The dynamics of these compressible nonlinear quantum. Bose einstein condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 nobel prize. 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. This work was supported by the sno paulo research foundation fapesp under grant no.
Boseeinstein condensation and superfluidity paperback. Universal themes of boseeinstein condensation edited by. Dalfovo f, giorgini s, pitaevskii l p and stringari s 1999 theory of boseeinstein condensation in trapped gases rev. It has been known for some time that this phenomenon gives rise to superfluidity in liquid helium. So far, both have remained apart with no quantum mechanical description of gravity available. Boseeinstein condensation can be described intuitively in the following way. Dec 19, 2003 we report on the bose einstein condensation of more than 105 li2 molecules in an optical trap starting from a spin mixture of fermionic lithium atoms. A coherent matter wave forms that comprises all particles in the ground state of the system. Numerical solution of the grosspitaevskii equation for bose. This book gives a comprehensive overview of exciting developments in. He has developed in a systematic way the sum rule approach to the collective behavior of interacting systems. We consider the case of spinless bosons so there is no spin factor in the density of states of section 4. Various theoretical approaches to describing the physics of interacting bosons and of interacting fermi gases, giving rise to. The authors also make sense of key experiments from the past twenty years with a.
Boseeinstein condensation can occur in quasiparticles, particles that are effective descriptions of collective excitations in materials. Boseeinstein condensation in this section we discuss the thermodynamic properties of the ideal bose gas. This volume introduces the basic concepts of bose einstein condensation and superfluidity. Pitaevskii is a researcher at the cnr trento research center on bose einstein condensation and at the kapitza institute for physical problems in moscow. The sudden collapse of bosons into the groundstate at temperatures below the bose temperature is known as bose einstein condensation. The early experiments on bose einstein condensation in dilute atomic gases accomplished three longstanding goals. The ability to achieve condensation by sympathetic cooling with a different species may provide a route to the. Boseeinstein condensation bec, grosspitaevskii equation, timesplitting spectral method, approximate ground state solution, defocusingfocusing nonlinearity. In a related context, dilute bose einstein condensates bec have been recently produced experimentally 57.
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. Gross pitaevskii equation for the order parameter and beyond. Sandro stringari university of trento 1 introduction to bose einstein condensation 3. Models considered include 2d and 3d gross pitaevskii equations, nordheim quantum kinetic equation, boltzmann equation and 1d nonlinear equation for optical wt in nematic liquid crystals. Boseeinstein condensation article about boseeinstein. Boseeinstein condensation and superfluidity hardcover.
After the studies at the university of pisa and at the scuola normale. Stringari pdf, epub ebook d0wnl0ad this book is an introductory text to the physics of bose einstein condensation. Ios press ebooks boseeinstein condensation in atomic gases. Because of the rapid thermalization of the two different atoms, the efficiency of the cooling process is high. Mar 14, 2002 the early experiments on boseeinstein condensation in dilute atomic gases accomplished three longstanding goals. The gross pitaevskii equation and boseeinstein condensates 249 of the system is the creation of vortices, which can be seen as small twisters inside the liquid that behave quite differently. Bose 1924 quantum statistical treatment of photons i a. This book is an introductory text to the physics of boseeinstein condensation. Their combined citations are counted only for the first article. Wieman led a team of physicists that created a nearly pure condensate by cooling a vapor of rubidium atoms to a temperature of. Conditions for condensation of various quasiparticles have been predicted and observed. The grosspitaevskii equation and boseeinstein condensates.
Boseeinstein condensates of excitonpolaritons have been stabilized in a range of crystalline systems. Stringari bose einstein condensation international series of monographs on physics by l. Boseeinstein condensates of dilute gases offer a rich field to study fundamental quantummechanical processes, manipulation of the speed at which light propogates, observation of atomic pair. Stringari this book is an introductory text to the physics of boseeinstein condensation. Bose einstein condensation is a phase transition in which a macroscopic number of particles all go into the same quantum state. Bose einstein condensates of excitonpolaritons have been stabilized in a range of crystalline systems. Wieman 1995 produced the rst gaseous condensate nobel price of physics 2001 about boseeinstein condensation bec history of bec 4 28 c. Bose einstein condensates portant, since bec in lower dimensions is not as simple as in 3d.
Cambridge core condensed matter physics, nanoscience and mesoscopic physics universal themes of boseeinstein condensation edited by nick p. Modern techniques and applications chapman and hallcrc financial mathematics series by edward e. In this paper, we motivate the derivation of the gpe in relationship to concepts. When the quantummechanical wave functions of bosonic particles spatially overlap, the matter waves start to oscillate in concert. Only 50% of pairs are bose einstein condensed at zero temperature strongly interacting gas. Boseeinstein condensation in spherically symmetric traps.
We report on the bose einstein condensation of potassium atoms, whereby quantum degeneracy is achieved by sympathetic cooling with evaporatively cooled rubidium. The gross pitaevskii equation is a nonlinear model equation for the order parameter or wavefunction of a bose einstein condensate. 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. Boseeinstein condensation and superfluidity ebook, 2016. Boseeinstein condensation and superfluidity international. In this chapter, wave turbulence wt in bose einstein condensates bec and nonlinear optics is considered. 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. The remainder is devoted specifically to the dilute alkali gases. Nevertheless, such a mathematical model provides the simplest example for the realization of boseeinstein condensation. Stringari boseeinstein condensation, oxford university press 2003 systematically employed in this course. It makes special reference to the physics of ultracold atomic gases.
