. Bosonic stimulation in the formation of a boseeinstein. As we have seen in this thesis, an increasingly controllable macroscopic quantum system is a bose einstein condensed state of a trapped dilute gas 25, 124.
Download bose einstein condensation in dilute gases. Meanfield theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Bose einstein condensation in dilute gases will be useful to newcomers to the field and will help researchers with diverse backgrounds communicate with each other. Proof of boseeinstein condensation for dilute trapped gases. Einstein 192425 extended bose s idea to material particles predicted bec in an ideal quantum gas i w. We study the superfluidity and the coherence in dipolar binary bose mixtures using the hydrodynamic approach. Boseeinstein condensation in dilute gases by pethick, c. The mathematical study of the bose gas goes back to the.
This gaseous state, a bose einstein condensate, was produced in the laboratory for the first time in 1995 and investigating such condensates is one of the most active areas in. The oneparticle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by. Sodium atoms were evaporatively cooled close to the onset of bose einstein condensation and then. The nature of superfuidity and boseeinstein condensation. This gaseous state, a bose einstein condensate, was produced in the laboratory for the first time in 1995 and investigating such condensates is one of the most active areas in contemporary physics. Atomic physics provides the basic methods for creating and manipulating these systems, and the physical data required to characterize them. The mathematics of the bose gas and its condensation elliott h. Read bose einstein condensation in dilute gases pdf online. The study of boseeinstein condensation in dilute gases draws on many di.
It is composed of bosons, which have an integer value of spin, and obey bose einstein statistics. Bose einstein condensate of dilute atomic gases in a perfect bose einstein condensate bec all ideal bosons occupy the same. These have been used to explore the transition between a superfluid and a mott insulator37 and may be useful in studying bose einstein condensation in fewer than three dimensions, for example the tonksgirardeau gas. Pdf the theory of boseeinstein condensation of dilute gases.
Bose einstein condensation in dilute gases by pethick, christopher. Description of the book boseeinstein condensation in dilute gases. We summarize all experimental studies of bose einstein condensation bec in dilute atomic gases reported thus far and discuss the experimental techniques used to produce, manipulate and observe nanokelvin samples of atoms. Pdf boseeinstein condensation in dilute gases pethick. Boseeinstein condensation in dilute gases in 1925 einstein. Boseeinstein condensation in atomic gases ios press. In 1925 einstein predicted that at low temperatures particles in a gas could all reside in the same quantum state. We summarize all experimental studies of boseeinstein condensation in dilute atomic gases reported thus far and discuss the experimental techniques used to produce, manipulate and observe nanokelvin samples of atoms. Densities from the limit of a dilute gas to a strongly interacting bose liquid are possible. Pdf boseeinstein condensation in dilute gases popular. A gapless theory of boseeinstein condensation in dilute gases at.
Boseeinstein condensation in dilute atomic gases and the. We also prove bose einstein condensation in the following sense. Introduction bose einstein condensation in dilute gases is determined by the nature of the twobody interactions between the atoms 1. Since the first realizations of bose einstein condensation bec in a dilute gas of alkali atoms, research in the interdisciplinary fields of atom optics and quantum fluids has flourished. Experimental and theoretical work showed that the onset of superfluidity for liquid helium in vycor shows features of dilute gas bose einstein condensation. Read book bose einstein condensation in dilute gases free books click here pdf. Wieman 1995 produced the rst gaseous condensate nobel price of physics 2001 about boseeinstein condensation bec history of bec 4 28 c stefan kienzle. Ketterle nobel lecture 2001 and his talk given at mits teachers program 240603. Download pdf bose einstein condensates and atom lasers.
Boseeinstein condensation in dilute gases will be useful to newcomers to the field and will help researchers with diverse backgrounds communicate with each other. This peculiar gaseous state, a bose einstein condensate, was produced in the laboratory for the. Bose einstein condensation in dilute gases pethick c j. Auch versuche, eine boseeinsteinkondensation in einem gas aus. Towards bose einstein condensation of excitons in potential traps. Read boseeinstein condensation in dilute gases pdf free. An ideal bose gas is a quantummechanical phase of matter, analogous to a classical ideal gas. Smith pethick and smith provide a unified introduction to the physics of ultracold atomic bose and fermi gases. His research has focused on experiments that trap and cool atoms to temperatures close to absolute zero, and he led one of the first groups to realize bose einstein condensation in these systems in 1995. Two pillars of modern physics are quantum mechanics and general relativity. The formation of a bose einstein condensate of a dilute atomic gas has been studied in situ with a nondestructive, timeresolved imaging technique.
The ground state of a gas of bosons confined in an external trap potential and interacting via repulsive twobody forces has recently been shown to exhibit complete bose einstein condensation in the dilute limit, yielding for the first time a rigorous proof of this phenomenon in a physically realistic setting. Boseeinstein condensation in dilute atomic gases a. It is an excellent text, a broad survey with some indepth discussions an excellent text such as this is. Boseeinstein condensation in dilute gases pdf free download. The pioneering achievement of bec in weaklyinteracting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the bec number, as. The book is meant to be introductory, but the authorsworld experts in transport phenomenaoffer sophisticated discussions of such nonequilibrium. I acknowledge the use of materials and slides from w. Proceedings of the international school of quantum electronics 27th course on bose einstein condensates and atom lasers, october 1924, 1999, erice, italy. Boseeinstein condensation bec, a form of matter first postulated in 1924, has famously been demonstrated in dilute atomic gases at ultralow temperatures. The ground state of bosonie atoms in a trap has been shown experimentally to display bose einstein condensation bec. Wieman jila, university of colorado and national institute of standards and techno. A boseeinstein condensate bec is a state of matter which is typically formed when a gas of.
Download boseeinstein condensation in dilute gases free. Theory of boseeinstein condensation in trapped gases arxiv. H, 4 he, 7 li, 23 na, and the two isotopes 85 rb and 87 rb. We summarize all experimental studies of boseeinstein condensation in dilute. Bose einstein condensation with neutral atoms, there was another possibility. Various properties of these systems are discussed, including the density profiles and the energy of the ground state configurations, the. Boseeinstein condensation of dilute gases in traps. Quench cooling the gas, they observed the condensate to grow, then subsequently collapse as the attraction overwhelmed the zeropoint energy of the confining potential, in a burst. Boseeinstein condensation in dilute gases second edition since an atomic boseeinstein condensate, predicted by einste. The formalism, based on the use of ursell operators, allows us to evaluate the oneparticle density operator with more flexibility than in meanfield theories, since it does not necessarily coincide with that of an ideal gas with. Useful analytical formula for the excitations spectrum, the correlation function and the superfluid fraction are derived. Bose einstein condensation in dilute gases in 1925 einstein predicted that at low temperatures particles in a gas could all reside in the same quantum state.
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