Boseeinstein condensation remains, however, fundamental to. Boseeinstein condensate definition is a state of matter that occurs when a set of atoms is cooled almost to absolute zero in which a statistical description of the positions of the atoms implies that they physically overlap each other and in effect form a single atom. Since boseeinstein condensation bec can be understood from statistical correlations, without the need of bosonboson interaction, there is a feasible possibility of discussing the phenomenon beyond the usual boseeinstein statistics. Boseeinstein condensation international series of monographs on physics 1st edition. Smith, bose einstein condensation in diluted gases university press, cambridge 2002 l. Although first proposed by einstein in 1924, boseeinstein 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. I a mean eld approach leads to the grosspitaevskii equation which has to be ful lled by the singleparticle wave functions in order to minimize the total energy in the system. Bose in 1924 predicted a different statistics for the light quanta and derived plancks radiation formula through very simple arguments. Properties of vortices in boseeinstein condensates sciencedirect. Written by world renowned experts in the field, this book gives a comprehensive overview of exciting developments in boseeinstein condensation and superfluidity from a. Boseeinstein condensation in dilute gases will be useful to newcomers to the field and will help researchers with diverse backgrounds communicate with each other. With these results, we solve the gross pitaevskii equation in phase space and obtained the wigner function for the system considered.
Meanfield theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Bec is a biennial conference on boseeinstein condensation open to all scientists interested in this field. Boseeinstein condensation and superfluidity pitaevskii. The state is described by a quasiprobability amplitude that is in association with the wigner function. Lev pitaevskii and sandro stringari, oxford university press, oxford, 2003. Bose einstein condensation definition, a phase of matter in which all bosons in a given physical system have been cooled to a temperature near absolute zero and enter the same quantum state. With that in mind, the aim of this paper is to enable students and lecturers to approach the. Ios press ebooks boseeinstein condensation in atomic gases. The ability to achieve condensation by sympathetic cooling with a different species may provide a route to the. Boseeinstein condensates of dilute gases offer a rich field to study fundamental quantummechanical processes, manipulation of the speed at which light propogates. Various properties of these systems are discussed, including the density profiles and the energy of the ground state configurations, the.
Numerical solution of the grosspitaevskii equation for. Equilibration time scales in homogeneous boseeinstein. Analytical solution for the grosspitaevskii equation in. Introduction of boseeinstein condensation biography wolfgang ketterle outline bec achieving in mit summary 6. Bose einstein condensation definition of bose einstein. Sandro stringari is an italian theoretical physicist, who has contributed to the theory of quantum manybody physics, including atomic nuclei, quantum liquids and ultracold atomic bose and fermi gases. He has developed in a systematic way the sum rule approach to. Based on the principle of hamilton dynamics and the principle of lagrangian dynamics, a general pattern formation equation for the spinor boseeinstein condensates is established. In this paper i will discuss some issues concerning the behaviour of the order parameter and the dynamic and superfluid effects exhibited by such systems. Boseeinstein condensates of dilute gases offer a rich. Sakurai, modern quantum mechanics addisonwesley, redwood city 1985 112 bibliography for part i.
The main aim of this paper is to study the bifurcation solutions associated with the spinor boseeinstein condensates. Boseeinstein condensation and superfluidity paperback. Because of the rapid thermalization of the two different atoms, the efficiency of the cooling process is high. Boseeinstein condensation by pitaevskii and coauthor sandro stringari, who is another major contributor to the recent theoretical literature, reflects the brief history just sketched. The condensate is actually a new state of matter, where quantummechanical wave functions. Some of the assumptions of the grosspitaevskii equation gpe are. Boseeinstein condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 nobel prize. Ultracold atomic gases is a rapidly developing area of physics that attracts many young researchers around the world. Conclusions i below a critical temperature t c boseeinstein condensation takes place. Direct evidence of spatial stability of boseeinstein condensate of. Ketterle nobel lecture 2001 and his talk given at mits teachers program 240603.
Lectures on the boseeinstein condensation valentin a. We report on the boseeinstein condensation of potassium atoms, whereby quantum degeneracy is achieved by sympathetic cooling with evaporatively cooled rubidium. Universal themes of boseeinstein condensation edited by. Massive bosons consider a gas of massive, noninteracting, nonrelativistic, identical, spin0 bosons. Boseeinstein condensation bec refers to a prediction of quantum statistical. Boseeinstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid helium4 and superconductors. Grosspitaevskii equation in boseeinstein condensates. Stringari this book is an introductory text to the physics of boseeinstein condensation.
We consider the case of spinless bosons so there is no spin factor in the density of states of section 4. In particular the recent experiments carried out at mit on 23na 2 and at jila on. Meanfield theory provides a framework to understand the main features of the. Pdf theory of boseeinstein condensation in trapped gases. Moreover, three kinds of critical conditions for eigenvalues are obtained under spectrum analysis. Roomtemperature boseeinstein condensation of cavity. This phenomenon, first predicted by einstein in 1925 has been realized experimentally in 1995 in a remarkable series of experiments whose importance has been recognized by the award of the 2001 nobel prize in physics. Boseeinstein condensate definition of boseeinstein.