Roomtemperature boseeinstein condensation of cavity exciton. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum phenomena, particularly wavefunction interference. The results for the compressibility, effective mass and velocity of sound are analysed as a function of the lattice depth and of the strength of the. Boseeinstein condensation by pitaevskii and coauthor sandro stringari, who is another major contributor to the recent theoretical literature, reflects the brief history just sketched. Written by world renowned experts in the field, this book gives a comprehensive overview of exciting developments in bose einstein condensation and superfluidity from a theoretical perspective. In this lecture some basic concepts of bose einstein condensation bec were discussed. First, cooling of neutral atoms into their motional ground state, thus. S stringari ultracold atomic gases is a rapidly developing field of physics that attracts many young researchers around the world. We consider an interacting, dilute bose gas trapped in a harmonic potential at a positive temperature.
Boseeinstein condensation and free dkp field sciencedirect. The book is an introductory text to the physics of boseeinstein condensation. Theory of boseeinstein condensation in trapped gases. 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. Salasnich for sharing their findings concerning bose einstein condensation on the surface of a sphere. I a mean eld approach leads to the gross pitaevskii equation which has to be ful lled by the singleparticle wave functions in order to minimize the total energy in the system. A bose einstein condensate bec is a state of matter also called the fifth state of matter which is typically formed when a gas of bosons at low densities is cooled to temperatures very close to absolute zero 273. The phenomenon of superfluidity is often, though not exclusively, studied and described through bose einstein condensation 1,18,28. Wieman 1995 produced the rst gaseous condensate nobel price of physics 2001 about bose einstein condensation bec history of bec 4 28 c.
We discuss the blochstate solutions of the stationary gross pitaevskii equation and of the bogoliubov equations for a bose einstein condensate in the presence of a onedimensional optical lattice. The interacting bose gas with repulsive potential is considered in the polymer representation and some of the yet unsolved mathematical questions for establishing the existence of bose condensation in this setting are discussed. 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. The presence of bose einstein condensation means that a single quantum state has macroscopic occupation. I a mean eld approach leads to the gross pitaevskii equation. Roomtemperature boseeinstein condensation of cavity. Two pillars of modern physics are quantum mechanics and general relativity. Introduction to boseeinstein condensation 6 andthecriticaltemperature tc. Salasnich for sharing their findings concerning boseeinstein condensation on the surface of a sphere. 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 bose einstein condensation takes place. Below t c,thecondensatepopula tionvarieswithtemperatureas n0 n 1. Providing a useful introduction to one of the most exciting field of physics today, this text will be of interest. Bose einstein 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. Bose einstein condensates confined in traps exhibit unique features which have been the object of extensive experimental and theoretical studies in the last few years. Boseeinstein condensation of quasiparticles wikipedia. Universal themes of boseeinstein condensation edited by nick. Lev pitaevskii, senior researcher, university of trento,sandro stringari, professor of theoretical physics, university of trento lev p. Einstein 192425 extended boses idea to material particles predicted bec in an ideal quantum gas i w. Egawa was a member of our journal club on boseeinstein condensation by pitaevskii and stringari, together with mr. Boseeinstein condensation of potassium atoms by sympathetic. This book is an introductory text to the physics of bose einstein condensation. A new state of matter intuitive picture of bose einstein condensation consider a gas of identical noninteracting bosons of massm at temperature t.
Bose einstein condensation international series of monographs on physics by l. Bose einstein condensation international series of monographs on physics 9780198507192 by pitaevskii, l stringari, s. Apr 03, 2003 the book is an introductory text to the physics of bose einstein condensation. Boseeinstein condensate definition of boseeinstein. In the standard literature the gpe is usually obtained in the framework of the second quantization formalism, which in many cases goes beyond the material covered in many advanced undergraduate courses. Stringari this book is an introductory text to the physics of bose einstein condensation. These include the concept of long range order, the behaviour of the eigenvalues of the 1body density matrix and the concept of order parameter as a classical field. Hiroaki enomoto belonging to professors ohba and nakazatos group. Boseeinstein condensation in a dilute, trapped gas at.
Now, polaritons are shown to condense at room temperature using a microcavity within an. The gross pitaevskii equation gpe is discussed at the level of an advanced course on statistical physics. A bose einstein condensate bec is a remarkable state of. Dynamic structure factor of a bose einstein condensate in a 1d optical lattice c.
Smith pethick and smith provide a unified introduction to the physics of ultracold atomic bose and fermi gases for students, experimentalists and theorists alike. Boseeinstein condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 nobel prize. A 67, 053609 2003 macroscopic dynamics of a bose einstein condensate containing a vortex lattice marco cozzini and sandro stringari, phys. Grosspitaevskii dynamics of boseeinstein condensates and. Cambridge core condensed matter physics, nanoscience and mesoscopic physics universal themes of bose einstein condensation edited by nick p. The condensate is actually a new state of matter, where quantummechanical wave functions. Written by world renowned experts in the field, this book gives a comprehensive overview of exciting developments in boseeinstein condensation and superfluidity from a theoretical perspective. Some have integer spins and can be expected to obey boseeinstein statistics like traditional particles. In a fermi gas, bose einstein 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. Boseeinstein condensation of an ideal gas an ideal gas consisting of noninteracting bose particles is a. A boseeinstein condensate bec is a state of matter also called the fifth state of matter which is typically formed when a gas of bosons at low densities is cooled to temperatures very close to absolute zero 273.
Boseeinstein condensation and superfluidity oxford. Additional literature about boseeinstein condensation can be found in. Nevertheless, such a mathematical model provides the simplest example for the realization of bose einstein condensation. Theory of bose einstein condensation in trapped gases. During forced evaporative cooling, the molecules are formed by threebody recombination near a feshbach resonance and finally condense in a longlived thermal equilibrium state. The ability to achieve condensation by sympathetic cooling with a different species may provide a route to the production. Einstein 192425 extended bose s idea to material particles predicted bec in an ideal quantum gas i w.