This is the first book devoted to boseeinstein condensation bec as an interdisciplinary subject, covering atomic and. A corresponding graph of numerically determined from equation when is shown in figure 8. We report on the boseeinstein condensation of more than 10 5 li 2 molecules in an optical trap starting from a spin mixture of fermionic lithium atoms. Providing a useful introduction to one of the most exciting field of physics today, this text will be of interest. Stringari, theory of boseeinstein condensation in trapped gases, rev. Stringari this book is an introductory text to the physics of bose einstein condensation. It is an excellent text, a broad survey with some indepth discussions an excellent text such as this is. Numerical solution of the grosspitaevskii equation for boseeinstein condensation. Boseeinstein condensation in 1, 2 and 3 dimensions for massive and massless bosons in a box i. The equilibration times are shown to be inversely proportional to. Einstein 192425 extended boses idea to material particles predicted bec in an ideal quantum gas i w.
This is the first book devoted to boseeinstein condensation bec as an interdisciplinary subject, covering atomic and molecular physics, laser physics, low temperature physics and astrophysics. We quantitatively characterize the departure from thermal equilibrium and observe the presence of two equilibration time scales. The sudden collapse of bosons into the groundstate at temperatures below the bose temperature is known as boseeinstein condensation. In a fermi gas, boseeinstein condensation of pairs was measured by ramping the scattering length to the bec side and detecting the resulting bimodal distribution condensation of pairs measured at unitarity 1a0 as a function of temperature. Lev pitaevskii, senior researcher, university of trento,sandro stringari, professor of theoretical physics, university of trento lev p. Below t c,thecondensatepopula tionvarieswithtemperatureas n0 n 1. Bifurcation solutions of grosspitaevskii equations for. The book is an introductory text to the physics of boseeinstein condensation. This book is an introductory text to the physics of boseeinstein condensation.
This phenomenon, first predicted by einstein in 1925, has been realized experimentally in 1995 in a remarkable series of experiments whose importance has been recognized by the award of the 2001 nobel prize in physics. Author links open overlay panel weizhu bao a dieter. Boseeinstein condensation in this section we discuss the thermodynamic properties of the ideal bose gas. Boseeinstein condensation with neutral atoms, there was another possibility. A good reference is the book boseeinstein condensation in dilute gases by pethick and smith. Theory of boseeinstein condensation in trapped gases arxiv. Derivation of the grosspitaevskii equation for the dynamics of bose. The field of boseeinstein condensation of atomic gases has continued to progress rapidly, driven by the combination of new experimental techniques and theoretical advances. Wieman led a team of physicists that created a nearly pure condensate by cooling a vapor of. We study the nonequilibrium growth of a weakly interacting homogeneous bose gas after a quench from a hightemperature state to a temperature below the bose einstein critical condensation temperature. Only 50% of pairs are boseeinstein condensed at zero temperature strongly interacting gas. Unusual transition patterns in boseeinstein condensation. It provides an outstanding scientific forum with the possibility to share the last developments and offers networking opportunities. Boseeinstein condensation has been predicted in 19241925 by satyendra nath bose and albert einstein.
Cambridge core condensed matter physics, nanoscience and mesoscopic physics universal themes of boseeinstein condensation edited by nick p. I acknowledge the use of materials and slides from w. Critical readings and discussions with them in the journal club deepened my understanding of the phenomenon of the boseeinstein condensation and made me con. Although first proposed by einstein in 1924, boseeinstein condensation bec in a gas was not achieved until 1995 when, using a combination of laser cooling. Boseeinstein condensates confined in traps exhibit unique features which have been the object of extensive experimental and theoretical studies in the last few years.
Hiroaki enomoto belonging to professors ohba and nakazatos group. Boseeinstein condensation in atomic gases ios press ebooks. Now, polaritons are shown to condense at room temperature using a microcavity within an. Theory of boseeinstein condensation in trapped gases. Boseeinstein condensation is a phase transition in which a macroscopic number of. During forced evaporative cooling, the molecules are formed by threebody recombination near a feshbach resonance and finally condense in a longlived thermal equilibrium state. Bose 1924 quantum statistical treatment of photons i a. The remainder is devoted specifically to the dilute alkali gases.
Stringari, bose einstein condensation clarendon press, oxford 2003 j. Starting from the simplest case with onecomponent bec of the weakly interacting bosons, we study the reduction of gpe to lower dimensions, the ground states of bec including the existence and uniqueness as well as. Wieman 1995 produced the rst gaseous condensate nobel price of physics 2001 about boseeinstein condensation bec history of bec 4 28 c. Boseeinstein condensation in 1, 2 and 3 dimensions for. Our findings solve a longstanding problem, providing a new insight into the physics of magnon boseeinstein condensates. Unusual transition patterns in bose einstein condensation. Boseeinstein condensation and superfluidity in trapped. Get your kindle here, or download a free kindle reading app. Boseeinstein condensates of excitonpolaritons have been stabilized in a range of crystalline systems. Russian, born in saratov russia january 18, 1933 s.
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